Fall 2008

Math 20-550-01: Calculus III

Course Information

Instructor: Zhiliang Xu, zxu2@nd.edu

Office Hours: MWF 2:00pm-4:00pm, Hayes-Healy 226, and by appointment

Textbook: Stewart, Multivariable Calculus, 6th ed.

Class Time: MWF 8:30am-9:20am, in Edward J. DeBartolo Hall 126

Tutorials:

Teaching Assistant: Sarah G. Cotter cotter.12@nd.edu,

Office Hours: Tue: 4:00pm - 6:00pm HH217

Syllabus: PDF Format.

Class Schedule: PDF Format.

Homework Assignments: Word Format.

Math Tools

Mathematica Demos
Maple Demos

Week 1:

Aug 27: Section 13.1
Homework: Sec. 13.1: 4, 7, 12, 15, 23.
Aug 29: Section 13.2
Homework: Sec. 13.2: 6, 14, 17, 20, 23, 25.

Week 2:

Sep 01: Section 13.3 Dot Products
Homework: Sec. 13.3: 5, 17, 23, 27, 39, 40, 41, 43, 51.
Sep 03: Section 13.4 Cross Products
Homework: Sec. 13.4: 5, 6, 13, 17, 19, 29, 30, 34.
Sep 05: Section 13.5 Eqns of Lines and Planes
Homework: Sec. 13.5: 3, 4, 5, 7, 10, 13, 19, 21, 23, 25, 27, 31, 35, 43, 51, 53, 55, 57, 69, 71.

Week 3:

Sep 08: Section 13.5 Eqns of Lines and Planes
Homework: Sec. 13.5: 3, 4, 5, 7, 10, 13, 19, 21, 23, 25, 27, 31, 35, 43, 51, 53, 55, 57, 69, 71.

Homework due on 09/11 covers Section 13.5.

Sep 10: Section 14.1 Vector Functions & Space Curves
Homework: Sec. 14.1: 2--4, 8, 11, 12, 19--24, 37.
Sep 12: Section 14.2 Derivatives and Integrals
Homework: Sec. 14.2: 3, 8, 9, 13, 19, 23, 25, 32, 36, 37, 39.

Week 4:

Sep 15: Section 14.3 Arc Length and Normal/Binormal vectors
Homework: Sec. 14.3: 2--4, 17a, 18a, 43.

Practice Exams

PracticeExam1.pdf

Review: DBRT 141 is reserved for the math 20550 review on 9-22-08 from 7 p.m. - 9 p.m.
The cut-off line of the exam is Section 15.1

Sep 15: Section 14.4 Motion in Space
Homework: Sec. 14.4: 5, 7, 10, 13, 18(a), 19, 20, 21, 23, 35.
Sep 17: Section 15.1 Functions of Multiple Variables
Homework: Sec. 15.1: 11, 12, 14, 23, 24, 26, 30, 35, 40, 45, 48, 55, 56, 57, 59.

Week 5:

Sep 22: Section 15.2 Limits and Continuity
Homework: Sec. 15.2: 9, 10, 13, 14, 18, 21, 24, 29, 31, 32, 38, 39, 40.
Sep 24: Section 15.2 Limits and Continuity
Homework: Sec. 15.2: 9, 10, 13, 14, 18, 21, 24, 29, 31, 32, 38, 39, 40.
Sep 26: Section 15.3 Partial Derivatives

Week 6:

Homework due this week: Section 15.2

Sep 29: Section 15.3 Partial Derivatives
Homework: Sec. 15.3: 15, 17, 22, 28, 29, 39, 41, 52, 56, 63, 64, 87, 89.
Oct 01: Section 15.5 The Chain Rule
Homework: Sec. 15.5: 5, 6, 10, 11, 13, 14, 17, 21, 22, 29, 32, 35, 39, 42.
Oct 03: Section 15.6 Directional Derivatives & Gradient Vector
Homework: Sec. 15.6: 2, 5, 6, 7, 8, 12, 15, 19--22, 24, 28, 33, 34, 36, 40, 41, 42, 45, 52, 59.

Week 7:

Homework due this week: Section 15.3, 15.5, 15.6.

Oct 06: Section 15.6 Directional Derivatives & Gradient Vector
Homework: Sec. 15.6: 2, 5, 6, 7, 8, 12, 15, 19--22, 24, 28, 33, 34, 36, 40, 41, 42, 45, 52, 59.
Oct 08: Section 15.7 Max/Min Values
Homework: Sec. 15.7: 3--6, 8, 10, 14, 31, 32, 34, 42, 47, 48.
Oct 10: Section 15.8 Lagrange Multipliers
Homework: Sec. 15.8: 4--6, 15, 16, 18, 19, 29, 40, 41.

Week 8:

Homework due this week: Section 15.7, 15.8

Oct 13: Section 16.1 Double Integrals over Rectangles
Homework: Sec. 16.1: 11--14.
Oct 15: Section 16.2 Iterated Integrals
Homework: Sec. 16.2: 6, 8, 9, 16, 20, 28, 29, 30.

Exam 2 Review: 7-9 pm, Monday Oct. 27, DBRT 102.

Practice Exam 2

PracticeExam2.pdf

Oct 15: Section 16.3 Double Integrals over General Regions
Homework: Sec. 16.3: 4, 6, 11, 14, 16, 19, 20, 22, 26, 31, 43, 45, 46.

Week 9:

Fall break

Week 10:

Homework due this week: Section 16.1, 16.2, 16.3.

Oct 27: Section 16.3 Double Integrals over General Regions; Exam Review
Oct 29: Section 16.4 Double Integrals in Polar Coordinate
Homework: Sec. 16.4: 8, 9, 14, 15, 17, 18, 19, 22, 24, 30, 32.
Oct 31: Section 16.5 Applications
Homework: Sec. 16.5: 3, 6, 10, 12.

Week 11:

Homework due this week: Section 16.4, 16.5.

Nov 3: Section 16.6 Triple Integrals
Homework: Sec. 16.6: 3, 10, 11, 13, 14, 22, 34, 40, 51.
Nov 5: Section 16.7 Triple Integrals in Cylindrical Coords
Homework: Sec. 16.7: 7, 11, 15, 17, 18, 19, 21, 22, 25, 28.
Nov 6 (Tutorials): Section 16.8 Triple Integrals in Spherical Coords.
Nov 7: Section 16.9 Change of variables in multiple integrals
Homework: Sec. 16.9: 2, 6, 7, 8, 11, 13, 14, 17, 21--23.

Week 12:

Nov 10: Section 16.9 Change of variables in multiple integrals
Homework: Sec. 16.9: 2, 6, 7, 8, 11, 13, 14, 17, 21--23.
Nov 12: Section 17.2 Line integrals
Homework: Sec. 17.2: 3, 4, 6, 7, 9, 11, 15--20, 40, 41, 43.
Nov 14: Section 17.1 Vector fields; 17.2 Line integrals of vector fields; 17.3 Fundamental thm of line integrals
Homework: Sec. 17.1: 2, 5, 11--19, 23, 24, 2; Sec. 17.3: 4--6, 11, 12, 14, 15, 17, 18, 20, 21, 23, 33.

Exam 3 Review: 7-9 pm, Monday Nov. 17, DBRT 102.

Practice Exam 3

PracticeExam3.pdf

Week 13:

Homework due this week: Section 16.6 - 9; 17.1 - 3.
Exam 3: 11/18/08, 8:00am - 9:15 am, DBRT 131.

Nov 17: Exam Review
Nov 19: Section 17.4 Green's Thm
Homework: Sec. 17.4: 1, 2, 7--10, 12, 13, 27.
Nov 21: Section 17.5 Curl & Divergence
Homework: Sec. 17.5: 1, 3, 8, 14, 15, 19, 21.

Week 14:

Nov 24: Section 17.6 Parametric surfaces
Homework: Sec. 17.6: 12--23, 29, 32, 33, 38, 40--43.

Week 15:

Homework due this week: Section 17.4 - 6.

Dec 1: Section 17.6 Parametric surfaces
Homework: Sec. 17.6: 12--23, 29, 32, 33, 38, 40--43.
Dec 3: Section 17.7 Surface Integrals
Homework: Sec. 17.7: 6, 9, 11, 13, 15, 16, 19--22.
Dec 5: Section 17.8 Stokes' Thm.
Homework: Sec. 17.8: 2, 3, 5, 8, 11a, 13, 17--19.

Week 16:

Dec 8: Section 17.9 The divergence thm.
Homework: Sec. 17.9: 5, 7, 9, 11, 13, 17, 24.

Final Exam Review: 7:00pm - 9:00pm, 12/16/08, DBRT 101
Final Exam: 1:45pm - 3:45pm, 12/17, 356A, Fitzpatrick Hall of Engr