Won Y. Yang, Young K. Choi, Jaekwon Kim, Man Cheol Kim, H. Jin Kim, Taeho Im

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Engineering Mathematics with MATLAB

PDF Free Download | Engineering Mathematics with MATLAB by Won Y. Yang, Young K. Choi, Jaekwon Kim, Man Cheol Kim, H. Jin Kim, Taeho Im

Contents of Engineering Mathematics with MATLAB

  • Chapter 1. Vectors and Matrics
  • Vectors
  • Geometry with Vector
  • Dot Product
  • Cross Product
  • Lines and Planes
  • Vector Space
  • Coordinate Systems
  • Gram Schmidt Orthonolization
  • Matrices
  • Matrix Algebra
  • Rank and Row Column Spaces
  • Determinant and Trace
  • Eigenvalues and Eigenvectors
  • Inverse of a Matrix
  • Similarity Transformation and Diagonalization
  • Special Matrices
  • Positive Definiteness
  • Matrix Inversion Lemma
  • LU Cholesky QR and Singular Value Decompositions
  • Geometrical Meaning of Eigenvalues Eigenvectors
  • Systems of Linear Equations
  • Nonsingular Case
  • Undetermined Case Minimum Norm Solution
  • Overdetermined Case Least Squares Error Solution
  • Gauss ian Elimination
  • RLS Recursive Least Squares Algorithm
  • Chapter 2. Vector Calculus
  • Derivatives
  • Vector Functions
  • Velocity and Acceleration
  • Divergence and Curl
  • Line Integrals and Path Independence
  • Line Integrals
  • Path Independence
  • Double Integrals
  • Green s Theorem
  • Surface Integrals
  • Stokes Theorem
  • Triple Integrals
  • Divergence Theorem
  • Chapter 3. Ordinary Differential Equations
  • First Order Differential Equations
  • Separable Equations
  • Exact Differential Equations and Integrating Factors
  • Linear First Order Differential Equations
  • Nonlinear First Order Differential Equations
  • Systems of First Order Differential Equations
  • Higher Order Differential Equations
  • Undetermined Coefficients
  • Variation of Parameters
  • Cauchy Euler Equations
  • Systems of Linear Differential Equations
  • Special Second Order Linear ODEs
  • Bessel s Equation
  • Legendre s Equation
  • Chebyshev s Equation
  • Hermite s Equation
  • Laguerre s Equation
  • Boundary Value Problems
  • Chapter 4. The Laplace Transform
  • Definition of the Laplace Transform
  • Laplace Transform of the Unit Step Function
  • Laplace Transform of the Unit Impulse Function
  • Laplace Transform of the Ramp Function
  • Laplace Transform of the Exponential Function
  • Laplace Transform of the Complex Exponential Function
  • Properties of the Laplace Transform
  • Linearity
  • Time Differentiation
  • Time Integration
  • Time Shifting Real Translation
  • Frequency Shifting Complex Translation
  • Real Convolution
  • Partial Differentiation
  • Complex Differentiation
  • Initial Value Theorem IVT
  • Final Value Theorem FVT
  • The Inverse Laplace Transform
  • Using the Laplace Transform
  • Transfer Function of a Continuous Time System
  • Chapter 5. The Z transform
  • Definition of the Z transform
  • Properties of the Z transform
  • Linearity
  • Time Shifting Real Translation
  • Frequency Shifting Complex Translation
  • Time Reversal
  • Real Convolution
  • Complex Convolution
  • Complex Differentiation
  • Partial Differentiation
  • Initial Value Theorem
  • Final Value Theorem
  • The Inverse Z transform
  • Using the Z transform
  • Transfer Function of a Discrete Time System
  • Differential Equation and Difference Equation
  • Chapter 6. Fourier Series and Fourier Transform
  • Continuous Time Fourier Series CTFS
  • Definition and Convergence Conditions
  • Examples of CTFS
  • Continuous Time Fourier Transform CTFT
  • Definition and Convergence Conditions
  • Generalized CTFT of Periodic Signals
  • Examples of CTFT
  • Properties of CTFT
  • Discrete Time Fourier Transform DTFT
  • Definition and Convergence Conditions
  • Examples of DTFT
  • DTFT of Periodic Sequences
  • Properties of DTFT
  • Discrete Fourier Transform DFT
  • Fast Fourier Transform FFT
  • Decimation in Time DIT FFT
  • Decimation in Frequency DIF FFT
  • Computation of IDFT Using FFT Algorithm
  • Interpretation of DFT Results
  • Fourier Bessel Legendre Chebyshev Cosine Sine Series
  • Fourier Bessel Series
  • Fourier Legendre Series
  • Fourier Chebyshev Series
  • Fourier Cosine Sine Series
  • Chapter 7. Partial Differential Equation
  • Elliptic PDE
  • Parabolic PDE
  • The Explicit Forward Euler Method
  • The Implicit Backward Euler Method
  • The Crank Nicholson Method
  • Using the MATLAB Function pdepe
  • Two Dimensional Parabolic PDEs
  • Hyperbolic PDES
  • The Explict Central Difference Method
  • Two Dimensional Hyperbolic PDEs
  • PDES in Other Coordinate Systems
  • PDEs in Polar Cylindrical Coordinates
  • PDEs in Spherical Coordinates
  • Laplace Fourier Transforms for Solving PDES
  • Using the Laplace Transform for PDEs
  • Using the Fourier Transform for PDEs
  • Chapter 8. Complex Analysis
  • Functions of a Complex Variable
  • Complex Numbers and Their Powers Roots
  • Functions of a Complex Variable
  • Cauchy Riemann Equations
  • Exponential and Logarithmic Functions
  • Trigonometric and Hyperbolic Functions
  • Inverse Trigonometric Hyperbolic Functions
  • Conformal Mapping
  • Conformal Mappings
  • Linear Fractional Transformations
  • Integration of Complex Functions
  • Line Integrals and Contour Integrals
  • Cauchy Goursat Theorem
  • Cauchy s Integral Formula
  • Series and Residues
  • Sequences and Series
  • Taylor Series
  • Laurent Series
  • Residues and Residue Theorem
  • Real Integrals Using Residue Theorem
  • Chapter 9. Optimization
  • Unconstrained Optimization
  • Golden Search Method
  • Quadratic Approximation Method
  • Nelder Mead Method
  • Steepest Descent Method
  • Newton s Method
  • Constrained Optimization
  • Lagrange Multiplier Method
  • Penalty Function Method
  • MATLAB Built in Functions for Optimization
  • Unconstrained Optimization
  • Constrained Optimization
  • Linear Programming LP
  • Mixed Integer Linear Programing MILP
  • Chapter 10. Probability
  • Probability
  • Definition of Probability
  • Permutations and Combinations
  • Joint Probability Conditional Probability and Bayes Rule
  • Random Variables
  • Random Variables and Probability Distribution Density Function
  • Joint Probability Density Function
  • Conditional Probability Density Function
  • Independence
  • Function of a Random Variable
  • Expectation Variance and Correlation
  • Conditional Expectation
  • Central Limit Theorem Normal Convergence Theorem
  • ML Estimator and MAP Estimator

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