Numerical Methods using MATLAB

Table of contents

1. Cover
2. Title
3. Copyright
4. Dedication
5. Contents at a Glance
6. Contents
7. About the Author
8. Acknowledgments
9. Introduction
10. Chapter 1: Introduction to MATLAB
    1. Introduction
    2. Interface
       1. Command Window
       2. Current Directory
       3. Workspace
       4. Figures
       5. Command History
       6. Editor
       7. Help Browser
    3. Getting Started
       1. Creating a Matrix
    4. Functions
       1. The Difference Between Functions and Scripts
       2. Special Matrices
    5. Other Variable Types
       1. Character Variables
       2. Cells
       3. Logical Variables
       4. Structures
    6. Saving/Loading Variables
    7. Plots
11. Chapter 2: Matrix Representation, Operations and Vectorization
    1. Matrix Representation
       1. Conventional Sense: Matrices
       2. Data Sense: Arrays
       3. Model Representation
    2. Operations
       1. Matrix Operations
       2. Dot (array) Operators
       3. Operations for Models
    3. Indexing
       1. Normal Indexing
       2. Linear Indexing
       3. Logical Indexing
    4. Vectorization
       1. Example 1. Creating C such that C(i,j)=A(i)^B(j)
       2. Example 2. Calculating the Sum of Harmonics
       3. Example 3. Conversion to Matrix Operations
       4. Example 4. Selective Inversion
    5. Tips for Performance Improvement
       1. Vectorization
       2. Preallocating Arrays
       3. Fixed Type Variables
12. Chapter 3: Numerical Techniques
    1. Differentiation
       1. Partial Differentiation
       2. Computing Higher Derivatives
    2. Integration
       1. Multi-dimensional Integration
       2. Integration Over an Infinite Range
       3. Multidimensional Integration over Non-rectangular Intervals
    3. Solving Equations
       1. Polynomial Functions
       2. Zeros of a General Function
    4. Interpolation
       1. One-dimensional Interpolation
       2. Data Fitting and Polynomial Interpolation
       3. Arbitrary Interpolation
13. Chapter 4: Visualization
    1. Line Plots
       1. Plot Options
       2. Multiple Plots
       3. Annotations
       4. Handles
    2. 2D plots
    3. Quiver Plots
    4. 3D Plots
    5. Animations
       1. A Clock Animation
       2. Wave Motion
    6. Movies
14. Chapter 5: Introduction to Simulation
    1. One Step Simulations
    2. Iterative Methods
    3. Simulation of Real World Processes
       1. Discrete Processes
       2. Simulation of Continuous Time Processes
    4. Example: Balls in a 2D Box
       1. Animation
       2. Motion in a Force Field
    5. Event-based Simulations
15. Chapter 6: Monte Carlo Simulations
    1. Random Sampling
       1. The Third Moment of a Gaussian Random Variable
       2. Moments of Random Processes
    2. Sampling from a Given Distribution
       1. Inbuilt Functions
       2. Rejection Sampling
       3. Gibbs Sampling
    3. Statistical Performance
       1. Computation of pi
       2. Communication Channels
       3. Birth-Death Processes
    4. Multidimensional Integrals
    5. Summary
16. Chapter 7: Optimization
    1. Optimization Overview
       1. The Optimization Goal
       2. Design Parameters
       3. Constraints
       4. The Optimization Domain
       5. The Optimization Problem
       6. Mathematical Approach
    2. Implementation
       1. Extensive Search
       2. The Gradient Descent Method
    3. Built-in Functions in MATLAB
       1. Defining an Objective Function
       2. Defining Constraints
       3. Optimization Options
       4. Problem Structures
       5. Output Format
       6. Minimization Problems
       7. Equation Solving
    4. Summary
17. Chapter 8: Evolutionary Computations
    1. The Rastrigin Function
    2. Particle Swarm Optimization
       1. Algorithm
       2. Implementation
       3. Example
    3. The Genetic Algorithm
       1. Representation
       2. Initialization
       3. Selection
       4. Crossover
       5. Mutation
       6. New Generation
       7. Store the Best Chromosome of the Generation
       8. Termination Conditions
       9. Iterations
       10. Output
       11. Function Definition
       12. Example
       13. The Inbuilt Function ga
    4. Summary
18. Chapter 9: Regression and Model Fitting
    1. Regression
       1. Linear Regression
       2. Nonlinear Regression
       3. Generalized Linear Regression
    2. Time Series Analysis
       1. Autocorrelation and Proposing Models
       2. Regression
       3. Forecasting
    3. Neural Networks
       1. Feedforward Networks
    4. Summary
19. Chapter 10: Differential Equations and System Dynamics
    1. Differential Equations
       1. Ordinary Differential Equations
       2. Partial Differential Equations
    2. System Dynamics
       1. Simulation of the System
    3. Summary
20. Index