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Lecture
Integrals in C: Curvilinear Integration
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Curvilinear Integrals
Covers curvilinear integrals in R^n, focusing on continuous functions and curves.
Curvilinear Coordinates: Calculations and Examples
Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.
Curves with Poritsky Property and Liouville Nets
Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.
Integration: Taylor Approximation & Convex Functions
Covers Taylor approximation, convex functions, and integrable properties.
Integration Techniques: Part 2
Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.
Residue Theorem: Applications in Complex Analysis
Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.
Vector Calculus: Line Integrals
Covers the concept of line integrals and their application in vector fields.
Integral Calculus: Fundamentals
Covers the fundamentals of integral calculus, including properties of definite integrals and Riemann sums.
Complex Analysis: Simply Connected Domains
Explores simply connected domains in complex analysis, including holomorphic functions, Cauchy's integral formula, and Taylor series.
Integration Basics
Covers the fundamentals of integration and various methods for solving integration problems.