Scientific Computing with MATLAB
Published on 6. December 2012
IX, 257 pages
978-3-642-59339-0 (ISBN)
Description
"It is important to prove, is more but it important to improve." This textbook is an introduction to Scientific Computing. We will illustrate several numerical methods for the computer solution of cer tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. With this aim, in Chapter 1 we will illustrate the rules of the game that computers adopt when storing and operating with real and complex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will adopt the programming environment MATLAB ® 1 as a faithful companion. We will gradually discover its principal commands, statements and con structs. We will show how to execute all the algorithms that we intro duce throughout the book. This will enable us to furnish an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raised through exercises and examples, often stemming from specific ap plications.
Reviews / Votes
From the reviews:
"Can be used either as a complement to a basic or more advanced course in numerical analysis, or as a do-book for a short and practical introduction to the subject . . closing section of each chapter is a list of exercises, adapted to the level of the reader. . exercises are essential because the emphasis is clearly on the practical implementation . . after working through this book, the reader is brought to a relatively experienced lower step up the ladder of scientific computing." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)More details
Other editions
Additional editions
Alfio Quarteroni | Fausto Saleri
Scientific Computing with MATLAB
Book
06/2004
Springer
€85.55
Article exhausted; check different version
Alfio Quarteroni | Fausto Saleri
Scientific Computing with MATLAB
Problems and Exercises Solved by MATLAB
Book
06/2003
Springer
€85.55
Article exhausted; check for reprint
Content
1. What can't be ignored.- 1.1 Real numbers.- 1.2 Complex numbers.- 1.3 Matrices.- 1.4 Real functions.- 1.5 To err is not only human.- 1.6 A few more words about MATLAB.- 1.7 What we haven't told you.- 1.8 Exercises.- 2. Nonlinear equations.- 2.1 The bisection method.- 2.2 The Newton method.- 2.3 Fixed point iterations.- 2.4 What we haven't told you.- 2.5 Exercises.- 3. Approximation of functions and data.- 3.1 Interpolation.- 3.2 Piecewise linear interpolation.- 3.3 Approximation by spline functions.- 3.4 The least squares method.- 3.5 What we haven't told you.- 3.6 Exercises.- 4. Numerical differentiation and integration.- 4.1 Approximation of function derivatives.- 4.2 Numerical integration.- 4.3 Simpson adaptive formula.- 4.4 What we haven't told you.- 4.5 Exercises.- 5. Linear systems.- 5.1 The LU factorization method.- 5.2 The technique of pivoting.- 5.3 How accurate is the LU factorization?.- 5.4 How to solve a tridiagonal system.- 5.5 Iterative methods.- 5.5.1 How to construct an iterative method.- 5.6 When should an iterative method be stopped?.- 5.7 Richardson method.- 5.8 What we haven't told you.- 5.9 Exercises.- 6. Eigenvalues and eigenvectors.- 6.1 The power method.- 6.2 Generalization of the power method.- 6.3 How to compute the shift.- 6.4 Computation of all the eigenvalues.- 6.5 What we haven't told you.- 6.6 Exercises.- 7. Ordinary differential equations.- 7.1 The Cauchy problem.- 7.2 Euler methods.- 7.3 The Crank-Nicolson method.- 7.4 Zero-stability.- 7.5 Stability on unbounded intervals.- 7.6 High order methods.- 7.7 The predictor-corrector methods.- 7.8 Systems of differential equations.- 7.9 What we haven't told you.- 7.10 Exercises.- 8. Numerical methods for boundary-value problems.- 8.1 Approximation of boundary-value problems.-8.2 Finite differences in 2 dimensions.- 8.3 What we haven't told you.- 8.4 Exercises.- 9. Solutions of the exercises.- 9.1 Chapter 1.- 9.2 Chapter 2.- 9.3 Chapter 3.- 9.4 Chapter 4.- 9.5 Chapter 5.- 9.6 Chapter 6.- 9.7 Chapter 7.- 9.8 Chapter 8.- Index of MATLAB Programs.
