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Numerical Methods with Programming

Leonid Kovalev

Front Matter
- Acknowledgements
- Preface
I Using Matlab
1 Scalars, vectors and matrices
2 Linear systems, array operations, plots
3 Built-in functions, input, output
4 Control flow: loops and conditional statements
5 User-defined functions
II Solving Equations
6 Systems of linear equations
7 Root finding: bisection
8 Root finding: fixed point iteration
9 Newton's method and its relatives
10 Systems of several nonlinear equations: multivariate Newton's method
11 Broyden's method
III Numerical Calculus
12 Numerical differentiation
13 Numerical integration: basic rules
14 Simpson's rule and other Newton-Cotes rules
15 Legendre polynomials and Laguerre polynomials
16 Gauss-Legendre and Gauss-Laguerre integration
17 Adaptive integration
18 Multivariable integration
19 Differential equations: Euler's method and its relatives
20 Modeling with differential equations
IV Modeling Data
21 Polynomial Interpolation
22 Chebyshev Polynomials and Interpolation
23 Spline Interpolation
24 Spline Approximation
25 Discrete Fourier Transform
26 Applications of Discrete Fourier Transform
27 Linear Least Squares
28 Transforming Data for LLS
29 Nonlinear Least Squares
V Optimization
30 Single Variable Minimization
31 Parabolic Interpolation and Gradient Descent
32 Gradient methods and Newton's method
33 The Nelder-Mead method
34 Constrained Optimization
35 Linear Programming
36 Classification Problems

Authored in PreTeXt

Part III Numerical Calculus

12 Numerical differentiation
13 Numerical integration: basic rules
14 Simpson's rule and other Newton-Cotes rules
15 Legendre polynomials and Laguerre polynomials
16 Gauss-Legendre and Gauss-Laguerre integration
17 Adaptive integration
18 Multivariable integration
19 Differential equations: Euler's method and its relatives
20 Modeling with differential equations