MIT Unified Engineering, Fall 2005

MIT 18.02 Multivariable Calculus, Fall 2007

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates. License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms

Lec 1 - MIT 18.02 Multivariable Calculus, Fall 2007 [Dot product.]

Lec 2 - MIT 18.02 Multivariable Calculus, Fall 2007 [Determinants; cross product.]

Lec 3 - MIT 18.02 Multivariable Calculus, Fall 2007 [Matrices; inverse matrices.]

Lec 4 - MIT 18.02 Multivariable Calculus, Fall 2007 [Square systems; equations of planes.]

Lec 5 - MIT 18.02 Multivariable Calculus, Fall 2007 [Parametric equations for lines and curves.]

Lec 6 - MIT 18.02 Multivariable Calculus, Fall 2007 [Velocity, acceleration; Kepler's second law.]

Lec 7 - MIT 18.02 Multivariable Calculus, Fall 2007 [Review.]

Lec 8 - MIT 18.02 Multivariable Calculus, Fall 2007 [Level curves; partial derivatives; tangent plane approximation.]

Lec 9 - MIT 18.02 Multivariable Calculus, Fall 2007 [Max-min problems; least squares.]

Lec 10 - MIT 18.02 Multivariable Calculus, Fall 2007 [Second derivative test; boundaries and infinity.]

Lec 11 - MIT 18.02 Multivariable Calculus, Fall 2007 [Differentials; chain rule.]

Lec 12 - MIT 18.02 Multivariable Calculus, Fall 2007 [Gradient; directional derivative; tangent plane.]

Lec 13 - MIT 18.02 Multivariable Calculus, Fall 2007 [Lagrange multipliers.]

Lec 14 - MIT 18.02 Multivariable Calculus, Fall 2007 [Non-independent variables.]

Lec 15 - Lecture 15: Partial differential equations; review.

Lec 16 - Double integrals.

Lec 17 - Double integrals in polar coordinates; applications.

Lec 18 - Change of variables.

Lec 19 -Vector fields and line integrals in the plane

Lec 20 - Path independence and conservative fields.

Lec 21 - Lecture 21: Gradient fields and potential functions.

Lec 22 - Green's theorem.

Lec 23 -Flux; normal form of Green's theorem. 

Lec 24 - Simply connected regions; review 

Lec 25 - Triple integrals in rectangular and cylindrical coordinates. 

Lec 26 - Spherical coordinates; surface area. 

Lec 27 - Vector fields in 3D; surface integrals and flux. 

Lec 28 - Divergence theorem. 

Lec 29 -  Divergence theorem (cont.): applications and proof.

Lec 30- Line integrals in space, curl, exactness and potentials.

Lec 31- Stokes' theorem.

Lec 32- Stokes' theorem (cont.); review.

Lec 33-Topological considerations; Maxwell's equations. 

Lec 33- Final review.