Hjem

Vectors and Matrices. Vectors. Matrices. Systems of Linear Equations. Problems. Vector Calculus. Derivatives. Vector Functions. Velocity and Acceleration. Divergence and Curl. Line Integrals and Path. Independence. Double Integrals. Green's Theorem. Surface Integrals. Stokes' Theorem. Triple Integrals. Divergence Theorem. Problems. Ordinary Differential Equation. First-Order Differential Equations. Higher-Order Differential Equations. Special Second-Order Linear ODEs. Boundary Value Problems. Problems. Laplace Transform. Definition of the Laplace Transform. Properties of the Laplace Transform. The Inverse Laplace Transform. Using of the Laplace Transform. Transfer Function of a Continuous-Time System. Problems. The Z-transform. Definition of the Z-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. Problems. Fourier Series and Fourier Transform. Continuous-Time Fourier Series (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. Problems. Partial Differential Equation. Elliptic PDE. Parabolic PDE. Hyperbolic PDES. PDES in Other Coordinate Systems. Laplace/Fourier Transforms for Solving PDES. Problems. Complex Analysis. Functions of a Complex Variable. Conformal Mapping. Integration of Complex Functions. Series and Residues. Optimization. Unconstrained Optimization. Constrained Optimization. MATLAB Built-in Functions for Optimization. Problems. Probability. Probability. Random Variables. ML Estimator and MAP Estimator. Problems.