| Description |
1 online resource |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- PREFACE -- 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 Gramâ#x80;#x93;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 Geometrical Meaning of Eigenvalues/Eigenvectors -- 1.3 Systems of Linear Equations -- 1.3.1 Nonsingular Case -- 1.3.2 Undetermined Case â#x80;#x94; Minimum-Norm Solution -- 1.3.3 Overdetermined Case â#x80;#x94; 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 Equations -- 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 |
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3.2.2 Variation of Parameters -- 3.2.3 Cauchyâ#x80;#x93;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: The 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 â#x80;#x94; Real Translation -- 4.2.5 Frequency Shifting â#x80;#x94; 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 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 â#x80;#x94; Real Translation -- 5.2.3 Frequency Shifting â#x80;#x94; 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 |
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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 Fourierâ#x80;#x93;Bessel/Legendre/Chebyshev/Cosine/Sine Series -- 6.6.1 Fourierâ#x80;#x93;Bessel Series -- 6.6.2 Fourierâ#x80;#x93;Legendre Series -- 6.6.3 Fourierâ#x80;#x93;Chebyshev Series -- 6.6.4 Fourierâ#x80;#x93;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 Backward Euler Method -- 7.2.3 The Crankâ#x80;#x93;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 Two-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 -- 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 Cauchyâ#x80;#x93;Riemann Equations |
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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 Cauchyâ#x80;#x93;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 Nelderâ#x80;#x93;Mead Method -- 9.1.4 Steepest Descent Method -- 9.1.5 Newton's 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 â#x80;#x94; Normal Convergence Theorem -- 10.3 ML Estimator and MAP Estimator -- Problems -- Appendices -- Appendix A: Tables of Various Transforms -- Appendix B: Differentiation w.r.t. Vector |
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Appendix C: Useful Formulas -- Appendix D: Gamma Function -- Appendix E: MATLAB -- Appendix F: Simulink -- References -- Index |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record cip data provided by publisher |
| SUBJECT |
MATLAB. http://id.loc.gov/authorities/names/n92036881
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MATLAB fast |
| Subject |
Engineering mathematics.
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Engineering mathematics -- Data processing
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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TECHNOLOGY & ENGINEERING -- Reference.
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Engineering mathematics
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Engineering mathematics -- Data processing
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| Form |
Electronic book
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| LC no. |
2020691127 |
| ISBN |
9781315163680 |
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1315163683 |
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9781351671897 |
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1351671898 |
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9781351671903 |
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1351671901 |
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9781351671880 |
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135167188X |
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