Engineering mathematics with MATLAB /
Won Y. Yang, Young K. Choi, Jaekwon Kim, Man Cheol Kim, H. Jin Kim, Taeho Im.
- Boca Raton : CRC Press, c2018.
- xiv, 741 pages : illustrations ; 29 cm
Includes bibliographical references and index.
Chapter 1: Vectors and matrices -- Vectors -- Matrices -- Systems of linear equations -- Chapter 2: Vector calculus -- Derivatives -- Vector functions -- Velocity and acceleration -- Divergence and curl -- Lien integrals and path independence -- Double integrals -- Green’s theorem -- Surface integrals -- Stokes’ theorem -- Triple integrals -- Divergence theorem -- Chapter 3: Ordinary differential equations -- First-order differential equations -- Higher-order differential equations -- Special second-order linear ODEs -- Boundary value problems -- Chapter 4: The Laplace transform -- Definition of the Laplace transform -- Properties of the Laplace transform -- The inverse Laplace transform -- Using the Laplace Transform -- Transfer function of a continuous-time system -- Chapter 5: The Z-transform -- Definition of the-transform -- Properties of the Z-transform -- 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 transform (CTFS) -- Continuous-time Fourier transform (CTFT) -- Discrete-time Fourier transform (DTFT) -- Discrete Fourier transform (DFT) -- Fast Fourier transform (FFT) -- Fourier – Bessel/Legendre/chebyshev/cosine/sine series -- Chapter 7: Partial differential equation -- Elliptic PDE -- Parabolic PDE -- Hyperbolic PDES -- PDES in other coordinate systems -- Laplace/Fourier transforms for solving PDES -- Chapter 8: Complex analysis -- Functions of complex variable -- Conformal mapping -- Integration of complex functions -- Series and residues -- Chapter 9: Optimization -- Unconstrained optimization -- Constrained optimization -- MATLAB built-in functions for optimization -- Chapter 10: Probability -- Probability -- Random variables -- MC estimator and MAP estimator -- Appendix A: Tables of various transforms -- Appendix B: Differentiation w.r.t. vector -- Appendix C: Useful formulas -- Appendix D: Gamma function -- Appendix E: MATLAB -- Appendix F: Simulink.
"Engineering mathematics with MATLAB aims to bridge the gap between MATLAB software and theory, and equations appearing in the field of engineering mathematics. Thus, readers can feel free to utilize the MATLAB software for the study of mathematical content and become much more interested in engineering mathematics than ever before."--Back cover