Curvilinear Coordinates: Calculations and Examples

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Curvilinear Integrals: Interpretation and Convexity

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

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Change of Variables in Double Integrals

Explores changing variables in double integrals through examples and curvilinear coordinates.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

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.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Polar Coordinates: Calculus Applications

Covers the application of calculus in polar coordinates, including examples of domains defined by level curves.

Differential Forms Integration

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

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.