Textbook: Numerical Methods with Applications

  • Abridged Print Version Available
  • Dedicated Website for book
  • Authors: Autar K Kaw | Co-Author: Egwu E Kalu, Duc Nguyen
  • Contributors: Glen Besterfield, Sudeep Sarkar, Henry Welch, Ali Yalcin, Venkat Bhethanabotla
1: Introduction, Approximation, and Errors
      • Chapter 01.01 Introduction to Scientific Computing [PDF] [DOC] [MORE]
      • Chapter 01.02 Measuring Errors [PDF] [DOC] [MORE]
      • Chapter 01.03 Sources of Error [PDF] [DOC] [MORE]
      • Chapter 01.04 Binary Representation of Numbers [PDF] [DOC] [MORE]
      • Chapter 01.05 Floating Point Representation [PDF] [DOC] [MORE]
      • Chapter 01.06 Propagation of Errors [PDF] [DOC] [MORE]
      • Chapter 01.07 Taylor Series Revisited [PDF] [DOC] [MORE]
2: Differentiation
      • Chapter 02.01 Primer on Differential Calculus [PDF] [DOC]
      • Chapter 02.02 Differentiation of Continuous Functions [PDF] [DOC] [MORE]
      • Chapter 02.03 Differentiation of Discrete Functions [PDF] [DOC] [MORE]
3: Nonlinear Equations
      • Chapter 03.01 Solving Quadratic Equations Exactly [PDF] [DOC] [MORE]
      • Chapter 03.02 Solving Cubic equations Exactly [PDF] [DOC] [MORE]
      • Chapter 03.03 Bisection Method [PDF] [DOC] [MORE]
      • Chapter 03.04 Newton-Raphson Method [PDF] [DOC] [MORE]
      • Chapter 03.05 Secant Method [PDF] [DOC] [MORE]
      • Chapter 03.06 False Position Method [PDF] [DOC] [MORE]
4: Simultaneous Linear Equations
      • Chapter 04.01 Introduction [PDF] [DOC] [MORE]
      • Chapter 04.02 Vectors [PDF] [DOC] [MORE]
      • Chapter 04.03 Binary Matrix Operations [PDF] [DOC] [MORE]
      • Chapter 04.04 Unary Matrix Operations [PDF] [DOC] [MORE]
      • Chapter 04.05 System of Equations [PDF] [DOC] [MORE]
      • Chapter 04.06 Gaussian Elimination Method [PDF] [DOC] [MORE]
      • Chapter 04.07 LU Decomposition Method [PDF] [DOC] [MORE]
      • Chapter 04.08 How does Gauss-Seidel method work? [PDF] [DOC] [MORE]
      • Chapter 04.09 Adequacy of Solutions [PDF] [DOC][MORE]
      • Chapter 04.10 Eigenvalues and Eigenvectors [PDF] [DOC][MORE]
      • Chapter 04.11 Cholesky and LDLT Method [PDF] [DOC] [MORE]
5: Interpolation
      • Chapter 05.01 History of Interpolation [PDF] [DOC][MORE]
      • Chapter 05.02 Direct Method [PDF] [DOC] [MORE]
      • Chapter 05.03 Newton’s Divided Difference Method [PDF] [DOC] [MORE]
      • Chapter 05.04 Lagrange Method [PDF] [DOC] [MORE]
      • Chapter 05.05 Spline Method [PDF] [DOC] [MORE]
      • Chapter 05.06 The lurking dangers of extrapolation! [PDF] [DOC]
      • Chapter 05.07 Why is higher order interpolation a bad idea? [PDF] [DOC]
      • Chapter 05.08 Why do we need spline interpolation [PDF] [DOC]
      • Chapter 05.09 How choice of points of interpolation affects approximations! [PDF] [DOC]
      • Chapter 05.10 How splines can help in developing a shorter path for a robot! [PDF] [DOC]
6: Regression
      • Chapter 06.01 Primer on statistical terminology [PDF] [DOC]
      • Chapter 06.02 Introduction to Regression [PDF] [DOC]
      • Chapter 06.03 Linear Regression [PDF] [DOC] [MORE]
      • Chapter 06.04 Nonlinear Regression [PDF] [DOC] [MORE]
      • Chapter 06.05 Adequacy of Regression Models [PDF] [DOC] [MORE]
7: Integration
      • Chapter 07.01 Primer on Integral Calculus [PDF] [DOC] [MORE]
      • Chapter 07.02 Trapezoidal Rule [PDF] [DOC] [MORE]
      • Chapter 07.03 Simpson’s 1/3 Rule [PDF] [DOC] [MORE]
      • Chapter 07.04 Romberg Rule [PDF] [DOC] [MORE]
      • Chapter 07.05 Gauss-Quadrature Rule [PDF] [DOC] [MORE]
      • Chapter 07.06 Discrete Data Integration [PDF] [DOC] [MORE]
      • Chapter 07.07 Improper Integration [PDF] [DOC] [MORE]
      • Chapter 07.08 Simpson’s 3/8 rule [PDF] [DOC] [MORE]
8: Ordinary Differential Equations
      • Chapter 08.01 Primer on Ordinary Differential Equations [PDF] [DOC] [MORE]
      • Chapter 08.02 Euler’s method [PDF] [DOC] [MORE]
      • Chapter 08.03 Runge-Kutta 2nd order method [PDF] [DOC] [MORE]
      • Chapter 08.04 Runge-Kutta 4th order method [PDF] [DOC] [MORE]
      • Chapter 08.05 On solving higher order & coupled ordinary differential equations [PDF] [DOC] [MORE]
      • Chapter 08.06 Shooting Method [PDF] [DOC] [MORE]
      • Chapter 08.07 Finite Difference Method [PDF] [DOC] [MORE]
9: Optimization
      • Chapter 09.01 Golden Section Search Method [PDF] [DOC] [MORE]
      • Chapter 09.02 Newton’s Method [PDF] [DOC] [MORE]
      • Chapter 09.03 Multidimensional Direct Search Method [PDF] [DOC] [MORE]
      • Chapter 09.04 Multidimensional Gradient Method [PDF] [DOC] [MORE]
      • Chapter 09.05 Simplex Method [PDF] [DOC]
10: Partial Differential Equations
      • Chapter 10.01 Introduction to Partial Differential Equations [PDF] [DOC] [MORE]
      • Chapter 10.02 Parabolic Partial Differential Equations [PDF] [DOC] [MORE]
      • Chapter 10.03 Elliptic Partial Differential Equations [PDF] [DOC] [MORE]
      • Chapter 10.04 Finite Element Methods [PDF] [DOC]
11: Fast Fourier Transforms
        • Chapter 11.01 Introduction to Fourier Series [PDF] [DOC] [MORE]
        • Chapter 11.02 Continuous Fourier Series [PDF] [DOC] [MORE]
        • Chapter 11.03 Fourier Transform Pair [PDF] [DOC] [MORE]
        • Chapter 11.04 Discrete Fourier Transform [PDF] [DOC] [MORE]
        • Chapter 11.05 Informal Development of Fast Fourier Transform [PDF] [DOC] [MORE]