Integration Techniques: Fundamental Theorems and Methods

Related lectures (24)

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Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Covers linear differential equations with constant coefficients and introduces the method of good choice for finding particular solutions.

Discusses the residue theorem and its applications in calculating complex integrals.

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Introduces the basics of trigonometric functions, their properties, and practical applications in geometry and physics.

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.