**PDF Free Download | Advanced Engineering Mathematics With MATLAB Third Edition by Dean G. Duffy**

## Contents of Advanced Engineering Mathematics With MATLAB

**Chapter 1: Complex Variables**- Complex Numbers
- Finding Roots
- The Derivative in the Complex Plane:
- The Cauchy-Riemann Equations
- Line Integrals
- The Cauchy-Goursat Theorem
- Cauchy’s Integral Formula
- Taylor and Laurent Expansions and Singularities
- Theory of Residues
- Evaluation of Real Definite Integrals
- Cauchy’s Principal Value Integral
**Chapter 2: First-Order Ordinary**- Differential Equations
- Classification of Differential Equations
- Separation of Variables
- Homogeneous Equations
- Exact Equations
- Linear Equations
- Graphical Solutions
- Numerical Methods
**Chapter 3: Higher-Order Ordinary**- Differential Equations
- Homogeneous Linear Equations
- with Constant Coefficients
- Simple Harmonic Motion
- Damped Harmonic Motion
- Method of Undetermined Coefficients
- Forced Harmonic Motion
- Variation of Parameters
- Euler-Cauchy Equation
- Phase Diagrams
- Numerical Methods amplitude spectrum (ft) times
- Bay bridge and tunnel
**Chapter 4: Fourier Series**- Fourier Series
- Properties of Fourier Series
- Half-Range Expansions
- Fourier Series with Phase Angles
- Complex Fourier Series
- The Use of Fourier Series in the Solution of Ordinary
- Differential Equations
- Finite Fourier Series
**Chapter 5: The Fourier Transform**- Fourier Transforms
- Fourier Transforms Containing the Delta Function
- Properties of Fourier Transforms
- Inversion of Fourier Transforms
- Convolution
- Solution of Ordinary Differential Equations by Fourier Transforms
**Chapter 6: The Laplace Transform**- Definition and Elementary Properties
- The Heaviside Step and Dirac Delta Functions
- Some Useful Theorems
- The Laplace Transform of a Periodic Function
- Inversion by Partial Fractions:
- Heaviside’s Expansion Theorem
- Convolution
- Integral Equations
- Solution of Linear Differential Equations
- with Constant Coefficients
- Inversion by Contour Integration
- Ratio of quadrature amplitudes to ideal integration
- Trapezoidal
- Simpson’s
**Chapter 7: The Z-Transform**- The Relationship of the Z-Transform to the Laplace
- Transform
- Some Useful Properties
- Inverse Z-Transforms
- Solution of Difference Equations
- Stability of Discrete-Time Systems
**Chapter 8: The Hilbert Transform**- Definition
- Some Useful Properties
- Analytic Signals
- Causality: The Kramers-Kronig Relationship
**Chapter 9: The Sturm-Liouville**- Problem
- Eigenvalues and Eigenfunctions
- Orthogonality of Eigenfunctions
- Expansion in Series of Eigenfunctions
- A Singular Sturm-Liouville Problem:
- Legendre’s Equation
- Another Singular Sturm-Liouville Problem:
- Bessel’s Equation
- Finite Element Method
**Chapter 10: The Wave Equation**- The Vibrating String
- Initial Conditions: Cauchy Problem
- Separation of Variables
- D’Alembert’s Formula
- The Laplace Transform Method
- Numerical Solution of the Wave Equation
**Chapter 11: The Heat Equation**- Derivation of the Heat Equation
- Initial and Boundary Conditions
- Separation of Variables
- The Laplace Transform Method
- The Fourier Transform Method
- The Superposition Integral
- Numerical Solution of the Heat Equation
**Chapter 12: Laplace’s Equation**- Derivation of Laplace’s Equation
- Boundary Conditions
- Separation of Variables
- The Solution of Laplace’s Equation
- on the Upper Half-Plane
- Poisson’s Equation on a Rectangle
- The Laplace Transform Method
- Numerical Solution of Laplace’s Equation
- Finite Element Solution of Laplace’s Equation
**Chapter 13: Green’s Functions**- What Is a Green’s Function?
- Ordinary Differential Equations
- Joint Transform Method
- Wave Equation
- Heat Equation
- Helmholtz’s Equation
**Chapter 14: Vector Calculus**- Review
- Divergence and Curl
- Line Integrals
- The Potential Function
- Surface Integrals
- Green’s Lemma
- Stokes’ Theorem
- Divergence Theorem
**Chapter 15: Linear Algebra**- Fundamentals of Linear Algebra
- Determinants
- Cramer’s Rule
- Row Echelon Form and Gaussian Elimination
- Eigenvalues and Eigenvectors
- Systems of Linear Differential Equations
- Matrix Exponential
**Chapter 16: Probability**- Review of Set Theory
- Classic Probability
- Discrete Random Variables
- Continuous Random Variables
- Mean and Variance
- Some Commonly Used Distributions
- Joint Distributions
**Chapter 17: Random Processes**- Fundamental Concepts
- Power Spectrum
- Differential Equations Forced by Random Forcing
- Two-State Markov Chains
- Birth and Death Processes
- Poisson Processes
- Random Walk