**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