Fall 2007

Math 20-550-04: Calculus III

Course Information

Instructor: Zhiliang Xu, zxu2@nd.edu

Office Hours: MWF 5:00pm-6:00pm, Hayes-Healy 226, and by appointment

Text: Stewart, Multivariable Calculus, 5th ed.

Class Time: MWF 11:45am-12:35pm, Edward J. Debartolo Hall 126.

Tutorials:

Teaching Assistant: Jacob M. Carson carson.27@nd.edu, 221HH.

Office Hours: Tue 18:00pm-20:00pm, 221 HH

Syllabus PDF Format.

Class Schedule PDF Format.

Week 1:

Aug 29: 13.1-2 3D Coordinates, Vectors
Homework: Sec. 13.1: 4, 7, 12, 15, 23; Sec. 13.2: 2
Aug 30: 13.2 Vectors (tutorial)
Homework: Sec. 13.2: 6, 14, 20, 21, 25
Aug 31: 13.3 Dot Product
Homework: Sec. 13.3: 5, 17, 23, 27, 39, 40, 41, 43, 51.

Week 2:

Sep 3: 13.4 3D Cross Product
Homework: Sec. 13.4: 5, 6, 9, 11, 13, 15, 25, 26, 30.
Sep 5: 13.5 Line Planes
Homework: Sec. 13.5: 3, 4, 5, 7, 10, 13, 19, 21, 23, 25, 27.
Sep 7: 13.5 Planes
Homework: Sec. 13.5: 31, 35, 39, 47, 49, 51, 53, 65, 67.

Week 3:

Sep 10: 14.1 Vector Functions, Space Curves
Homework: Sec. 14.1: 2-4, 8, 11-12, 19-24, 35.

Matlab program to plot helix (Ex. 4).

Sep 12: 14.2 Derivatives, Integrals
Homework: Sec. 14.2: 3, 8, 9, 14, 19, 24, 25, 29, 32, 36, 37, 39.
Sep 14: 14.3 Arc Length (Skip Curvature)
Homework: Sec. 14.3: 2-4, 13a, 14a, 39, 41.

Practice Exam 1.

Week 4:

Sep 17: 14.4 Motion in Space

Motion in Space Handout

Homework: Sec 14.4: 6, 7, 10, 13, 18(a), 19, 20, 21, 23, 33.
Sep 19: 15.1 Functions of Several Variables
Homework: Sec. 15.1: 11, 12, 15, 23, 24, 26, 30, 35, 38, 43, 46, 53-55, 57, 58.
To make a 3D plot with Mathematica, type: Plot3D[Sin[x+y],{x,0,6},{y,0,6}], then press "shift"+"enter"

Mathematica program to plot graph of f(x,y) = sin(sqrt(x^2 + y^2)).

Mathematica program to plot contour map of f(x,y) = sin(sqrt(x^2 + y^2)).

More programs can be found at Professor Peter Cholak's webpage "http://www.nd.edu/~cholak/math20550/index.html"
Sep 21: 15.2 Limits, Continuity
Homework: Sec. 15.2: 7, 8, 11, 12, 16, 19, 22, 27, 29, 30, 36, 37, 38.

Week 5:

Exam on 9-25-07 -8:00 a.m.- 9:15 a.m. - STEP 100

Sep 24: Review
Sep 26: 15.3 Partial Derivatives
Homework: Sec. 15.3: 14, 15, 18, 24, 25, 36, 37, 41, 42, 48, 51, 59, 60, 83, 85
Sep 28: 15.5 Chain Rule
Homework: Sec. 15.5: 5, 6, 10, 11, 13, 14, 17, 21, 22, 29, 32, 35, 36, 39, 42

Week 6:

Oct 01: 15.6 Directional Derivatives, Gradients
Homework: Sec. 15.6. 2, 5, 6, 7, 8, 14, 15, 19-22, 24, 28, 33, 34, 36, 40
Oct 03: 15.6 Tangent Planes, Normal Lines
Homework: Sec. 15.6: 41, 42, 45, 52, 59; Sec. 15.7: 3-6.

Mathematica program for Ex1

Mathematica program for Ex2

Mathematica program for Ex3

Oct 05: 15.7 Maxima, Minima, Saddle Points
Homework: Sec. 15.7: 8, 10, 15, 29, 30, 32, 40, 45, 46.

Mathematica program for Section 15.7

Week 7:

Oct 08: 15.7 Abs. Max. and Min
Homework: Sec. 15.7: 27, 28, 29, 30, 32, 33.
Oct 10: 15.8 Lagrange Multipliers
Homework: Sec. 15.8: 4-6, 18, 19, 27, 15, 16, 38, 39.
Oct 12: 15.8 Two Constraints & 16.1 Double Integrals over Rectangles
Homework: Sec. 16.1: 11-14

Practice Exam2.1 for midterm

Practice Exam2.2 for midterm

Week 8:

Oct 15: 16.2 Iterated Integrals; 16.3 Double Integrals over General Regions
Homework: Sec. 16.2: 6, 8, 9, 14, 18, 26, 27, 29; Sec. 16.3: 3, 4, 11, 14, 16, 19.
Oct 17: 16.3 Double Integrals over General Regions
Homework: Sec.
Oct. 18: Midterm Exam from 8:00 a.m. to 9:15 a.m. in STEP 100
Oct 19: 16.4 Double Integrals over Polar Coordinates
Homework: Sec. 16.4: 10, 11, 16, 17, 19, 20.

Week 9:

Fall break

Week 10:

Oct 29: 16.4 Double Integrals over Polar Coordinates & 16.5 Center of Mass
Homework: Sec. 16.4: 20, 21, 22, 24, 30, 31. Sec. 16.5: 3
Oct 31: 16.5 Center of Mass & 16.6 Surface Area
Homework: Sec. 16.5: 6, 9, 12. Sec. 16.6: 2, 3, 5, 6, 10.
Nov 02: 16.7 Triple Integrals
Homework: Sec. 16.7: 8, 9, 11, 13, 14.

Week 11:

Nov 05: 16.7 & 16.8

Class note for 16.7 & 16.8

Homework: Sec. 16.7: 20, 32, 38, 47. Sec. 16.8: 2, 3, 7, 8, 9, 11, 15, 33

Class notes for Section 16.9

Nov 07: 16.8 & 16.9 Triple Integrals in Cylindrical and Spherical Coords. & Change of Variables
Homework: Sec. 16.8: 17, 20, 21, 23, 24; 16.9: 2, 5, 7, 8, 11, 13, 14
Nov 07: Section 17.1 & 17.2 Line Integrals

Class notes for Section 17.1 & 17.2

Nov 09: 17.1 & 17.2 Vector fields & Line integrals
Homework: Sec. 16.9: 17, 21-23; Sec. 17.1: 2,5,11-19,23,24,27; Sec. 17.2: 3, 4, 10, 11

Week 12:

Nov 12: 17.2 Line Integrals

Class notes for Section 17.2 (line integrals of vector fields)

Homework: Sec. 16.8: 25, 35; Sec. 17.2: 5, 6, 7, 15-20, 38, 39, 41
Nov 14: 17.3 Funamental Theorem for Line Integrals
Homework: Sec. 17.3: 4-6, 11-14, 15, 17, 18; Sec. 16.8: 29, 30
Nov 16: 17.4 Green's Theorem
Homework: Sec. 17.3: 20, 21, 23, 33; Sec. 17.4: 1-4, 9-12, 14-15.

Week 13:

Nov 19: 17.5 Curl & Divergence
Homework: Sec. 17.5: 5-8, 14-15, 20-21.

Practice exam 3

Week 14:

Nov 28: 17.6 Parametric Surfaces
Homework: Sec. 17.6: 9-21.
Nov 30: 17.6 Parametric Surfaces
Homework: Sec. 17.6: 27, 30, 31-32, 35-39.

Week 15:

Dec 05: 17.5 Surface Integrals
Homework: Sec. 17.7: 5-7, 9-12, 15-18.
Dec 07: 17.7 17.8 Stokes' Thm & 17.9 Divergence Thm
Homework: Sec. 17.8: 2, 3, 5, 7, 8, 11a, 13, 17-19. Sec. 17.9: 7, 9, 11, 13.

Week 15:

Dec 10: 17.9 Divergence Thm & Review

Final:

DBRT 141 is reserved for the math 20550 review on 12-13-07 from 2 p.m. - 4 p.m.
Final exam: Saturday, December 15, 1:45-3:45, 138 DeBartolo
Make-up exam: HAYE 229 on 12-17-07 from 10 a.m. - 12 p.m.