Lectures related to Green's theorem

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

Newtonian Potential: Bounded Domains

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Green Theorems: Divergence Theorem and Identities of Green

Explores the application of Green theorems in 2D and 3D spaces.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Darboux Theorem: Advanced Analysis I

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Surface Integrals, Divergence Theorem

Covers surface integrals, divergence theorem, and regular domains in 2D and 3D.

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Nonlinear Equations: Bisection and Fixed-Point Methods

Explores nonlinear equations, bisection, fixed-point methods, error control, and graphical interpretations of fixed points.

Green's Theorem: Demonstration and Applications

Covers the demonstration of Green's Theorem and its applications in various scenarios.

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Green Theorem: Proof of Corollary 2

Explains the proof of Corollary 2 of the Green Theorem in a regular domain.

Green Theorem: Corollary 1 Proof

Explains the proof of Corollary 1 of Green's Theorem in the context of the Divergence Theorem.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Fourier Series: Stokes Theorem

Introduces Fourier series for periodic functions and explores Stokes' theorem in 3D vector fields.

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Green's Theorem: Demonstration and Applications

Covers the demonstration and applications of Green's Theorem in vector fields.

The Cauchy Theorem for Sequences

Explores the Cauchy theorem for sequences, highlighting the importance of convergence and boundedness.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.