Lectures related to Vector Fields on Cylinders

Covers the conservation of mass in one-dimensional flows and the necessity of mass conservation in supersonic flows.

Explores notational meaning in Analyse III through examples of shear flow and rotational equations, emphasizing the significance of vector fields and line integrals.

Fluid Dynamics: Newton's Second Law and Momentum Conservation

Discusses Newton's Second Law in fluid dynamics, focusing on momentum conservation and its applications in engineering problems.

Understanding Jacobian and Normal Vectors in Surfaces

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

Electric Fields: Curl and Path Integrals, Spherical Coordinates Supplement

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

Surface Integrals: Change of Variables

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

Local Invertibility: Vector Fields

Covers local invertibility of vector fields and the Inverse Function Theorem.

Curvilinear Integrals: Interpretation and Convexity

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