Single Variable Calculus by Prof. David Jerison of MIT

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Watch video here.......

Differential and Integral Calculus

This video lecture series on Differential and Integral Calculus by Professor Steve Butler provides insight into differential calculus and applications as well as an introduction to integration.

Watch video here........

Multivariable Calculus by Prof. Denis Auroux of MIT

This course covers vector and multi-variable calculus.Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space

Watch video here........

Vector Calculus

This is a series of lectures for MATH2111 "Higher Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney.

Watch video here.........

Differential Equations

This video lecture course on Differential Equations includes Solution of first-order ODEs by analytical, graphical and numerical methods; Linear ODEs, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams...

Watch video here.........

The Fourier Transform and its Applications

Fourier series, the Fourier transform of continuous and discrete signals and its properties. The Dirac delta, distributions, and generalized transforms. Convolutions and correlations and applications; probability distributions, sampling theory, filters, and analysis of linear systems. The discrete Fourier transform and the FFT algorithm.

Watch video here........

Mathematical Methods for Engineers II

Difference Methods for Ordinary Differential Equations. Finite Differences, Accuracy, Stability, Convergence.One way Wave equation and CFL/ von Neumann Stability. Second order wave equation, wave profiles, heat equation / point source, Finite differences for heat equation. Convection-diffusion/ conservation laws/ analysis/ shocks. Level Set Method. Matrices in difference equations(1D, 2D, 3D). Sparse Matrices.Black-scholes equation. Iterative, General, Multigrid, Conjugate gradient and Krylov Methods. Fast Poisson solver.Weight least squares, calculus of variations/weak form. Error estimates/ projections and many more....

Watch video here........