Numerical Analysis Using MATLAB

Table of Contents
Chapter 1
Introduction to MATLAB
Command Window
Roots of Polynomials
Polynomial Construction from Known Roots
Evaluation of a Polynomial at Specified Values
Rational Polynomials
Using MATLAB to Make Plots
Subplots
Multiplication, Division and Exponentiation
Script and Function Files
Display Formats
Summary
Exercises
Solutions to Exercises

Chapter 2
Root Approximations
Newton’s Method for Root Approximation
Approximations with Spreadsheets
The Bisection Method for Root Approximation
Summary
Exercises
Solutions to Exercises

Chapter 3
Sinusoids and Phasors
Alternating Voltages and Currents
Characteristics of Sinusoids
Inverse Trigonometric Functions
Phasors
Addition and Subtraction of Phasors
Multiplication of
Division of Phasors
Exponential and Polar Forms of Phasors
Summary
Exercises
Solutions to Exercises

Chapter 4
Matrices and Determinants
Matrix Definition
Matrix Operations
Special Forms of Matrices
Determinants
Minors and Cofactors
Cramer’s Rule
Gaussian Elimination Method
The Adjoint of a Matrix
Singular and Non-Singular Matrices
The Inverse of a Matrix
Solution of Simultaneous Equations with Matrices
Summary
Exercises
Solutions to Exercises

Chapter 5
Differential Equations, State Variables, and State Equations
Simple Differential Equations
Classification
Solutions of Ordinary Differential Equations (ODE)
Solution of the Homogeneous ODE
Using the Method of Undetermined Coefficients for the Forced Response
Using the Method of Variation of Parameters for the Forced Response
Expressing Differential Equations in State Equation Form
Solution of Single State Equations
The State Transition Matrix
Computation of the State Transition Matrix
Eigenvectors
Summary
Exercises
Solutions to Exercises

Chapter 6
Fourier, Taylor, and Maclaurin Series
Wave Analysis
Evaluation of the Coefficients
Symmetry
Waveforms in Trigonometric Form of Fourier Series
Alternate Forms of the Trigonometric Fourier Series
The Exponential Form of the Fourier Series
Line Spectra
Numerical Evaluation of Fourier Coefficients
Power Series Expansion of Functions
Taylor and Maclaurin Series
Summary
Exercises
Solutions to Exercises

Chapter 7
Finite Differences and Interpolation
Divided Differences
Factorial Polynomials
Antidifferences
Newton’s Divided Difference Interpolation Method
Lagrange’s Interpolation Method
Gregory-Newton Forward Interpolation Method
Gregory-Newton Backward Interpolation Method
Interpolation with MATLAB
Summary
Exercises
Solutions to Exercises

Chapter 8
Linear and Parabolic Regression
Curve Fitting
Linear Regression
Parabolic Regression
Regression with Power Series Approximations
Summary
Exercises
Solutions to Exercises

Chapter 9
Solution of Differential Equations by Numerical Methods
Taylor Series Method
Runge-Kutta Method
Adams’ Method
Milne’s Method
Summary
Exercises
Solutions to Exercises

Chapter 10
Integration by Numerical Methods
The Trapezoidal Rule
Simpson’s Rule
Summary
Exercises
Solution to Exercises
Chapter 11
Difference Equations
Definition, Solutions, and Applications
Fibonacci Numbers
Summary
Exercises
Solutions to Exercises

Chapter 12
Partial Fraction Expansion
Partial Fraction Expansion
Alternate Method of Partial Fraction Expansion
Summary
Exercises
Solutions to Exercises

Chapter 13
The Gamma and Beta Functions and Distributions
The Gamma Function
The Gamma Distribution
The Beta Function
The Beta Distribution
Summary
Exercises
Solutions to Exercises

Chapter 14
Orthogonal Functions and Matrix Factorizations
Orthogonal Functions
Orthogonal Trajectories
Orthogonal Vectors
The Gram-Schmidt Orthogonalization Procedure
The LU Factorization
The Cholesky Factorization
The QR Factorization
Singular Value Decomposition
Summary
Exercises
Solutions to Exercises

Chapter 15
Bessel, Legendre, and Chebyshev Functions
The Bessel Function
Legendre Functions
Laguerre Polynomials
Chebyshev Polynomials
Summary
Exercises
Solutions to Exercises

Chapter 16
Optimization Methods
Linear Programming
Dynamic Programming
Network Analysis
Summary
Exercises
Solutions to Exercises


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