Engineering Mathematics with MATLAB

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Engineering Mathematics with MATLAB

MATLAB을 사용한 공업수학

PDF 스트리밍 752p 19.6 MB 수학.물리.화학 Won Y. Yang et. al 유페이퍼 모두

10,000원 구매 1,000원 2일대여

Chapter 1: Vectors and Matrices
1.1 Vectors
1.1.1 Geometry with Vector
1.1.2 Dot Product
1.1.3 Cross Product
1.1.4 Lines and Planes
1.1.5 Vector Space
1.1.6 Coordinate Systems
1.1.7 Gram-Schmidt Orthonolization
1.2 Matrices
1.2.1 Matrix Algebra
1.2.2 Rank and Row/Column Spaces
1.2.3 Determinant and Trace
1.2.4 Eigenvalues and Eigenvectors
1.2.5 Inverse of a Matrix
1.2.6 Similarity Transformation and Diagonalization
1.2.7 Special Matrices
1.2.8 Positive Definiteness
1.2.9 Matrix Inversion Lemma
1.2.10 LU, Cholesky, QR, and Singular Value Decompositions
1.2.11 Physical Meaning of Eigenvalues/Eigenvectors
1.3 Systems of Linear Equations
1.3.1 Nonsingular Case
1.3.2 Undetermined Case - Minimum-Norm Solution
1.3.3 Overdetermined Case - Least-Squares Error Solution
1.3.4 Gauss(ian) Elimination
1.3.5 RLS (Recursive Least Squares) Algorithm
Problems

Chapter 2: Vector Calculus
2.1 Derivatives
2.2 Vector Functions
2.3 Velocity and Acceleration
2.4 Divergence and Curl
2.5 Line Integrals and Path Independence
2.5.1 Line Integrals
2.5.2 Path Independence
2.6 Double Integrals
2.7 Green's Theorem
2.8 Surface Integrals
2.9 Stokes' Theorem
2.10 Triple Integrals
2.11 Divergence Theorem
Problems

Chapter 3: Ordinary Differential Equation
3.1 First-Order Differential Equations
3.1.1 Separable Equations
3.1.2 Exact Differential Equations and Integrating Factors
3.1.3 Linear First-Order Differential Equations
3.1.4 Nonlinear First-Order Differential Equations
3.1.5 Systems of First-Order Differential Equations
3.2 Higher-Order Differential Equations
3.2.1 Undetermined Coefficients
3.2.2 Variation of Parameters
3.2.3 Cauchy-Euler Equations
3.2.4 Systems of Linear Differential Equations
3.3 Special Second-Order Linear ODEs
3.3.1 Bessel's Equation
3.3.2 Legendre's Equation
3.3.3 Chebyshev's Equation
3.3.4 Hermite's Equation
3.3.5 Laguerre's Equation
3.4 Boundary Value Problems
Problems

Chapter 4: Laplace Transform
4.1 Definition of the Laplace Transform
4.1.1 Laplace Transform of the Unit Step Function
4.1.2 Laplace Transform of the Unit Impulse Function
4.1.3 Laplace Transform of the Ramp Function
4.1.4 Laplace Transform of the Exponential Function
4.1.5 Laplace Transform of the Complex Exponential Function
4.2 Properties of the Laplace Transform
4.2.1 Linearity
4.2.2 Time Differentiation
4.2.3 Time Integration
4.2.4 Time Shifting - Real Translation
4.2.5 Frequency Shifting - Complex Translation
4.2.6 Real Convolution
4.2.7 Partial Differentiation
4.2.8 Complex Differentiation
4.2.9 Initial Value Theorem (IVT)
4.2.10 Final Value Theorem (FVT)
4.3 The Inverse Laplace Transform
4.4 Using of the Laplace Transform
4.5 Transfer Function of a Continuous-Time System
Problems

Chapter 5: The Z-transform
5.1 Definition of the Z-transform
5.2 Properties of the Z-transform
5.2.1 Linearity
5.2.2 Time Shifting - Real Translation
5.2.3 Frequency Shifting - Complex Translation
5.2.4 Time Reversal
5.2.5 Real Convolution
5.2.6 Complex Convolution
5.2.7 Complex Differentiation
5.2.8 Partial Differentiation
5.2.9 Initial Value Theorem
5.2.10 Final Value Theorem
5.3 The Inverse Z-transform
5.4 Using The Z-transform
5.5 Transfer Function of a Discrete-Time System
5.6 Differential Equation and Difference Equation
Problems

Chapter 6: Fourier Series and Fourier Transform
6.1 Continuous-Time Fourier Series (CTFS)
6.1.1 Definition and Convergence Conditions
6.1.2 Examples of CTFS
6.2 Continuous-Time Fourier Transform (CTFT)
6.2.1 Definition and Convergence Conditions
6.2.2 (Generalized) CTFT of Periodic Signals
6.2.3 Examples of CTFT
6.2.4 Properties of CTFT
6.3 Discrete-Time Fourier Transform (DTFT)
6.3.1 Definition and Convergence Conditions
6.3.2 Examples of DTFT
6.3.3 DTFT of Periodic Sequences
6.3.4 Properties of DTFT
6.4 Discrete Fourier Transform (DFT)
6.5 Fast Fourier Transform (FFT)
6.5.1 Decimation-in-Time (DIT) FFT
6.5.2 Decimation-in-Frequency (DIF) FFT
6.5.3 Computation of IDFT Using FFT Algorithm
6.5.4 Interpretation of DFT Results
6.6 Fourier-Bessel/Legendre/Chebyshev/Cosine/Sine Series
6.6.1 Fourier-Bessel Series
6.6.2 Fourier-Legendre Series
6.6.3 Fourier-Chebyshev Series
6.6.4 Fourier-Cosine/Sine Series
Problems

Chapter 7: Partial Differential Equation
7.1 Elliptic PDE
7.2 Parabolic PDE
7.2.1 The Explicit Forward Euler Method
7.2.2 The Implicit Forward Euler Method
7.2.3 The Crank-Nicholson Method
7.2.4 Using the MATLAB Function 'pdepe()'
7.2.5 Two-Dimensional Parabolic PDEs
7.3 Hyperbolic PDES
7.3.1 The Explict Central Difference Method
7.3.2 Tw-Dimensional Hyperbolic PDEs
7.4 PDES in Other Coordinate Systems
7.4.1 PDEs in Polar/Cylindrical Coordinates
7.4.2 PDEs in Spherical Coordinates
7.5 Laplace/Fourier Transforms for Solving PDES
7.5.1 Using the Laplace Transform for PDEs
7.5.2 Using the Fourier Transform for PDEs
Problems

Chapter 8: Complex Analysis 509
8.1 Functions of a Complex Variable
8.1.1 Complex Numbers and their Powers/Roots
8.1.2 Functions of a Complex Variable
8.1.3 Cauchy-Riemann Equations
8.1.4 Exponential and Logarithmic Functions
8.1.5 Trigonometric and Hyperbolic Functions
8.1.6 Inverse Trigonometric/Hyperbolic Functions
8.2 Conformal Mapping
8.2.1 Conformal Mappings
8.2.2 Linear Fractional Transformations
8.3 Integration of Complex Functions
8.3.1 Line Integrals and Contour Integrals
8.3.2 Cauchy-Goursat Theorem
8.3.3 Cauchy's Integral Formula
8.4 Series and Residues
8.4.1 Sequences and Series
8.4.2 Taylor Series
8.4.3 Laurent Series
8.4.4 Residues and Residue Theorem
8.4.5 Real Integrals Using Residue Theorem
Problems

Chapter 9: Optimization
9.1 Unconstrained Optimization
9.1.1 Golden Search Method
9.1.2 Quadratic Approximation Method
9.1.3 Nelder-Mead Method
9.1.4 Steepest Descent Method
9.1.5 Newton Method
9.2 Constrained Optimization
9.2.1 Lagrange Multiplier Method
9.2.2 Penalty Function Method
9.3 MATLAB Built-in Functions for Optimization
9.3.1 Unconstrained Optimization
9.3.2 Constrained Optimization
9.3.3 Linear Programming (LP)
9.3.4 Mixed Integer Linear Programing (MILP)
Problems

Chapter 10: Probability
10.1 Probability
10.1.1 Definition of Probability
10.1.2 Permutations and Combinations
10.1.3 Joint Probability, Conditional Probability, and Bayes' Rule
10.2 Random Variables
10.2.1 Random Variables and Probability Distribution/Density Function
10.2.2 Joint Probability Density Function
10.2.3 Conditional Probability Density Function
10.2.4 Independence
10.2.5 Function of a Random Variable
10.2.6 Expectation, Variance, and Correlation
10.2.7 Conditional Expectation
10.2.8 Central Limit Theorem - Normal Convergence Theorem
10.3 ML Estimator and MAP Estimator
Problems

양원영(Won Y. Yang): 중앙대학교 전자진기공학부 명예교수
최영기(Young K. Choi): 중앙대학교 기계공학부 명예교수
김재권(Jaekwon Kim): 연세대학교 (원주캠퍼스) 소프트웨어학부 교수
김만철(Man Cheol Kim): 중앙대학교 에너지시스템공학부 교수
김현진(H. Jin Kim): 서울대학교 항공우주공학과 교수
임태호(Taeho Im): 호서대학교 정보통신공학부 교수

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Engineering Mathematics with MATLAB

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