## e-books in Numerical Analysis category

**First Semester in Numerical Analysis with Julia**

by

**Giray Ökten**-

**Florida State University**,

**2019**

The book presents the theory and methods, together with the implementation of the algorithms using the Julia programming language. The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory.

(

**1428**views)

**Geometric Transformation of Finite Element Methods: Theory and Applications**

by

**M. Holst, M. Licht**-

**arXiv.org**,

**2018**

We present a new technique to apply finite element methods to partial differential equations over curved domains. Bramble-Hilbert lemma is key in harnessing regularity in the physical problem to prove finite element convergence rates for the problem.

(

**1619**views)

**Programming for Computations - Python**

by

**Svein Linge, Hans Petter Langtangen**-

**Springer**,

**2016**

This book presents Python programming as a key method for solving mathematical problems. The style is accessible and concise, the emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

(

**4016**views)

**Finite Difference Computing with PDEs**

by

**Hans Petter Langtangen, Svein Linge**-

**Springer**,

**2017**

This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners.

(

**2063**views)

**Solving PDEs in Python**

by

**Hans Petter Langtangen, Anders Logg**-

**Springer**,

**2017**

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, it guides readers through the essential steps to quickly solving a PDE in FEniCS.

(

**2043**views)

**Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics**

by

**Justin Solomon**-

**CRC Press**,

**2015**

Using examples from a broad base of computational tasks, including data processing and computational photography, the book introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into theoretical tools.

(

**5027**views)

**Introduction to Numerical Methods and Matlab Programming for Engineers**

by

**Todd Young, Martin J. Mohlenkamp**-

**Ohio University**,

**2017**

The goals of these notes are to introduce concepts of numerical methods and introduce Matlab in an Engineering framework. The notes were developed by the author in the process of teaching a course on applied numerical methods for Civil Engineering.

(

**2697**views)

**Introduction to Numerical Methods**

by

**Jeffrey R. Chasnov**-

**The Hong Kong University**,

**2012**

This is primarily for non-mathematics majors and is required by several engineering departments. Contents: IEEE Arithmetic; Root Finding; Systems of equations; Least-squares approximation; Interpolation; Integration; Ordinary differential equations.

(

**3880**views)

**Scientific Computing**

by

**Jeffrey R. Chasnov**-

**Harvey Mudd College**,

**2013**

This course consists of both numerical methods and computational physics. MATLAB is used to solve various computational math problems. The course is primarily for Math majors and supposes no previous knowledge of numerical analysis or methods.

(

**3472**views)

**The Numerical Approximation of Functional Differential Equations**

by

**Daniele Venturi**-

**arXiv**,

**2016**

The purpose of this manuscript is to provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.

(

**3551**views)

**Tea Time Numerical Analysis**

by

**Leon Q. Brin**-

**Southern Connecticut State University**,

**2014**

A one semester introduction to numerical analysis. Includes typical introductory material, root finding, numerical calculus, and interpolation techniques. The focus is on the mathematics rather than application to engineering or sciences.

(

**4975**views)

**Computing of the Complex Variable Functions**

by

**Solomon I. Khmelnik, Inna S. Doubson**-

**MiC**,

**2011**

Hardware algorithms for computing of all elementary complex variable functions are proposed. Contents: A method 'digit-by-digit'; Decomposition; Compositions; Two-step-by-step operations; Taking the logarithm; Potentiation; and more.

(

**5867**views)

**Parallel Spectral Numerical Methods**

by

**Gong Chen, et al.**-

**Wikibooks**,

**2013**

We start with finite-precision arithmetic. We then discuss how to solve ordinary differential equations and partial differential equations using the technique of separation of variables. We then introduce numerical time-stepping schemes...

(

**5391**views)

**Numerical Solutions of Engineering Problems**

by

**K. Nandakumar**-

**University of Alberta**,

**1998**

Contents: On mathematical models; Single nonlinear algebraic equation; System of linear and nonlinear algebraic equations; Numerical differentiation and integration; Ordinary differential equations; Boundary value problems; etc.

(

**8106**views)

**Lectures on Numerical Methods in Bifurcation Problems**

by

**H.B. Keller**-

**Tata Institute Of Fundamental Research**,

**1986**

These lectures introduce the modern theory and practical numerical methods for continuation of solutions of nonlinear problems depending upon parameters. The treatment is elementary, advanced calculus and linear algebra are the omly prerequisites.

(

**5585**views)

**Lectures on Numerical Methods for Non-Linear Variational Problems**

by

**R. Glowinski**-

**Tata Institute of Fundamental Research**,

**1980**

Many physics problems have variational formulations making them appropriate for numerical treatment. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations.

(

**6909**views)

**Lectures on Topics In Finite Element Solution of Elliptic Problems**

by

**Bertrand Mercier**-

**Tata Institute of Fundamental Research**,

**1979**

Contents: Sobolev Spaces; Abstract Variational Problems and Examples; Conforming Finite Element Methods; Computation of the Solution of the Approximate Problem; Problems with an Incompressibility Constraint; Mixed Finite Element Methods; etc.

(

**5628**views)

**Numerical Methods For Time Dependent Equations**

by

**P. Lascaux**-

**Tata Institute of Fundamental Research**,

**1976**

The solution of time dependent equations of hydrodynamics is a subject of great importance. This book is mainly concentrated on the study of the stability of the various schemes. We have considered only the stability for linearized problems.

(

**5930**views)

**Lectures on The Finite Element Method**

by

**Ph. Ciarlet**-

**Tata Institute of Fundamental Research**,

**1975**

Our basic aim has been to present some of the mathematical aspects of the finite element method, as well as some applications of the finite element method for solving problems in Elasticity. This is why some important topics are not covered here.

(

**6604**views)

**Numerical Analysis I**

by

**Mark Embree**-

**Rice University**,

**2012**

This course takes a tour through many algorithms of numerical analysis. We aim to assess alternative methods based on efficiency, to discern well-posed problems from ill-posed ones, and to see these methods in action through computer implementation.

(

**9849**views)

**Iterative Methods for Linear and Nonlinear Equations**

by

**C.T. Kelley**-

**SIAM**,

**1995**

This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods.

(

**7266**views)

**Numerical Methods for Large Eigenvalue Problems**

by

**Yousef Saad**-

**SIAM**,

**2011**

This book discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods for solving matrix eigenvalue problems that arise in various engineering applications.

(

**9522**views)

**Numerical Analysis for Engineering**

by

**Douglas W. Harder, Richard Khoury**-

**University of Waterloo**,

**2010**

Contents: Error Analysis, Numeric Representation, Iteration, Linear Algebra, Interpolation, Least Squares, Taylor Series, Bracketing, The Five Techniques, Root Finding, Optimization, Differentiation, Integration, Initial-value Problems, etc.

(

**9459**views)

**Numerical Analysis: Theory and Application**

by

**Jan Awrejcewicz**-

**InTech**,

**2011**

The book introduces theoretical approach to numerical analysis as well as applications of various numerical methods to solving numerous theoretical and engineering problems. The book is useful for both theoretical and applied research.

(

**7031**views)

**Lectures on Numerical Analysis**

by

**Dennis Deturck, Herbert S. Wilf**-

**University of Pennsylvania**,

**2002**

Contents: Differential and Difference Equations (Linear equations with constant coefficients, Difference equations, Stability theory); The Numerical Solution of Differential Equations (Euler's method); Numerical linear algebra.

(

**8033**views)

**Notes on Numerical Linear Algebra**

by

**George Benthien**,

**2006**

Tutorial describing many of the standard numerical methods used in Linear Algebra. Topics include Gaussian Elimination, LU and QR Factorizations, The Singular Value Decomposition, Eigenvalues and Eigenvectors via the QR Method, etc.

(

**10085**views)

**Notes on Harmonic Analysis**

by

**George Benthien**,

**2006**

Tutorial discussing some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, etc.

(

**7048**views)

**Robust Geometric Computation**

by

**Kurt Mehlhorn, Chee Yap**-

**New York University**,

**2004**

Contents: Introduction to Geometric Nonrobustness; Modes of Numerical Computation; Geometric Computation; Arithmetic Approaches; Geometric Approaches; Exact Geometric Computation; Perturbation; Filters; Algebraic Background; Zero Bounds; etc.

(

**7045**views)

**Numerical Stability**

by

**M.N. Spijker**-

**Leiden University**,

**1998**

Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc.

(

**6490**views)

**Introduction to the Numerical Integration of PDEs**

by

**B. Piette**-

**University of Durham**,

**2004**

In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.

(

**8741**views)

**The Calculus Of Finite Differences**

by

**L. M. Milne Thomson**-

**Macmillan and co**,

**1933**

The object of this book is to provide a simple account of the subject of Finite Differences and to present the theory in a form which can be readily applied -- not only the useful material of Boole, but also the more modern developments.

(

**8903**views)

**Introduction to Fortran 95 and Numerical Computing**

by

**Adrian Sandu**-

**Virginia Tech**,

**2001**

Contents: a quick tour of fortran 95; the building blocks of a fortran application; flow control; computer arithmetic; applications; intrinsic functions; input and output; arrays; more on procedures; parametrized intrinsic types; derived types; etc.

(

**8581**views)

**Computational Mathematics for Differential Equations**

by

**N. V. Kopchenova, I. A. Maron**,

**1975**

This is a manual on solving problems in computational mathematics. The book is intended primarily for engineering students, but may also prove useful for economics students, graduate engineers, and postgraduate students in the applied sciences.

(

**13533**views)

**Iterative Methods for Sparse Linear Systems**

by

**Yousef Saad**-

**PWS**,

**1996**

The book gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

(

**8115**views)

**First Steps in Numerical Analysis**

by

**R. Hosking, S. Joe, D. Joyce, and J. Turner**,

**1998**

This book provides an excellent introduction to the elementary concepts and methods of numerical analysis for students meeting the subject for the first time. The subject matter is organized into fundamental topics and presented as a series of steps.

(

**10045**views)

**Lectures in Basic Computational Numerical Analysis**

by

**James M. McDonough**-

**University of Kentucky**,

**2001**

These notes cover the following topics: Numerical linear algebra; Solution of nonlinear equations; Approximation theory; Numerical solution of ordinary differential equations; Numerical solution of partial differential equations.

(

**8771**views)

**Numerical Recipes in Fortran 90**

by

**William H. Press, at al.**-

**Cambridge University Press**,

**1996**

Numerical Recipes in Fortran 90 contains a detailed introduction to the Fortran 90 language and to the basic concepts of parallel programming, plus source code for all routines from the second edition of Numerical Recipes.

(

**11859**views)

**Handbook of Mathematical Functions**

by

**M. Abramowitz, I. A. Stegun**-

**GPO**,

**1964**

Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. A classic resource for special functions, standard trig, and exponential logarithmic definitions and extensions.

(

**26787**views)

**Linear Optimisation and Numerical Analysis**

by

**Ian Craw**-

**University of Aberdeen**,

**2002**

The book describes the simplex algorithm and shows how it can be used to solve real problems. It shows how previous results in linear algebra give a framework for understanding the simplex algorithm and describes other optimization algorithms.

(

**10763**views)

**Mathematical Computation**

by

**Ian Craw**-

**University of Aberdeen**,

**2003**

The overall aim of the course is to present modern computer programming techniques in the context of mathematical computation and numerical analysis and to foster the independence needed to use these techniques as appropriate in subsequent work.

(

**10533**views)

**Numerical Methods Course Notes**

by

**Steven E. Pav**-

**University of California at San Diego**,

**2005**

From the table of contents: A 'Crash' Course in octave/Matlab; Solving Linear Systems; Finding Roots; Interpolation; Spline Interpolation; Approximating Derivatives; Integrals and Quadrature; Least Squares; Ordinary Differential Equations.

(

**10982**views)

**Fundamental Numerical Methods and Data Analysis**

by

**George W. Collins, II**-

**NASA ADS**,

**2003**

'Fundamental Numerical Methods and Data Analysis' can serve as the basis for a wide range of courses that discuss numerical methods used in science. The author provides examples of the more difficult algorithms integrated into the text.

(

**11889**views)

**Numerical Methods with Applications**

by

**Autar K Kaw, Egwu Eric Kalu**-

**Lulu.com**,

**2008**

The textbook is written for engineering undergraduates taking a course in numerical methods. It offers a treatise to numerical methods based on a holistic approach and short chapters. The authors included examples of real-life applications.

(

**12641**views)

**Templates for the Solution of Linear Systems**

by

**Richard Barrett et al.**-

**Society for Industrial Mathematics**,

**1987**

The book focuses on the use of iterative methods for solving large sparse systems of linear equations. General and reusable templates are introduced to meet the needs of both the traditional user and the high-performance specialist.

(

**11771**views)