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Engineering Mathematics with MATLAB [Hardback]

, , , , (Department of Mechanical Engineering, Chung-Ang University, Republic of Korea),
  • Formāts: Hardback, 741 pages, height x width: 280x210 mm, weight: 1927 g, 16 Tables, black and white; 315 Line drawings, black and white
  • Izdošanas datums: 26-Feb-2018
  • Izdevniecība: CRC Press
  • ISBN-10: 1138059331
  • ISBN-13: 9781138059337
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Engineering Mathematics with MATLABPalielināt
  • Formāts: Hardback, 741 pages, height x width: 280x210 mm, weight: 1927 g, 16 Tables, black and white; 315 Line drawings, black and white
  • Izdošanas datums: 26-Feb-2018
  • Izdevniecība: CRC Press
  • ISBN-10: 1138059331
  • ISBN-13: 9781138059337
Citas grāmatas par šo tēmu:
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The aim of this book is to help the readers understand the concepts, techniques, terminologies, and equations appearing in the existing books on engineering mathematics using MATLAB. Using MATLAB for computation would be otherwise time consuming, tedious and error-prone. The readers are recommended to have some basic knowledge of MATLAB.

Preface xiii
Chapter 1 Vectors and Matrices 1(98)
1.1 Vectors
1(31)
1.1.1 Geometry with Vector
1(1)
1.1.2 Dot Product
2(4)
1.1.3 Cross Product
6(3)
1.1.4 Lines and Planes
9(8)
1.1.5 Vector Space
17(1)
1.1.6 Coordinate Systems
18(11)
1.1.7 Gram-Schmidt Orthonolization
29(3)
1.2 Matrices
32(23)
1.2.1 Matrix Algebra
32(1)
1.2.2 Rank and Row/Column Spaces
32(2)
1.2.3 Determinant and Trace
34(1)
1.2.4 Eigenvalues and Eigenvectors
35(4)
1.2.5 Inverse of a Matrix
39(3)
1.2.6 Similarity Transformation and Diagonalization
42(2)
1.2.7 Special Matrices
44(3)
1.2.8 Positive Definiteness
47(1)
1.2.9 Matrix Inversion Lemma
48(1)
1.2.10 LU, Cholesky, QR, and Singular Value Decompositions
49(1)
1.2.11 Geometrical Meaning of Eigenvalues/Eigenvectors
50(5)
1.3 Systems of Linear Equations
55(14)
1.3.1 Nonsingular Case
55(1)
1.3.2 Undetermined Case Minimum-Norm Solution
56(2)
1.3.3 Overdetermined Case Least-Squares Error Solution
58(3)
1.3.4 Gauss(ian) Elimination
61(4)
1.3.5 RLS (Recursive Least Squares) Algorithm
65(4)
Problems
69(30)
Chapter 2 Vector Calculus 99(92)
2.1 Derivatives
99(5)
2.2 Vector Functions
104(3)
2.3 Velocity and Acceleration
107(6)
2.4 Divergence and Curl
113(14)
2.5 Line Integrals and Path Independence
127(7)
2.5.1 Line Integrals
127(5)
2.5.2 Path Independence
132(2)
2.6 Double Integrals
134(4)
2.7 Green's Theorem
138(4)
2.8 Surface Integrals
142(7)
2.9 Stokes' Theorem
149(6)
2.10 Triple Integrals
155(5)
2.11 Divergence Theorem
160(9)
Problems
169(22)
Chapter 3 Ordinary Differential Equations 191(86)
3.1 First-Order Differential Equations
192(21)
3.1.1 Separable Equations
192(3)
3.1.2 Exact Differential Equations and Integrating Factors
195(5)
3.1.3 Linear First-Order Differential Equations
200(4)
3.1.4 Nonlinear First-Order Differential Equations
204(1)
3.1.5 Systems of First-Order Differential Equations
205(8)
3.2 Higher-Order Differential Equations
213(20)
3.2.1 Undetermined Coefficients
213(9)
3.2.2 Variation of Parameters
222(3)
3.2.3 Cauchy-Euler Equations
225(4)
3.2.4 Systems of Linear Differential Equations
229(4)
3.3 Special Second-Order Linear ODES
233(15)
3.3.1 Bessel's Equation
233(6)
3.3.2 Legendre's Equation
239(2)
3.3.3 Chebyshev's Equation
241(3)
3.3.4 Hermite's Equation
244(2)
3.3.5 Laguerre's Equation
246(2)
3.4 Boundary Value Problems
248(9)
Problems
257(20)
Chapter 4 The Laplace Transform 277(32)
4.1 Definition of the Laplace Transform
277(4)
4.1.1 Laplace Transform of the Unit Step Function
277(1)
4.1.2 Laplace Transform of the Unit Impulse Function
278(2)
4.1.3 Laplace Transform of the Ramp Function
280(1)
4.1.4 Laplace Transform of the Exponential Function
281(1)
4.1.5 Laplace Transform of the Complex Exponential Function
281(1)
4.2 Properties of the Laplace Transform
281(6)
4.2.1 Linearity
281(1)
4.2.2 Time Differentiation
281(1)
4.2.3 Time Integration
282(1)
4.2.4 Time Shifting Real Translation
282(1)
4.2.5 Frequency Shifting Complex Translation
282(1)
4.2.6 Real Convolution
282(1)
4.2.7 Partial Differentiation
283(1)
4.2.8 Complex Differentiation
283(1)
4.2.9 Initial Value Theorem (IVT)
284(1)
4.2.10 Final Value Theorem (FVT)
284(3)
4.3 The Inverse Laplace Transform
287(2)
4.4 Using the Laplace Transform
289(6)
4.5 Transfer Function of a Continuous-Time System
295(5)
Problems
300(9)
Chapter 5 The Z-transform 309(28)
5.1 Definition of the Z-transform
309(5)
5.2 Properties of the Z-transform
314(4)
5.2.1 Linearity
314(1)
5.2.2 Time Shifting - Real Translation
314(1)
5.2.3 Frequency Shifting Complex Translation
315(1)
5.2.4 Time Reversal
315(1)
5.2.5 Real Convolution
316(1)
5.2.6 Complex Convolution
316(1)
5.2.7 Complex Differentiation
317(1)
5.2.8 Partial Differentiation
317(1)
5.2.9 Initial Value Theorem
317(1)
5.2.10 Final Value Theorem
318(1)
5.3 The Inverse Z-transform
318(4)
5.4 Using the Z-transform
322(2)
5.5 Transfer Function of a Discrete-Time System
324(3)
5.6 Differential Equation and Difference Equation
327(2)
Problems
329(8)
Chapter 6 Fourier Series and Fourier Transform 337(86)
6.1 Continuous-Time Fourier Series (CTFS)
337(11)
6.1.1 Definition and Convergence Conditions
337(3)
6.1.2 Examples of CTFS
340(8)
6.2 Continuous-Time Fourier Transform (CTFT)
348(15)
6.2.1 Definition and Convergence Conditions
348(3)
6.2.2 (Generalized) CTFT of Periodic Signals
351(1)
6.2.3 Examples of CTFT
352(5)
6.2.4 Properties of CTFT
357(6)
6.3 Discrete-Time Fourier Transform (DTFT)
363(10)
6.3.1 Definition and Convergence Conditions
363(1)
6.3.2 Examples of DTFT
364(3)
6.3.3 DTFT of Periodic Sequences
367(2)
6.3.4 Properties of DTFT
369(4)
6.4 Discrete Fourier Transform (DFT)
373(4)
6.5 Fast Fourier Transform (FFT)
377(8)
6.5.1 Decimation-in-Time (DIT) FFT
377(3)
6.5.2 Decimation-in-Frequency (DIF) FFT
380(2)
6.5.3 Computation of IDFT Using FFT Algorithm
382(1)
6.5.4 Interpretation of DFT Results
382(3)
6.6 Fourier-Bessel/Legendre/Chebyshev/Cosine/Sine Series
385(10)
6.6.1 Fourier-Bessel Series
385(3)
6.6.2 Fourier-Legendre Series
388(1)
6.6.3 Fourier-Chebyshev Series
389(2)
6.6.4 Fourier-Cosine/Sine Series
391(4)
Problems
395(28)
Chapter 7 Partial Differential Equation 423(86)
7.1 Elliptic PDE
424(6)
7.2 Parabolic PDE
430(11)
7.2.1 The Explicit Forward Euler Method
432(1)
7.2.2 The Implicit Backward Euler Method
433(1)
7.2.3 The Crank-Nicholson Method
434(1)
7.2.4 Using the MATLAB Function 'pdepe()'
435(3)
7.2.5 Two-Dimensional Parabolic PDEs
438(3)
7.3 Hyperbolic PDES
441(7)
7.3.1 The Explict Central Difference Method
443(2)
7.3.2 Two-Dimensional Hyperbolic PDEs
445(3)
7.4 PDES in Other Coordinate Systems
448(17)
7.4.1 PDEs in Polar/Cylindrical Coordinates
448(13)
7.4.2 PDEs in Spherical Coordinates
461(4)
7.5 Laplace/Fourier Transforms for Solving PDES
465(16)
7.5.1 Using the Laplace Transform for PDEs
465(8)
7.5.2 Using the Fourier Transform for PDEs
473(8)
Problems
481(28)
Chapter 8 Complex Analysis 509(58)
8.1 Functions of a Complex Variable
509(14)
8.1.1 Complex Numbers and Their Powers/Roots
509(3)
8.1.2 Functions of a Complex Variable
512(1)
8.1.3 Cauchy-Riemann Equations
513(7)
8.1.4 Exponential and Logarithmic Functions
520(1)
8.1.5 Trigonometric and Hyperbolic Functions
521(1)
8.1.6 Inverse Trigonometric/Hyperbolic Functions
522(1)
8.2 Conformal Mapping
523(7)
8.2.1 Conformal Mappings
523(3)
8.2.2 Linear Fractional Transformations
526(4)
8.3 Integration of Complex Functions
530(8)
8.3.1 Line Integrals and Contour Integrals
530(3)
8.3.2 Cauchy-Goursat Theorem
533(3)
8.3.3 Cauchy's Integral Formula
536(2)
8.4 Series and Residues
538(13)
8.4.1 Sequences and Series
538(2)
8.4.2 Taylor Series
540(2)
8.4.3 Laurent Series
542(2)
8.4.4 Residues and Residue Theorem
544(2)
8.4.5 Real Integrals Using Residue Theorem
546(5)
Problems
551(16)
Chapter 9 Optimization 567(52)
9.1 Unconstrained Optimization
567(11)
9.1.1 Golden Search Method
567(2)
9.1.2 Quadratic Approximation Method
569(2)
9.1.3 Nelder-Mead Method
571(2)
9.1.4 Steepest Descent Method
573(2)
9.1.5 Newton's Method
575(3)
9.2 Constrained Optimization
578(7)
9.2.1 Lagrange Multiplier Method
578(5)
9.2.2 Penalty Function Method
583(2)
9.3 MATLAB Built-in Functions for Optimization
585(18)
9.3.1 Unconstrained Optimization
585(3)
9.3.2 Constrained Optimization
588(1)
9.3.3 Linear Programming (LP)
589(5)
9.3.4 Mixed Integer Linear Programing (MILP)
594(9)
Problems
603(16)
Chapter 10 Probability 619(76)
10.1 Probability
619(5)
10.1.1 Definition of Probability
619(1)
10.1.2 Permutations and Combinations
620(2)
10.1.3 Joint Probability, Conditional Probability, and Bayes' Rule
622(2)
10.2 Random Variables
624(29)
10.2.1 Random Variables and Probability Distribution/Density Function
624(3)
10.2.2 Joint Probability Density Function
627(1)
10.2.3 Conditional Probability Density Function
628(4)
10.2.4 Independence
632(1)
10.2.5 Function of a Random Variable
632(5)
10.2.6 Expectation, Variance, and Correlation
637(11)
10.2.7 Conditional Expectation
648(3)
10.2.8 Central Limit Theorem Normal Convergence Theorem
651(2)
10.3 ML Estimator and MAP Estimator
653(6)
Problems
659(36)
Appendices 695(31)
Appendix A: Tables of Various Transforms
695(10)
Appendix B: Differentiation w.r.t. Vector
705(1)
Appendix C: Useful Formulas
706(1)
Appendix D: Gamma Function
707(1)
Appendix E: MATLAB
708(10)
Appendix F: Simulink
718(8)
References 726(1)
Index 727
Won Y. Yang has been a Professor in the Department of Electrical Engineering at Chung-Ang University, Seoul, Korea, since 1986. He has written a number of books, including Applied Numerical Methods Using MATLAB (2005), Signals and Systems with MATLAB (2009) and MIMO-OFDM Wireless Communications with MATLAB (2010).