100 Best Numerical Analysis Books of All Time
We've researched and ranked the best numerical analysis books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more
Featuring recommendations from Eric Weinstein, and 1 other experts. 1
For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten, and enlarged the material. Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation. less
2
Learn to master basic programming tasks from scratch with real-life scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to quickly gain proficiency. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving onto the NumPy, SciPy and... more
3
This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods. less
4
Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics. less
5
The first edition, published in 1973, has become a classic reference in the field. Now with the second edition, readers will find information on key new topics such as neural networks and statistical pattern recognition, the theory of machine learning, and the theory of invariances. Also included are worked examples, comparisons between different methods, extensive graphics, expanded exercises and computer project topics.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
lessRecommended by Eric Weinstein, and 1 others. Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)
6
Instructors love "Numerical Methods for Engineers" because it makes teaching easy! Students love it because it is written for them--with clear explanations and examples throughout. The text features a broad array of applications that span all engineering disciplines. The sixth edition retains the successful instructional techniques of earlier editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation. This prepares the student for upcoming problems in a motivating and engaging manner. Each part closes... more
7
The new Seventh Edition of Burden and Faires' well-respected Numerical Analysis provides a foundation in modern numerical-approximation techniques. Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life... more
8
A comprehensive introduction to sampling-based methods in statistical computingThe use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods."An Introduction to Statistical Computing" introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible... more
9
The Finite Element Method for Elliptic Problems is the only book available that fully analyzes the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, and also a working textbook for graduate courses in numerical analysis. It includes many useful figures, as well as exercises of varying difficulty. Although nearly 25 years have passed since this book was first published, the majority of its content remains up-to-date. Chapters 1 through 6, which cover the basic error... more
10
Based on courses taught to advanced undergraduate students, this textbook is divided into two parts to provide a broad introduction to the methods of numerical linear algebra and optimization respectively. less
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13
Just as a prism separates white light into its component bands of colored light, so the discrete Fourier transform (DFT) is used to separate a signal into its constituent frequencies. Just as a pair of sunglasses reduces the glare of white light, permitting only the softer green light to pass, so the DFT may be used to modify a signal to achieve a desired effect. In fact, by analyzing the component frequencies of a signal or any system, the DFT can be used in an astonishing variety of problems. Among the applications of the DFT are digital signal processing, oil and gas exploration, medical... more
14
If you want top grades and thorough understanding of numerical analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples--and lack of dreary minutiae--Schaum's Outlines have sold more than 30 million copies worldwide. This guide will show you why! less
15
The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the -boundary integral equation method-, which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an... more
16
This classic text focuses on elliptic boundary value problems in domains with nonsmooth boundaries and on problems with mixed boundary conditions. Its contents are essential for an understanding of the behavior of numerical methods for partial differential equations (PDEs) on two-dimensional domains with corners. Elliptic Problems in Nonsmooth Domains provides a careful and self-contained development of Sobolev spaces on nonsmooth domains, develops a comprehensive theory for second-order elliptic boundary value problems and addresses fourth-order boundary value problems and numerical... more
17
Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions. less
18
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking... more
19
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been... more
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21
This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization... more
22
One of the leading experts in the field discusses recent developments in the numerical analysis of nonlinear equations involving a finite number of parameters. Shows how these equations can be developed on a differential geometric basis. Topics include equilibrium manifolds, path-tracing on manifolds, aspects of computational stability analysis, discretization errors of parameterized equations, and computational error assessment and related questions. less
23
In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision... more
24
Applied Iterative Methods is a self-contained treatise suitable as both a reference and a graduate-level textbook in the area of iterative algorithms. It is the first book to combine subjects such as optimization, convex analysis, and approximation theory and organize them around a detailed and mathematically sound treatment of iterative algorithms. Such algorithms are used in solving problems in a diverse area of applications, most notably in medical imaging such as emission and transmission tomography and magnetic-resonance imaging, as well as in intensity-modulated radiation... more
25
Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide 'state of the art' techniques and analysis. less
27
Until recently, measurable dynamics has been regarded as a highly theoretical mathematical topic with few obvious links to areas of applied mathematics. The advent of high-speed computers, rapidly-developing algorithms, and new numerical methods has, however, allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for... more
28
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra. Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed... more
29
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation.This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped... more
30
This introduction to the important interplay between nonlinear dynamics and statistical theories for geophysical flows is designed for a multi-disciplinary audience ranging from graduate students to senior researchers. Novel applications of information theory are utilized to simplify, unify, and compare the equilibrium statistical theories. Topics and related background concepts are introduced and developed through elementary examples and discussion throughout the text as they arise. No previous background in geophysical flows is needed to read the text. less
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32
Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables... more
33
The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss... more
34
Whatever regrets may be, we have done our best." (Sir Ernest Shack 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations.... more
35
This book is an integrated work published in two volumes. The first volume treats the basic Markov process and its variants; the second, semi-Markov and decision processes. Its intent is to equip readers to formulate, analyze, and evaluate simple and advanced Markov models of systems, ranging from genetics and space engineering to marketing. More than a collection of techniques, it constitutes a guide to the consistent application of the fundamental principles of probability and linear system theory.
Author Ronald A. Howard, Professor of Management Science and Engineering at Stanford... more
Author Ronald A. Howard, Professor of Management Science and Engineering at Stanford... more
36
This book provides a fundamental introduction to numerical analysis. KEY TOPICS: This book covers numerous topics including Interpolation and Polynomial Approximation, Curve Fitting, Numerical Differentiation, Numerical Integration, and Numerical Optimization. MARKET: For engineering and computer science fields. less
37
Save 10% when you order the complete set! A monumental 4-volume reference, 15 years in the making, The World of Mathematics was specially designed to make mathematics more accessible to the inexperienced. It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers. less
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This book is an integrated work published in two volumes. The first volume treats the basic Markov process and its variants; the second, semi-Markov and decision processes. It equips readers to formulate, analyze, and evaluate simple and advanced Markov models of systems, ranging from genetics to space engineering to marketing. 1971 edition. less
40
Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow.
For practical reasons, the finite element method, used more often for... more
For practical reasons, the finite element method, used more often for... more
Don't have time to read the top Numerical Analysis books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
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- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
41
Numerical Methods that Work, originally published in 1970, has been reissued by the MAA with a new preface and some additional problems. Acton deals with a commonsense approach to numerical algorithms for the solution of equations: algebraic, transcendental, and differential. He assumes that a computer is available for performing the bulk of the arithmetic. The book is divided into two parts, either of which could form the basis of a one-semester course in numerical methods. Part I discusses most of the standard techniques: roots of transcendental equations, roots of polynomials, eigenvalues... more
42
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to... more
43
Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. William McLean provides the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book affords an ideal background for studying the modern research... more
44
Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible. less
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Normal 0 false false false Numerical Analysis, Second Edition, is a modern and readable text. This book covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers--topics such as compression, forward and backward error analysis, and iterative methods of solving equations--all while maintaining a level of discussion appropriate for undergraduates. Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB(R) is used... more
46
This monograph is a technical survey of concepts and techniques for describing and analyzing large-scale time-series data streams. Some topics covered are algorithms for query by humming, gamma-ray burst detection, pairs trading, and density detection. Included are self-contained descriptions of wavelets, fast Fourier transforms, and sketches as they apply to time-series analysis. Detailed applications are built on a solid scientific basis. less
47
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory.... more
48
This book covers a broad spectrum of the most important, basic numerical and analytical techniques used in physics including ordinary and partial differential equations, linear algebra, Fourier transforms, integration and probability. Now language-independent. Features attractive new 3-D graphics. Offers new and significantly revised exercises. Replaces FORTRAN listings with C++, with updated versions of the FORTRAN programs now available on-line. Devotes a third of the book to partial differential equations e.g., Maxwell's equations, the diffusion equation, the wave equation, etc. This... more
49
In this age of omnipresent digital computers and their capacity for implementing numerical methods, no applied mathematician, physical scientist, or engineer can be considered properly trained without some understanding of those methods. This text, suitable for advanced undergraduate and graduate-level courses, supplies the required knowledge — not just by listing and describing methods, but by analyzing them carefully and stressing techniques for developing new methods.
Based on each author's more than 40 years of experience in teaching university courses, this book offers lucid,... more
Based on each author's more than 40 years of experience in teaching university courses, this book offers lucid,... more
50
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book... more
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51
This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents atheory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory. less
52
This book is intended to serve as a textbook for an entry level graduate course on electromagnetics (first seven chapters) and for an advanced level graduate course on computational electromagnetics (last five chapters). Whereas there are several textbooks available for the graduate electromagnetics course, no textbook is available for the advanced course on computational electromagnetics. This book is intended to fill this void and present electromagnetic theory in a systematic manner so that students can advance from the first course to the second without much difficulty. Even though the... more
53
This book gives a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. The coverage of the first edition has been expanded and updated, involving numerous improvements. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank... more
54
This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from
interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a... more
interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a... more
55
This class-tested text is appropriate for both undergraduate and beginning graduate courses, as well as for use by working scientists and engineers as a self-study tool and reference. A number of special, user-friendly features make it possible for readers to develop a firm grasp of the concepts of roundoff errors, stability, condition, and accuracy, as well as to develop an appreciation for the core algorithms, their usefulness, and implementations. less
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These example books published as part of the Numerical Recipes, Second Edition series are source programs that demonstrate all of the Numerical Recipes subroutines. less
57
This concisely written book gives an elementary introduction to a classical area of mathematics - approximation theory - in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Featuring classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression, the book is one of... more
59
Written by one of the pre-eminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections,... more
60
Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The... more
Don't have time to read the top Numerical Analysis books of all time? Read Shortform summaries.
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62
An IEEE reprinting of this classic 1968 edition, FIELD COMPUTATION BY MOMENT METHODS is the first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems. It presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis. Written especially for those who have a minimal amount of experience in electromagnetic theory, this book illustrates theoretical and mathematical concepts to prepare all readers with the skills they need to apply the method of moments... more
63
This textbook teaches students to create computer codes used to engineer antennas, microwave circuits, and other critical technologies for wireless communications and other applications of electromagnetic fields and waves. less
64
This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and... more
65
Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in... more
66
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands. less
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Are you familiar with the IEEE floating point arithmetic standard? Would you like to understand it better? This book gives a broad overview of numerical computing, in a historical context, with special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. It gives technical details that are not readily... more
68
Learning through doing is the foundation of Scientific Computing with Case Studies, which allows readers to explore case studies as well as expository material. The book provides a practical guide to the numerical solution of linear an nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats, standard problems and introduces important variants such as space systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis is emphasized, and the MATLAB algorithms are... more
69
This resource discusses advances in computational electromagnetics. It offers information on the multi-level fast multipole algorithm in both the time and frequency domains, as well as developments in fast algorithms for low frequencies and specialized structures, such as the planar and layered media. These algorithms solve large electromagnetics problems with shorter turn-around time, using less computer memory. less
70
This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents relatively few theorems and proofs. Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency, and it compares different solutions to the same problem.
Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms, interpolation, numerical differentiation and numerical quadrature, the numerical solution of ordinary differential equations, functional... more
Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms, interpolation, numerical differentiation and numerical quadrature, the numerical solution of ordinary differential equations, functional... more
Don't have time to read the top Numerical Analysis books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.
71
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. Exercises and student projects are available... more
72
The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har monic analysis to basic applications. The title of the series reflects the im portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi otic... more
74
This second edition of Simulation Modeling and Analysis includes a chapter on "Simulation in Manufacturing Systems" and examples. The text is designed for a one-term or two-quarter course in simulation offered in departments of industrial engineering, business, computer science and operations research. less
78
Topics are divided between review material on the mathematics background; numerical-analysis methods such as differentiation, integration, the solution of differential equations from engineering, life and physical sciences; data-analysis applications including least-squares fitting, splines and Fourier expansions. Unique in its project orientation, it features a vast amount of exercises with emphasis on realistic examples from current applications. less
79
Engineers and scientists who want to avoid insidious errors in their computer-assisted calculations will welcome this concise guide to trouble-shooting. Real Computing Made Real offers practical advice on detecting and removing bugs. It also outlines techniques for preserving significant figures, avoiding extraneous solutions, and finding efficient iterative processes for solving nonlinear equations.
Those who compute with real numbers (for example, floating-point numbers stored with limited precision) tend to develop techniques that increase the frequency of useful answers. But... more
Those who compute with real numbers (for example, floating-point numbers stored with limited precision) tend to develop techniques that increase the frequency of useful answers. But... more
80
A First Course on Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopaedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design... more
Don't have time to read the top Numerical Analysis books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
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81
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools... more
82
New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems less
83
This is an introduction to Bayesian statistics and decision theory, including advanced topics such as Monte Carlo methods. This new edition contains several revised chapters and a new chapter on model choice. less
84
The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background, and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers,... more
86
The Oxford Users' Guide to Mathematics represents a comprehensive handbook on mathematics. It covers a broad spectrum of mathematics including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimization, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. This is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics.
The book offers a broad modern... more
The book offers a broad modern... more
87
The method of least squares was discovered by Gauss in 1795 and has since become the principal tool for reducing the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing and tremendous progress has been made in numerical methods for least squares problems. Until now there has not been a monograph that covers the full spectrum of... more
88
Designed for first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommending which algorithms to use in various practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and... more
90
This book by a prominent mathematician is appropriate for a single-semester course in applied numerical analysis for computer science majors and other upper-level undergraduate and graduate students. Although it does not cover actual programming, it focuses on the applied topics most pertinent to science and engineering professionals.
An extensive range of topics includes round-off and function evaluation, real zeros of a function, simultaneous linear equations and matrices, interpolation and roundoff estimation, integration, and ordinary differential equations. Additional subjects... more
An extensive range of topics includes round-off and function evaluation, real zeros of a function, simultaneous linear equations and matrices, interpolation and roundoff estimation, integration, and ordinary differential equations. Additional subjects... more
Don't have time to read the top Numerical Analysis books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
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91
Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems--ranging from asset allocation to risk management and from option pricing to model calibration--can be efficiently handled using modern computational techniques. Numerical Methods and Optimization in Finance presents such computational techniques, with an emphasis on simulation and optimization, particularly so-called heuristics. This book treats quantitative analysis as an essentially computational discipline in which applications are put into software form and tested... more
92
Aspects of the theory most useful in developing and appraising computational methods for solving systems of linear equations and for finding characteristic roots. Basic identities and inequalities; norms, bounds and convergence; localization theorems and other inequalities; the solution of linear systems; much more. less
93
A comprehensive, up-to-date, and accessible introduction to the numerical solution of a large class of integral equations, this book builds an important foundation for the numerical analysis of these equations. It provides a general framework for the degenerate kernel, projection, and Nystrom methods and includes an introduction to the numerical solution of boundary integral equations (also known as boundary element methods). It is an excellent resource for graduate students and researchers trying to solve integral equation problems and for engineers using boundary element methods. less
94
Computational Methods for Electromagnetics is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment. Employing a unified coherent approach that is unmatched in the field, the authors detail both integral and differential equations using the method of moments and finite-element procedures. In addition, readers will gain a thorough understanding of numerical solution procedures. Topics covered include:
Two- and three-dimensional integral equation/method-of-moments formulations Open-region... more
Two- and three-dimensional integral equation/method-of-moments formulations Open-region... more
95
This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted... more
96
Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second... more
97
Welcome to Scientific Python and its community! With this practical book, you'll learn the fundamental parts of SciPy and related libraries, and get a taste of beautiful, easy-to-read code that you can use in practice. More and more scientists are programming, and the SciPy library is here to help.
"Finding" useful functions and "using" them correctly, efficiently, and in easily readable code are two very different things. You'll learn by example with some of the best code available, selected to cover a wide range of SciPy and related libraries including scikit-learn, scikit-image,... more
"Finding" useful functions and "using" them correctly, efficiently, and in easily readable code are two very different things. You'll learn by example with some of the best code available, selected to cover a wide range of SciPy and related libraries including scikit-learn, scikit-image,... more
98
This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions. less
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This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in... more
100
Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will... more
Don't have time to read the top Numerical Analysis books of all time? Read Shortform summaries.
Shortform summaries help you learn 10x faster by:
- Being comprehensive: you learn the most important points in the book
- Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises: apply the book's ideas to your own life with our educators' guidance.