Provides an introduction to numerical methods for students in engineering. It uses Python 3, an easy-to-use, high-level programming language.
Author(s): Jaan Kiusalaas
Edition: 3
Publisher: Cambridge University Press
Year: 2013
Language: English
Pages: 432
Contents
Preface
1 Introduction to Python
1.1 General Information
1.2 Core Python
1.3 Functions and Modules
1.4 Mathematics Modules
1.5 numpy Module
1.6 Plotting with matplotlib.pyplot
1.7 Scoping of Variables
1.8 Writing and Running Programs
2 Systems of Linear Algebraic Equations
2.1 Introduction
2.2 Gauss Elimination Method
2.3 LU Decomposition Methods
Problem Set 2.1
2.4 Symmetric and Banded Coefficient Matrices
2.5 Pivoting
Problem Set 2.2
2.6 Matrix Inversion
2.7 Iterative Methods
Problem Set 2.3
2.8 Other Methods
3 Interpolation and Curve Fitting
3.1 Introduction
3.2 Polynomial Interpolation
3.3 Interpolation with Cubic Spline
Problem Set 3.1
3.4 Least-Squares Fit
Problem Set 3.2
4 Roots of Equations
4.1 Introduction
4.2 Incremental Search Method
4.3 Method of Bisection
4.4 Methods Based on Linear Interpolation
4.5 Newton-Raphson Method
4.6 Systems of Equations
Problem Set 4.1
4.7 Zeros of Polynomials
Problem Set 4.2
4.8 Other Methods
5 Numerical Differentiation
5.1 Introduction
5.2 Finite Difference Approximations
5.3 Richardson Extrapolation
5.4 Derivatives by Interpolation
Problem Set 5.1
6 Numerical Integration
6.1 Introduction
6.2 Newton-Cotes Formulas
6.3 Romberg Integration
Problem Set 6.1
6.4 Gaussian Integration
Problem Set 6.2
6.5 Multiple Integrals
Problem Set 6.3
7 Initial Value Problems
7.1 Introduction
7.2 Euler's Method
7.3 Runge-Kutta Methods
Problem Set 7.1
7.4 Stability and Stiffness
7.5 Adaptive Runge-Kutta Method
7.6 Bulirsch-Stoer Method
Problem Set 7.2
7.7 Other Methods
8 Two-Point Boundary Value Problems
8.1 Introduction
8.2 Shooting Method
Problem Set 8.1
8.3 Finite Difference Method
Problem Set 8.2
9 Symmetric Matrix Eigenvalue Problems
9.1 Introduction
9.2 Jacobi Method
9.3 Power and Inverse Power Methods
Problem Set 9.1
9.4 Householder Reduction to Tridiagonal Form
9.5 Eigenvalues of Symmetric Tridiagonal Matrices
Problem Set 9.2
9.6 Other Methods
10 Introduction to Optimization
10.1 Introduction
10.2 Minimization Along a Line
10.3 Powell's Method
10.4 Downhill Simplex Method
Problem Set 10.1
Appendices
A1 Taylor Series
A2 Matrix Algebra
List of Program Modules (by Chapter)
Index
