Cover image for Advanced engineering mathematics with MATLAB
Title:
Advanced engineering mathematics with MATLAB
Personal Author:
Edition:
2nd ed.
Publication Information:
Australia : Brooks/Cole, 2000
ISBN:
9780534371647

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30000004741058 TA345 H38 2000 Open Access Book
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30000004558635 TA345 H38 2000 Open Access Book
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30000010077165 TA345 H38 2000 Unknown
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Summary

Summary

ADVANCED ENGINEERING MATHEMATICS WITH MATLAB® is written for engineers and engineering students who are interested in applying MATLAB® to solve practical engineering problems. The book emphasizes mathematical principles, not computations, with MATLAB® employed as a tool for analysis that shows how engineering problems are defined and solved. The book features complete MATLAB® integration throughout, abundant examples which show real practical applications, and end-of-chapter problems that reinforce techniques.


Table of Contents

1 Introduction Introduction to MATLAB®
MATLAB® Commands for Display and Plotting
Creating MATLAB® Programs
MATLAB® Programming Language
Problem Solving and Programming (Optional)
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 2 Numbers and Vectors Properties of Real Numbers
MATLAB® Computer Numbers (Optional)
Complex Numbers
Vectors in Two Dimensions and Three Dimensions
Vectors in Higher Dimensions
MATLAB® Vectors
Complex Vectors
Vector Spaces
Vector Spaces of Functions
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 3 Matrices Basic Properties of Matrices
MATLAB® Matrix Operations
Square and Symmetric Matrices
Determinants and Matrix Inverses
Orthogonal and Triangular Matrices
Systems of Linear Equations
MATLAB® Matrix Functions
Linear Transformations
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 4 Eigenvalues and Eigenvectors General Discussion of Eigenvalues
Eigenvalues and Eigenvectors
Matrix Eigenvalue Theorems
Complex Vectors and Matrices
MATLAB® Commands for Eigenvectors
Matrix Calculus
Similar and Diagonalizable Matrices
Special Matrices and Their Eigenvalues (Optional)
Applications to Differential Equations
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 5 Linear Differential Equations Classification of Differential Equations
Linear Differential Equations
Higher Order Differential Equations
Second Order Differential Equations
Particular Solutions of Differential Equations
Systems of Differential Equations
MATLAB® Solutions of Systems of Differential Equations
Homogeneous Systems with Repeated Eigenvalues
Nonhomogeneous Systems of Differential Equations
Transforming Differential Equations
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 6 Advanced Differential Equations Functions and Differential Equations
Sequences and Series
Taylor Series
Numerical Methods for Differential Equations
Stiff Differential Equations
Vector Equations
Boundary Value Problems
Equations with Variable Coefficients
Bessel and Legendre Equations
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 7 Approximation of Functions Polynomial Interpolation
Interpolation by Spline Functions
Least-Squares Curve Fitting
Orthogonal Functions
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 8 Fourier Analysis Fourier Series
Properties of Fourier Series
Fourier Transforms
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 9 Laplace Transforms Definition and Properties of the Laplace Transform
Computation of Inverse Laplace Transforms
MATLAB® and Laplace Transforms
Applications to Differential Equations
Applications of Laplace Transforms to Linear Systems
Relationship of Fourier and Laplace Transforms
Summary of Laplace Transform Properties
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 10 Discrete Systems Introduction to the Sequences and Discrete Functions
Linear Difference Equations
Approximation to Differential Equations
Smoothing and Digital Filters
Introduction to z-Transforms
MATLAB® Commands for Discrete Systems
z-Transform Solution of Difference Equations
Applications of z-transforms to Linear Discrete Systems
Frequency Response and Fourier Analysis
Summary of z-transform Properties
Reinforcement Exercises and Exploration Problems
Annotated Bibliography
Answers 11 The Discrete Fourier Transform and the Fft Frequency Analysis of Signals
Discrete and Fast Fourier Transforms
MATLAB® Fourier Commands
Practical Signal Analysis
Practical Signal Sampling and DFT Errors
Analysis of DFT for Computation (Optional)
Reinforcement Exercises and Exploration Problems
Annotated