Advanced Engineering Mathematics With MATLAB by Dean G. Duffy

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Advanced Engineering Mathematics With MATLAB by Duffy

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

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All books on this website are published in good faith and for educational information purpose only. So, we ask you to report us any copyrighted material published in our website and we will remove it immediately.