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APM3711
Numerical Methods II

Applied Numerical Analysis

(7th edition)

by Curtis F. Gerald, Patrick O. Wheatley

Add chapter or nested subsection Edit title & number Status: Pending → completed → Not required

0. Preliminaries Pending

0.1. Analysis Versus Numerical Analysis

0.2. Computers and Numerical Analysis

0.3. An Illustrative Example

0.4. Kinds of Errors in Numerical Procedures

0.5. Interval Arithmetic

0.6. Parallel and Distributed Computing

0.7. Measuring the Efficiency of Numerical Procedures

1. Solving Nonlinear Equations Pending

1.1. Interval Halving (Bisection)

1.2. Linear Interpolation Methods

1.3. Newton's Method

1.4. Muller's Method

1.5. Fixed-Point Iteration: x = g(x) Method

1.6. Multiple Roots

1.7. Nonlinear Systems

2. Solving Sets of Equations Pending

2.1. Matrices and Vectors

2.2. Elimination Methods

2.3. The Inverse of a Matrix and Matrix Pathology

2.4. Ill-Conditioned Systems

2.5. Iterative Methods

2.6. Parallel Processing

3. Interpolation and Curve Fitting Pending

3.1. Interpolating Polynomials

3.2. Divided Differences

3.3. Spline Curves

3.4. Bezier Curves and B-Splines Curves

3.5. Interpolating on a Surface

3.6. Least-Squares Approximations

4. Approximation of Functions Pending

4.1. Chebyshev Polynomials and Chebyshev Series

4.2. Rational Function Approximations

4.3. Fourier Series

5. Numerical Differentiation and Integration Pending

5.1. Differentiation with a Computer

5.2. Numerical Integration-The Trapezoidal Rule

5.3. Simpson's Rules

5.4. An Application of Numerical Integration-Fourier Series and Fourier Transforms

5.5. Adaptive Integration

5.6. Gaussian Quadrature

5.7. Multiple Integrals

5.8. Applications of Cubic Splines

6. Numerical Solution of Ordinary Differential Equations Pending

6.1. The Taylor-Series Method

6.2. The Euler Method and Its Modifications

6.3. Runge-Kutta Methods

6.4. Multistep Methods

6.5. Higher-Order Equations and Systems

6.6. Stiff Equations

6.7. Boundary-Value Problems

6.8. Characteristic-Value Problems

7. Optimization Pending

7.1. Finding the Minimum of y = f(x)

7.2. Minimizing a Function of Several Variables

7.3. Linear Programming

7.4. Nonlinear Programming

7.5. Other Optimizations

8. Partial-Differential Equations Pending

8.1. Elliptic Equations

8.2. Parabolic Equations

8.3. Hyperbolic Equations

9. Finite Element Analysis Pending

9.1. Mathematical Background

9.2. Finite Elements for Ordinary-Differential Equations

9.3. Finite Elements for Partial-Differential Equations

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