This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks, and they will know how to check and verify their own programs against hand calculations and by reference to theoretical results, special polynomial solutions and other specialized solutions. No previous programming experience with MATLAB is necessary.

Contents:

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  Rootfinding, Interpolation, Approximation and Quadrature:

  
  
  
  
  • Introduction to MATLAB
  
  
  • Roots of Equations
  
  
  • The Newton–Raphson Method
  
  
  • Multidimensional Newton's Method
  
  
  • Interpolation on Evenly-Spaced Points
  
  
  • Polynomial and Piecewise Linear Interpolation
  
  
  • Higher-Order Interpolation
  
  
  • Legendre Polynomials and L² Approximation
  
  
  • Quadrature
  
  
  • Topics in Quadrature and Roundoff
  
  
  
  


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  Differential Equations and Linear Algebra:

  
  
  
  
  • Explicit ODE Methods
  
  
  • Implicit ODE Methods
  
  
  • Boundary Value Problems and Partial Differential Equations
  
  
  • Vectors, Matrices, Norms and Errors
  
  
  • Solving Linear Systems
  
  
  • Factorizations
  
  
  • The Eigenvalue Problem
  
  
  • Singular Value Decomposition
  
  
  • Iterative Methods
  
  
  
  

Readership: Senior undergraduate and first year graduate students in mathematics, science and engineering.

Key Features:

• The book can be used for both senior undergraduate and first year graduate courses


• The presentation is well-suited for self-study


• No previous programming experience with MATLAB is required


• Each task is divided into small steps to simplify development and testing


• Most chapters are independent of the others so that individual chapters can be studied without material from previous chapters