This text is appropriate for undergraduate courses on numerical methods and numerical analysis found in engineering, mathematics & computer science depts.
Each chapter uses introductory problems from specific applications. These easy-to-understand problems clarify for the reader the need for a particular mathematical technique. Numerical techniques are explained with an emphasis on why they work.
Discussion of the contexts and reasons for selection of each problem and solution method.
Worked-out examples are very realistic and not contrived.
MATLAB code provides an easy testbed for algorithmic ideas.
2. Solving Equations of One Variable.
3. Solving Systems of Linear Equations: Direct Methods.
4. Solving Systems of Linear Equations: Iterative Methods.
5. Nonlinear Functions of Several Variables.
6. LU Factorization.
7. Eigenvalues, Eigenvectors, and QR Factorization.
9. Function Approximation.
10. Fourier Methods.
11. Numerical Differentiation and Integration.
12. Ordinary Differential Equations: Initial-Value Problems.
13. Systems of Ordinary Differential Equations.
14. Ordinary Differential Equations: Boundary Value Problems.
15. Partial Differential Equations.
Answers to Selected Exercises.