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This course analyzes the functions of a complex variable and the calculus of residues.
0
2
English
English [CC]
FREE
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Description
It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.
Course content
- 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
Instructor
Massachusetts Institute of Technology
5
5
1
1916
1520
