18.075 - Advanced Calculus for Engineers, Spring 2018

 

Syllabus

Two Lectures: Operators and Ordinary Differential Equations. (Read Chapter 1).

Two lectures: Complex Numbers, Analytic Functions, Cauchy--Riemann Equations. ( Read 2A and 2B).

Two lectures: Cauchy Integral Theorem, Taylor Series, Laurent Series. ( Read 2C).

Five lectures: Evaluation of Real Integrals. ( Read 2D).

Two lectures: Branch Cuts and Brabch Points. (Read 2E).

Four lectures: Fourier Integrals, Fourier Series, and Laplace transform. (Read 2F and 2G).

Four lectures: First Order PDE. ( Read Chapter 3 selectively).

Four lectures: Second Order Partial Differential Equations, Eigenfunctions, and Eigenvalues. (Read Chapter 4 selectively).

Three lectures: Separation of varaiables (Read Chapter 5).

One lecture: Eigenfunctions, and Eigenvalues. (Read Chapter 5).

Three lectures: Taylor Series Solutions. (Read 6A).

Three lectures: Frobenius Series. (Read 6B).

One lecture: Irregular Singular Points. (Read 6C).