Recommended video series
The concept of ordinary differential equations (ODEs), the Laplace transform, the inverse Laplace transform, homogeneous linear ordinary differential equations, nonhomogeneous linear ordinary differential equations, linearization of a dynamic system using numerical techniques. 15 episodes.
Introduction to partial differential equations, derivation of the 1D wave equation, heat equation, derivation of Laplace's equation, derivation of the 2D wave equation, numerically solving partial differential equations. 11 episodes.
Optimization, 4 different ways to use/call Matlab’s ‘fminsearch’ function to perform unconstrained optimization, how to convert a constrained optimization problem into an approximately equivalent unconstrained optimization problem using the penalty method, how to solve a system of equations using numerical optimization instead of analytically solving, how to find a trim point of a dynamic system using numerical optimization techniques, and discussion of the Taylor Series (and the closely related Maclaurin Series) . 5 episodes.
Calculus 1: Differentiation, Approximations, Optimization, 5 episodes.
Integration, 63 episodes.
Vector calculus, 27 episodes.
An in-depth linear algebra course with problems and exercises, 149 episodes.
An in-depth linear algebra course with problems and exercises, 28 episodes.
Part 3 Linear Algebra: Linear Transformations, 112 episodes.
Part 4 Linear Algebra: Inner Products, 43 episodes.
Partial differential equations, 47 episodes.
Introduction to Tensor Calculus, 49 episodes.
Prealgebra, 44 episodes.
Intermediate algebra, 46 episodes.
To The Point Math, 78 episodes.
Precalculus - college algebra/trigonometry 1, 73 episodes.
Calculus 1, 32 episodes.
Calculus 2, 27 episodes.
Calculus 3, 34 episodes.
Statistics, 28 episodes.
Differential equations, 39 episodes.
Introduction to complex numbers, 115 episodes.
Introduction to binomial theorem, 57 episodes.
Random variables, 38 episodes.
Applications of calculus, 75 episodes.
Introduction to differentiation, 113 episodes.
Basic algebraic techniques, 22 episodes.
Inverse trigonometric functions, 72 episodes.
Integral calculus, 184 episodes.
A geometric understanding of matrices, determinants, eigen-stuffs and more.
The goal here is to make calculus feel like something that you yourself could have discovered.
An overview of differential equations.
An introduction to multivariable functions, and a welcome to the multivariable calculus content as a whole.
Quaternions, Gimbal Lock, visualize derivatives, implicit differentiation, and more.
The real world uses of imaginary numbers, What does the Laplace Transform really tell us? A visual explanation (plus applications), The intuition behind Fourier and Laplace transforms I was never taught in school
Markov chains explained.
A 79-part series on derivatives.
A 66-part series on integrals.
A 8-part series on Game Theory.
Recommended books
Numerical Recipes is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986..