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Last updated:

November 4, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course analyzes the functions of a complex variable and the calculus of residues.

It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.

Course Curriculum

  • Number Systems and Algebra of Complex Numbers Unlimited
  • Elementary Complex Functions, Part 1 Unlimited
  • Elementary Complex Functions, Part 2 Unlimited
  • Branch Points and Branch Cuts Unlimited
  • Analytic Functions Unlimited
  • Complex Integrals Unlimited
  • Cauchy’s Formula, Properties of Analytic Functions Unlimited
  • Taylor Series, Laurent Series Unlimited
  • Laurent Series (cont.) Unlimited
  • Properties of Laurent Series, Singularities Unlimited
  • Singularities (cont.) Unlimited
  • Residue Theorem Unlimited
  • Evaluation of Real Definite Integrals, Case I Unlimited
  • Evaluation of Real Definite Integrals, Case II Unlimited
  • Evaluation of Real Definite Integrals, Case III Unlimited
  • Evaluation of Real Definite Integrals, Case IV Unlimited
  • Theorems for Contour Integration Unlimited
  • Series and Convergence Unlimited
  • Ordinary Differential Equations Unlimited
  • Singular Points of Linear Second-order ODEs Unlimited
  • Frobenius Method Unlimited
  • Frobenius Method – Examples Unlimited
  • Frobenius Method (cont.) and a “particular type” of ODE Unlimited
  • Bessel Functions Unlimited
  • Properties of Bessel Functions Unlimited
  • Modified Bessel Functions Unlimited
  • Differential Equations Satisfied by Bessel Functions Unlimited
  • Introduction to Boundary-Value Problems Unlimited
  • Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions Unlimited
  • Boundary Value Problems for Nonhomogeneous PDEs Unlimited
  • Sturm-Liouville Problem Unlimited
  • Fourier Series Unlimited
  • Fourier Sine and Cosine Series Unlimited
  • Complete Fourier Series Unlimited
  • Review of Boundary Value Problems for Nonhomogeneous PDEs Unlimited

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Massachusetts Institute of Technology
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