# Math 2163 - Calculus III

MWF 11:30, 004A HES

Instructor: Anatolii Grinshpan
Current office hours: 3:10-4 MW, 5:10-6 F or by appointment, 406 MS

Program Outline

Jan 9   Functions of two variables: level curves and limits.
Jan 11 Limits and continuity. Partial derivatives.
Jan 13 More on partial derivatives. Clairaut's theorem.
HW 1 due Jan 23: 15, 16, 24, 31-36 (p. 758), 6, 8, 10, 12, 14, 15 (p. 765), 5, 6, 14, 16, 18, 23, 24, 52, 62, 64 (pp. 777-78)
Jan 18 Harmonic functions. Wave equation. Tangent planes.
Jan 20 Tangent planes, linearization, differentiability. Differentials.
Jan 23 Tangent planes to parametric surfaces.
HW 2 due Jan 30: 60, 63 (p. 778), 2, 4, 9, 10, 13, 19-21, 40 (pp. 788-9), 2, 4, 6, 8, 20, 22, 24, 27, 32, 35, 43 (pp. 796-8)
Jan 25 Chain rule. Directional derivatives.
Jan 27 Directional derivatives, gradient and its properties.
Jan 30 Critical points and local extrema.
HW 3 due Feb 6: 4, 6, 8, 20, 23, 24, 33, 42 (pp. 808-10), 2, 6, 8, 10, 24, 28, 32, 45 (pp. 818-9)
Feb 1  Examples. Points of absolute extremum.
Feb 3  Points of absolute extremum (continued).
Feb 6  Functions of three variables.
HW 4 due Feb 13: 17, 18, 29 (pp. 765-6), 30, 44 (pp. 777-8), 21 (p. 789), 16 (p. 796), 45 (p. 798), 10, 22, 43, 44, 46(pp. 809-10), 3-10 (pp. 827-8)
Feb 8  Functions of three variables (continued).
Feb 10 Lagrange multipliers.
Feb 13 Lagrange multipliers (continued).
Feb 15 Review.
Feb 20 No class.
Feb 22 Double and iterated integrals.
Feb 24 Fubini's formula. Changing the order of integration.
Feb 27 Integration in polar coordinates.
HW 5 due March 6: 13, 16 (p. 853), 8, 10, 12, 36, 38 (pp. 861-2), 11, 26, 28, 32 (pp. 867-8)
Mar 1  Applications of integration: moments, probability, surface area.
Mar 3  Change of variables in a double integral. Notes.
Mar 6  Change of variables: examples.
HW 6 due March 20: 2, 4, 10, 14, 24 (p. 877), 3, 5, 6 (p. 881), 1, 2, 8, 10, 12, 15, 21, 24 (p. 909)
Mar 8  Surface area of parameterized surfaces.
Mar 10 Triple integrals. Practice session.
Mar 20 Triple integrals (continued).
HW 7 due March 27: 13, 24, 30, 32, 35 (pp. 891-2), 8, 16, 22 (pp. 898-9), 17, 18 (p. 909).
Mar 22 Change of variables in a triple integral. Cylindrical and spherical cases.
Mar 24 Examples.
Mar 27 Review.
Mar 31 Vector fields. Conservative fields. Line integrals. An example.
Apr 3   Line integrals.
HW 8 due April 10: 11-14, 15-18, 29-32 (pp. 922-23), 6, 8, 12, 14, 38 (pp. 934-5).
Apr 5   Conservative fields: path independence, conservation of energy.
Apr 7   Path independence and potentials.
Apr 10 Simply connected domains. Circulation. Green's theorem.
HW 9 due April 17: 4-10, 20-23 (pp. 943-4), 1-4, 7, 8, 18-21 (p. 951)
Apr 12 Green's theorem and applications.
Apr 14 Examples.
Apr 17 Vector forms of Green's theorem. Curl and divergence in space.
HW 10 due April 24: 7-10, 18-20, 28, 29 (pp. 958-9), 8, 9, 12, 19 (p. 970), 1, 2, 10, 13-15 (p. 976)
Apr 19 Surface integrals. Stokes' Theorem.
Apr 21 Normal field and orientation of surfaces. The Stokes and Divergence theorems.
Apr 24 Divergence Theorem.
Apr 26 Practice session. Review questions I.
Apr 28 Practice session. Review questions II.
An example: interchange of integrals.
The review questions are selected from the homework. Do no neglect the rest of the homework.
Office hours: Tue, Th 4-5 pm
May 5 Final Examination 10-11:50 am. Answers.