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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