Vectorial Calculus

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Related lectures (43)

Vector Calculus: 2D Curl Operator Log in to Mediaspace to watch this video

Explores the 2D curl operator, its calculation, and geometric interpretation, emphasizing the role of curve speed in curve integrals.

Curve Integrals: Gauss/Green Theorem Log in to Mediaspace to watch this video

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Surface Integrals, Divergence Theorem and Stocks' Theorem Log in to Mediaspace to watch this video

Covers surface integrals, the divergence theorem, and Stocks' theorem through examples and analogies.

Vector Analysis Review Log in to Mediaspace to watch this video

Covers unit vectors, coordinate system conversion, divergence, and rotational concepts in vector analysis.

Surface Integrals: Parameterization and Divergence Theorem Log in to Mediaspace to watch this video

Explores surface integrals using parameterization and the divergence theorem, with practical examples included.

Vector Analysis: Gradient, Divergence, Curl Log in to Mediaspace to watch this video

Covers the fundamental concepts of vector analysis, including the gradient, divergence, and curl operators.

Understanding Positive and Negative Orientation in Curves Log in to Mediaspace to watch this video

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

Green Theorem: Corollary 1 Proof Log in to Mediaspace to watch this video

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

Vector Calculus Review: Maxwell Equations and Physical Consequences Log in to Mediaspace to watch this video

Reviews vector calculus, Maxwell equations, and their physical consequences, emphasizing exercises and feedback.

Introduction: Lightboard 0-1 Log in to Mediaspace to watch this video

Serves as a helpful review for vector calculus topics before the final exam.

Electric Fields: Curl and Path Integrals, Spherical Coordinates Supplement Log in to Mediaspace to watch this video

Explores the integration of electric fields along paths and solutions for constant and radial fields.

Curvilinear Integrals and Conservative Fields Log in to Mediaspace to watch this video

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

Linear Momentum Balance Log in to Mediaspace to watch this video

Analyzes linear momentum balance equations and explores the consequences of continuity and divergence in angular momentum conservation.

Vector Fields Log in to Mediaspace to watch this video

Explains vector fields as derivations and their algebraic structure in Lie algebra.

Maxwell's Equations: Basics Log in to Mediaspace to watch this video

Covers the basics of Maxwell's equations, describing the behavior of electric and magnetic fields.

Nonlinear Equations: Bisection and Fixed-Point Methods Log in to Mediaspace to watch this video

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

Green's Theorem: Transforming Integrals in 2D Log in to Mediaspace to watch this video

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

Mathematical Complements: df or δf Log in to Mediaspace to watch this video

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Implicit Functions Theorem Log in to Mediaspace to watch this video

Covers the Implicit Functions Theorem and its applications in defining functions implicitly.

Spheres: The Hairy Ball Theorem Log in to Mediaspace to watch this video

Covers the Hairy Ball Theorem and vector fields on spheres.

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