MATHEMATICS with MATLAB: Interpolation, Optimization, Functions, Differential Equations and Fourier Transforms

by K. Douglas



The matrix structure of MATLAB enables fast Mathematics. The most important topics covered in this book are the following:

Interpolation
Interpolating Gridded Data
Gridded Data Representation
Interpolation of 2-D Selections in 3-D Grids
Interpolating Scattered Data
Triangulation
Extrapolating Scattered Data
Extrapolation of 3-D Data
Optimization
Function Summary
Optimizing Nonlinear Functions
Minimizing Functions of One Variable
Minimizing Functions of Several Variables
Maximizing Functions
Curve Fitting via Optimization
Curve Fitting by Optimization
Output Functions
Plot Functions
Function Handles
Parameterizing Functions
Calculus
Ordinary Differential Equations
Initial Value Problems
Types of Solvers
Solver Syntax
Integrator Options
Troubleshooting
Types of DDEs
Constant Delay DDEs
Time-Dependent and State-Dependent DDEs
DDEs of Neutral Type
Evaluating the Solution at Specific Points
History and Initial Values
Propagation of Discontinuities
Discontinuities in DDEs
DDE with Constant Delays
State-Dependent Delay Problem
DDE of Neutral Type
Initial Value DDE of Neutral Type
Boundary-Value Problems
BVP Solver
Integrator Options
Partial Differential Equations
Initial Value Problems
PDE Solver
Integration to Find Arc Length
Fourier Transforms
Discrete Fourier Transform (DFT)
Fast Fourier Transform (FFT)