Math 53 videos

Michael Hutchings, Spring 2014


Part 1: Geometric preliminaries.

Section 1.1: Introduction to the course, parametrized curves.

Section 1.2: Polar coordinates.

Section 1.3: Three-dimensional space, vectors, dot product, cross product.

Section 1.4: Lines, planes, and quadric surfaces.

Section 1.5: Vector-valued functions and space curves.

Part 2: Differentiation.

Section 2.1: Functions of several variables; limits and continuity.

Section 2.2: Partial derivatives, tangent planes, linear approximation.

Section 2.3: The chain rule.

Section 2.4: Directional derivatives and the gradient vector.

Section 2.5: Maxima and minima.

Section 2.6: Lagrange multipliers.

Part 3: Integration.

Section 3.1: Basics of double integrals.

Section 3.2: Double integrals in polar coordinates, and surface area

Section 3.3: Triple integrals.

Section 3.4: Triple integrals in cylindrical and spherical coordinates.

Section 3.5: Change of variables, Jacobians.

Part 4: Vector calculus.

Section 4.1: Vector fields and line integrals.

Section 4.2: Fundamental theorem of line integrals.

Section 4.3: Green's theorem.

Section 4.4: Curl and divergence.

Section 4.5: Parametrized surfaces and surface integrals.

Section 4.6: Stokes' theorem.

Section 4.7: The divergence theorem, conclusion.