110.202 Calculus III: SPRING 2005

Instructors: Jack Morava and Florin Spinu

Course description: functions of several variables, partial derivatives; multiple integrals, line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem.

Textbook: J. Marsden, A. Tromba, Vector Calculus, Fifth Edition, 2003.

Week 1 [Jan 31] Basics of vector geometry: lines and planes; dot and cross-product, distance, angles, orthogonality.

Week 2 [Feb 07] Vector geometry cont’d: matrices and linear maps; coordinates and higher-dimensional spaces

Week 3 [Feb 14] Real-valued functions and geometric visualization; introduction to derivatives. Gradients, parametrized curves.

Week 4 [Feb 21] Geometric significance of derivative; vector-valued functions; vector fields; chain rule.

Week 5 [Feb 28] Gradient and directional derivative; higher derivatives and Taylor series. Optimization.

Week 6 [Mar 07] Newton & Kepler; maxima and minima.

Ø      Midterm: March 09

Ø      [Practice problems] [answers]

Week of Mar 14: Spring Break

Week 07 [Mar 21] Lagrange multipliers. Div and curl.

Week 08 [Mar 28] Integration.

Week 09 [Apr 04] Integration.

Ø      Midterm: April 06

Ø      Practice problems: integrals

Ø      Practice problems: extrema

Ø      Ellipses (Prof. Morava’s notes)

Week 10 [Apr 11] Line integrals; parametrized surfaces.

Week 11 [Apr 18] Surface integrals and flux. Green’s theorem.

Week 12 [Apr 25] Stokes and Gauss theorem. Conservation laws.

Week 13 [May 02] Applications. Review material.

Ø      Final Exam: May 12, 9-12 noon.

Final exam solutions: [sections 1-4]              [sections 5-8]

 

EXAM SHOWING: (Krieger Hall Math building, second floor lounge)

Morava’s sections (1-4): Monday, May 16, 1-4 pm

Spinu’s sections (5-8): Monday, May 16, 11-12:30 pm