MATH-203(c): Analysis III

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Lectures in this course (28)

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Differential Equations and Heat Diffusion

Covers differential equations, heat diffusion, and advanced analysis for engineers.

Vector Analysis: Scalar Fields

Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.

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Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

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Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

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Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Green's Theorem: Demonstration and Applications

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

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Green's Theorem: Understanding Rotations and Closed Paths

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

Green's Theorem: Surface Integrals

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.

Understanding Normal Vectors in Calculus

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Understanding Jacobian and Normal Vectors in Surfaces

Clarifies the use of Jacobian, normal vectors in surfaces, and arccos(z) constraints.

Surface Integrals: Parameterized Surfaces

Explores surface integrals over parameterized orientable surfaces and their applications in flux and work evaluation.

Surface Integral: Understanding Variable Positions

Explores surface integrals and variable positions, emphasizing sign inversion and induced paths.

Fourier Analysis: Series and Divergence Theorem

Covers Fourier analysis, series convergence, divergence theorem, and vector analysis.

Fourier Series: Convergence and Coefficients

Explores Fourier series convergence and coefficient calculations through examples and derivations.

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