Chapter 1: Mathematical Preliminaries and Error AnalysisSection 1-1:
Review of Calculus
Section 1-2:
Round-Off Errors and Computer Arithmetic
Section 1-3:
Algorithms and Convergence
Exercise 3a
Exercise 3b
Exercise 3c
Exercise 3d
Exercise 9b
Exercise 9c
Exercise 9d
Exercise 10b
Exercise 10c
Exercise 10d
Exercise 11b
Exercise 11c
Exercise 11d
Exercise 12b
Exercise 12c
Exercise 12d
Exercise 16b
Exercise 17b
Exercise 17c
Exercise 17d
Exercise 17e
Exercise 22b
Chapter 2: Solutions of Equations in One Variable Section 2-1:
The Bisection Method
Section 2-2:
Fixed-Point Iteration
Section 2-3:
Newton's Method and Its Extensions
Section 2-4:
Error Analysis for Iterative Methods
Section 2-5:
Accelerating Convergence
Section 2-6:
Zeros of Polynomials and Muller's Method
Exercise 4b
Exercise 4c
Exercise 4d
Exercise 5b
Exercise 5c
Exercise 5d
Exercise 6c
Chapter 3: Interpolation and Polynomial Approximation Section 3-1:
Interpolation and the Lagarange Polynomial
Section 3-2:
Data Approximation and Neville's Method
Section 3-3:
Divided Differences
Section 3-4:
Hermite Interpolation
Section 3-5:
Cubic Spline Interpolation
Section 3-6:
Parametric Curves
Exercise 1b
Exercise 1c
Exercise 1d
Exercise 2b
Exercise 2c
Exercise 2d
Exercise 3b
Exercise 3c
Exercise 3d
Exercise 4b
Exercise 4c
Exercise 4d
Exercise 5b
Exercise 5c
Exercise 5d
Exercise 6b
Exercise 6c
Exercise 6d
Exercise 7b
Exercise 7c
Exercise 7d
Exercise 8b
Exercise 8c
Exercise 8d
Exercise 13b
Exercise 13c
Exercise 13d
Exercise 18b
Exercise 19b
Exercise 23b
Exercise 23c
Exercise 23d
Chapter 4: Numerical Differentiation and IntegrationSection 4-1:
Numerical Differentiation
Section 4-2:
Richardson's Extrapolation
Section 4-3:
Elements of Numerical Intergration
Section 4-4:
Composite Numerical Integration
Section 4-5:
Romberg Integration
Section 4-6:
Adaptive Quadrature Methods
Section 4-7:
Gaussian Quadrature
Section 4-8:
Multiple Integrals Section 4-9:
Improper Integrals
Exercise 2b
Exercise 5a
Exercise 5b
Exercise 5c
Exercise 5d
Exercise 8a
Exercise 8b
Exercise 8c
Exercise 8d
Exercise 18a
Exercise 18b
Exercise 19
Exercise 21a
Exercise 21b
Exercise 21c
Exercise 22
Exercise 23
Exercise 24a
Exercise 24b
Exercise 25
Exercise 26
Exercise 28
Exercise 29
Chapter 5: Initial-Value Problems for Ordinary Differential EquationsSection 5-1:
The Elementary Theory of Initial-Value Problems
Section 5-2:
Euler's Method
Section 5-3:
Higher-Order Taylor Methods
Section 5-4:
Runge-Kutta Methods
Section 5-5:
Error Control and the Runge-Kutta Fehlberg Method
Section 5-6:
Multistep Methods
Section 5-7:
Variable Step-Size Multistep Methods
Section 5-8:
Extrapolation Methods
Section 5-9:
Higher-Order Equations and Systems of Differential Equations
Section 5-10:
Stablity
Section 5-11:
Stiff Differential Equations
Chapter 6: Direct Methods for Solving Linear SystemsSection 6-1:
Linear Systems of Equations
Section 6-2:
Pivoting Strategies
Section 6-3:
Linear Algebra and Matrix Inversion
Section 6-4:
The Determinat of a Matrix
Section 6-5:
Matrix Factorization
Section 6-6:
Special Types of Matrices
Exercise 1b
Exercise 1c
Exercise 1d
Exercise 2b
Exercise 2c
Exercise 2d
Exercise 3b
Exercise 4b
Exercise 5b
Exercise 5c
Exercise 5d
Exercise 6b
Exercise 6c
Exercise 6d
Exercise 7b
Exercise 7c
Exercise 7d
Exercise 8b
Exercise 8c
Exercise 8d
Chapter 7: Iterative Techniques in Matrix AlgebraSection 7-1:
Norms of Vectors and Matrices
Section 7-2:
Eigenvalues and Eigenvectors
Section 7-3:
The Jacobi and Gauss-Siedel Iterative Techniques
Section 7-4:
Relaxation Techniques for Solving Linear Systems
Section 7-5:
Error Bounds and Iterative Refinement
Section 7-6:
The Conjugate Gradient Method
Exercise 1b
Exercise 1c
Exercise 1d
Exercise 2b
Exercise 2c
Exercise 4b
Exercise 4c
Exercise 4d
Exercise 5b
Exercise 5c
Exercise 5d
Exercise 6b
Exercise 6c
Exercise 6d
Exercise 8b
Exercise 8c
Exercise 8d
Exercise 9b
Exercise 9c
Exercise 14b
Exercise 15b
Chapter 8: Approximation TheorySection 8-1:
Discrete Least Squares Approximation
Section 8-2:
Orthogonal Polynomials and Least Squares Approximation
Section 8-3:
Chebyshev Polynomials and Economization of Power Series
Section 8-4:
Rational Function Approximation
Section 8-5:
Trigonometric Polynomial Approximation
Section 8-6:
Fast Fourier Transforms
Exercise 5b
Exercise 5c
Exercise 5d
Exercise 5e
Exercise 6b
Exercise 6c
Exercise 6d
Exercise 6e
Exercise 7b
Exercise 13b
Exercise 13c
Exercise 13d
Chapter 9: Approximating EigenvaluesSection 9-1:
Linear Algebra and Eigenvalues
Section 9-2:
Orthogonal Matrices and Similarity Transformations
Section 9-3:
The Power Method
Section 9-4:
Householder's Method
Section 9-5:
The QR Algorithm
Section 9-6:
Singular Value Decomposition
Exercise 1b
Exercise 1c
Exercise 1d
Exercise 2b
Exercise 2c
Exercise 2d
Exercise 3b
Exercise 3c
Exercise 3d
Exercise 4b
Exercise 4c
Exercise 4d
Exercise 13b
Exercise 13c
Exercise 13d
Exercise 14b
Exercise 14c
Exercise 14d
Exercise 17b
Exercise 17c
Exercise 17d
Chapter 10: Numerical Solutions of Nonlinear Systems of Equations Section 10-1:
Fixed Points for Functions of Several Variables
Section 10-2:
Newton's Method
Section 10-3:
Quasi-Newton Methods
Section 10-4:
Steepest Descent TechniquesSection 10-5:
Homotopy and Continuation MethodsExercise 5a
Exercise 5b
Exercise 5c
Exercise 12
Chapter 11: Boundary-Value Problems for Ordinary Differential EquationsSection 11-1:
The Linear Shooting Method
Section 11-2:
The Shooting Method for Nonlinear Problems
Section 11-3:
Finite-Difference Methods for Linear Problems
Section 11-4:
Finite-Difference Methods for Nonlinear ProblemsSection 11-5:
The Rayleigh-Ritz Method
Exercise 3a
Exercise 3b
Exercise 3c
Exercise 3d
Chapter 12: Numerical Solutions to Partial Differential EquationsSection 12-1:
Elliptic Partial Differential Equations
Section 12-2:
Parabolic Partial Differential EquationsSection 12-3:
Hyperbolic Partial Differential EquationsSection 12-4:
An Introduction to the Finite-Element MethodExercise 3b
Exercise 3c
Exercise 3d
Exercise 4
Exercise 5
Exercise 6a
Exercise 6b
Exercise 6c
Exercise 6d
Exercise 7
Exercise 8
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