Inside:
MATLAB Manual for Advanced Engineering Mathematics

  MATLAB Manual for Advanced Engineering Mathematics

Author: Ramin Esfandiari

Table of Contents

Chapter 1 Ordinary Differential Equations Symbolic Solutions

  • Verifying Solutions of First-Order ODE's
  • Solving ODE's and IVP's and Plotting the Solution
  • Orthogonal Trajectories
  • Second-Order ODE's
  • Series Solutions of ODE's
  • Legendre's Equation and Polynomials
  • Bessel's Equation and Functions

Chapter 2 Laplace Transformation

  • Laplace Transform
  • Transfer Function
  • Poles and Zeros
  • Impulse and Step Responses
  • Functions Defined Piecewise
  • Response using Transfer Function
  • Initial and Final-Value Theorems
  • Periodic Functions

Chapter 3 Fourier Analysis

  • Fourier Series
  • Symbolic Fourier Coefficients
  • Extension Beyond One Period
  • Even and Odd Functions
  • Even and Odd Periodic Extensions
  • Fourier Transformation
  • Using Fourier Transformation to Solve ODE's

Chapter 4 Partial Differential Equations

  • One-Dimensional Wave Equation; Free Vibration of an Elastic String Animation
  • Transverse Vibration of a Beam
  • One-Dimensional Heat Equation
  • Two-Dimensional Heat Equation
  • Two-Dimensional Wave Equation; Vibration of Rectangular Membranes
  • Free Lateral Vibration of Circular Membranes

Chapter 5 Complex Numbers, Variables, and Functions

  • Complex Symbolic Variables
  • Roots of a Complex Number
  • Complex Equations
  • Limit, Continuity and Differentiability
  • Analytic Functions
  • Regions in the Complex Plane
  • Mapping by Elementary Functions

Chapter 6 Complex Integrals and Series

  • Complex Integrals
  • Parametric Representation of the Path
  • Integral Evaluation by Parametric Representation
  • Complex Series
  • Tests of Convergence
  • General Form of Complex Series

Chapter 7 Residue Theory

  • Residues
  • Integral Evaluation via Residue Theory
  • Improper Real Integrals

Chapter 8 Conformal Mapping

  • Points, Lines and Curves in the Complex Plane
  • Plotting Points, Lines, Circles, Circular Arcs and Polygons
  • Measuring Interior Angles
  • Plotting Axes and Planes
  • Conformal Mapping
  • The Bilinear Transformation
  • Critical and Fixed Points of Mappings
  • Finding Mapping Based on Given Fixed Points
  • Finding Mapping from Images
  • Mapping Planes to Circles

Chapter 9 Linear Algebra Vectors and Matrices

  • Vectors
  • Accessing and Assigning Vector Elements
  • Matrices
  • Multiplying Matrices
  • Linear Indexing
  • Multidimensional Matrices
  • Matrix Addition and Multiplication
  • Matrix Inverse and Matrix Divisions
  • Exponents of Matrices
  • Dot and Cross Products
  • Determinant, Condition Number
  • Rank

Chapter 10 Matrix Eigenvalue Problem

  • Similarity Transformations
  • Generalized Eigenvectors
  • Modal Decomposition
  • Systems of Linear, First-Order Differential Equations
  • Simultaneous Diagonalization
  • Application: Undamped Dynamic Systems

Chapter 11 Fundamentals of Numerical Methods

  • Bisection Method
  • Newton's Method
  • Roots of Polynomials
  • Roots of Functions
  • Polynomial Approximation
  • One-, Two-, and Higher-Dimensional Interpolation
  • Scattered Data
  • Fourier Approximation and Interpolation
  • Fast Fourier Transform (FFT)
  • Numerical Differentiation
  • Numerical Integration

Chapter 12 Numerical Methods for Ordinary Differential Equations

  • Setting ODE Solver Options
  • Numerical Methods for Solving ODE's
  • Fourth-Order Runge-Kutta Method
  • Multi-step Methods - Predictor-Corrector Methods
  • Systems of First-Order ODE's

Chapter 13 Numerical Methods for Partial Differential Equations

  • Elliptic Equations
  • Dirichlet Problem; Difference Equations
  • Peaceman and Rachford Alternating Direction Implicit (PRADI) Method
  • Parabolic Equations
  • Finite Difference Method
  • Crank-Nicolson Method
  • Hyperbolic Equations

Chapter 14 Numerical Methods in Linear Algebra

  • Direct Methods for Solving Linear Systems of Equations
  • Gauss Elimination with Partial Pivoting
  • Vector and Matrix Norms
  • LU-Factorization
  • Doolittle's Method, Cholesky's Method
  • Iterative Methods for Solving Linear Systems of Equations
  • Jacobi and Gauss-Seidel Iterations
  • Curve Fit; Method of Least Squares
  • Overdetermined Linear Systems
  • Localization of Eigenvalues
  • Matrix Eigenvalue Approximation; Power Method
  • Wielandt's Deflation Methods
  • Householder and Lanczos Tridiagonalization Methods + QR Factorization

Chapter 15 Probability and Statistics

  • Set Operations
  • Permutations, Combinations
  • Discrete and continuous Random Variables and Probability Distributions
  • Random Number Generators
  • Normal Distribution
  • Joint Probability Distributions
  • Statistical Analysis
  • Binomial Distribution
  • Hypergeometric Distribution
  • Poisson Distribution
  • Expected Values
  • Moment-Generating Function

Index

Communication and Feedback

Please contact the author at Ramin.Esfandiari@csulb.edu for questions and/or feedback regarding this book.