Lectures in course MATH-203(a): Analysis III (for SV, MT)

Green Theorem Proof

Covers the proof of the Green theorem, showing how the integral of a vector field along a domain's boundary equals the integral of the curve within the domain.

Vector Fields and Potentials: Theorem Proof

Covers the proof of a theorem for determining if a vector field derives from a potential.

Equal Opportunity and Diversity at EPFL

Covers equal opportunity, diversity, course organization, Zoom interactions, coursebook, exercise series, exam, and feedback mechanisms at EPFL.

Differential Operators: Notation and Terminology

Covers the basics of differential operators and derivatives for n-tuples and vector fields.

Differential Operators: Gradient and Divergence

Introduces differential operators, gradient, and divergence in vector fields.

Differential Operators: Divergence Operator and Scalar Field

Explores differential operators, including divergence and Laplacian operators in vector and scalar fields.

Differential Operators: Theorems and Proofs

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Green Theorem: Corollary 1 Proof

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

Curvilinear Integrals and Green's Theorem

Introduces curvilinear integrals, parameterization, and Green's Theorem for conservative fields.

Curvilinear Integrals and Conservative Fields

Explains curvilinear integrals, conservative fields, and their relationship with potentials.

Green Theorem: Proof of Corollary 2

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

Curvilinear Integrals and Conservative Fields

Explores curvilinear integrals, conservative fields, and their implications in various contexts.

Curvilinear Integrals, Conservative Fields, and Green's Theorem

Covers curvilinear integrals, conservative fields, and Green's Theorem with examples.

Green Theorem: Corollary 3 Proof

Demonstrates the relationship between the gradient and the divergence of a scalar field.

Curvilinear Integrals and Conservative Fields

Explores curvilinear integrals, conservative fields, and domain potentials through practical examples and calculations.

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.

Green's Theorem: Transforming Integrals in 2D

Covers Green's Theorem, transforming 2D integrals into 1D line integrals.

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Surface Integrals and Parametrization

Explores the analogy between curves and surfaces, emphasizing the importance of choosing parameters for normal vectors.