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Book
Numerical Methods with Applications
"Mathematical models are an integral part in solving engineering problems. Many times, these mathematical models are derived from engineering and science principles, while at other times the models may be obtained from experimental data. Mathematical models generally result in need of using mathematical procedures that include but are not limited to differentiation, nonlinear equations, simultaneous linear equations, curve fitting by interpolation or regression, integration, and differential equations."
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| Added | 12 Feb 2009 |
| Updated | 12 Feb 2009 |
| Authors | Autar K Kaw, Egwu E Kalu |
Table of Content
1: INTRODUCTION, APPROXIMATION AND ERRORS
1.1 Introduction to Scientific Computing
1.2 Measuring Errors
1.3 Sources of Error
1.4 Binary Representation of Numbers
1.5 Floating Point Representation
1.6 Propagation of Errors
1.7 Taylor Series Revisited
2: DIFFERENTIATION
2.1 Primer on Differential Calculus
2.2 Differentiation of Continuous Functions
2.3 Differentiation of Discrete Functions
3: NONLINEAR EQUATIONS
3.1 Solving Quadratic Equations Exactly
3.2 Solving Cubic equations Exactly
3.3 Bisection Method
3.4 Newton-Raphson Method
3.5 Secant Method
4: SIMULTANEOUS LINEAR EQUATIONS
4.1 Introduction
4.2 Vectors
4.3 Binary Matrix Operations
4.4 Unary Matrix Operations
4.5 System of Equations
4.6 Gaussian Elimination Method
4.7 LU Decomposition Method
4.8 How does Gauss-Seidel method work?
4.9 Adequacy of Solutions
4.10 Eigenvalues and Eigenvectors
5: INTERPOLATION
5.1 History of Interpolation
5.2 Direct Method
5.3 Newton's Divided Difference Method
5.4 Lagrange Method
5.5 Spline Method
5.6 The lurking dangers of extrapolation!
5.7 Why is higher order interpolation is a bad idea?
5.8 Why do we need spline interpolation
5.9 How choice of points of interpolation affects approximations!
5.10 How splines can help in developing a shorter path for a robot!
6: REGRESSION
6.1 Primer on statistical terminology
6.2 Introduction to Regression
6.3 Linear Regression
6.4 Nonlinear Regression
7: INTEGRATION
7.1 Primer on Integral Calculus
7.2 Trapezoidal Rule
7.3 Simpson's 1/3rd Rule
7.4 Romberg Rule
7.5 Gauss-Quadrature Rule
7.6 Discrete Data Integration
7.7 Improper Integration
8: ORDINARY DIFFERENTIAL EQUATIONS
8.1 Primer on Ordinary Differential Equations
8.2 Euler's method
8.3 Runge-Kutta 2nd order method
8.4 Runge-Kutta 4th order method
8.5 On solving higher order & coupled ordinary differential equations
8.6 Shooting Method
8.7 Finite Difference Method
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