Spring 2007

Math 20-550-04: Calculus 3

Course Information

Instructor: Zhiliang Xu, zxu2@nd.edu

Office Hours: MWF 2:30pm-3:30pm, Hayes-Healy 226, and by appointment

Text: Stewart, Multivariable Calculus, 5th ed., Chapters 13-17

Class Time: MWF 12:55-1:45, DeBartolo Hall 155.

Tutorials:

Teaching Assistant: Florentiu D. Cibotaru, cibotaru.1@nd.edu, Hayes Healy 221.

Syllabus PDF Format.

Class Schedule PDF Format.

Week 1:

Jan 17: 13.1-2 3D Coordinates, Vectors
Homework: Section 13.1: 3, 4, 8, 11, 15, 25. Section 13.2: 2, 4, 6.
Jan 19: 13.3 Dot Product
Homework: Section 13.2: 14, 20, 21, 25. Section 13.3: 1, 7.

Week 2:

Jan 22: 13.3 Dot Product & 13.4 Cross Product
Homework: Section 13.3: 10, 11, 13, 18, 24, 31, 40
Jan 24: 13.4 Cross Product & 13.5 Lines, Planes
Homework: Section 13.4: 5, 9, 10, 12, 16, 19, 29, 31, 33, 39.
Jan 26: 13.5 Planes
Homework: Section 13.5: 4, 11, 15, 19, 21.

Week 3:

Jan 29: 14.1 Vector Functions, Space Curves
Homework: Section 13.5: 27, 31, 40, 45, 54, 59, 63, 68.
Jan 31: 14.1 Vector Functions, Space Curves & 14.2 Derivatives, Integrals
Homework: Section 14.1: 2, 5, 11, 17, 35. Section 14.2: 2, 19, 21, 29, 47
Feb 02: 14.3 Arc Length (Skip Curvature)
Homework: Section 14.2: 34, 38, 39. Section 14.3: 3, 9, 11, 14(a), 40.

Week 4:

PracticeExam1.1.pdf

PracticeExam1.2.pdf

Feb 05: 14.4 Motion in Space
Homework: Section 14.3: 39, 41, 45. Section 14.4: 11, 13, 16, 17(a), 18(a).
Feb 07: 15.1 Functions of Serveral Variables
Homework: Section 15.1: 6, 8, 17, 23,31, 35, 43, 44, 55, 57, 63(a), 64(a).
Feb 09: 15.2 Limits, Continuity
Homework: Section 15.2: 5, 6, 10, 11, 15, 16, 23, 30, 31, 35

Week 5:

Feb 12: 15.3 Partial Derivatives
Homework: Section 15.3: 14, 17, 20, 21, 32, 36, 37, 41, 46, 49, 68(b).
Feb 14: 15.5 Chain Rule
Homework: Section 15.5: 4, 5, 10, 11, 18, 25.
Feb 15: Exam 1: DBRT 101, 8:00am-9:15am
Feb 16: 15.6 Directional Derivatives, Gradients
Homework: Section 15.5: 32, 34. Section 15.6: 5, 9, 12, 14, 19

Week 6:

PracticeExam2.1.pdf

PracticeExam2.2.pdf

Feb 19: 15.6 Tangent Planes, Normal Lines
Homework: Section 15.4: 3, 4. Section 15.6: 21, 23, 28, 29, 41, 43, 49.
Feb 21: 15.7 Maxima, Minima, Saddle Points
Homework: Section 15.6: 53. Section 15.7: 2, 3, 5, 7, 11, 13, 15.
(For problems 5-15, you do not have to graph the function on the solution sheet)
Feb 23: 15.7 Maxima, Minima, Saddle Points
Homework: Section 15.7: 27, 28, 29, 31, 32, 33, 39, 46.

Week 7:

Feb 26: 15.8 Lagrange Multipliers
Homework: Section 15.8: 3, 5, 7, 9, 11, 18, 19, 25, 27, 28.
Feb 28: 15.8 Two Constraints
Homework: Section 15.8: 15, 16, 17, 33, 35, 38, 39, 40(b).
Mar 02: 16.1 Double Integrals over Rectangles
Homework: Section 16.1: 1, 2, 5, 7, 8, 11, 12, 13, 14, 18.

Week 8:

Mar 05: 16.2-16.3 Iterated Integrals, General Regions
Mar 07: 16.3-16.4 Double Integrals over General Regions
Mar 09: 16.4 Double Integrals in Polar Form

Week 9:

Spring Break

Week 10:

Mar 19: 16.5-16.6 Applications of Double Integrals
No homework
Mar 20: Exam 2
Mar 21: 16.7 Triple Integrals
Homework: Section 16.6: 7, 9. Section 16.7: 2, 3, 6, 7, 9, 15, 17, 28.
Mar 23: 16.8 Triple Integrals in Cylindrical and Spherical Coords.

PracticeExam3.1.pdf

PracticeExam3.2.pdf

Week 11:

Week 12:

Week 13:

Apr 11: 17.4 Green's Theorem
Homework: Section 17.3: 26, 28, 33(b) Does this contradict Thm. 6?. Section 17.4: 2, 3, 9, 10, 14, 15, 17, 19.
Apr 13: 17.5 Curl and Divergence
Homework: Section 17.5: 1, 5, 9, 12, 15, 17, 19, 25, 31, 32.

Week 14:

Apr 16: 17.6 Parametric Surfaces
Homework: Section 17.6: 2, 4, 12, 13, 14, 15, 16, 17.

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Apr 18: 17.6 Parametric Surface
Homework: Section 17.6: 19, 21, 27, 28, 31, 33, 37, 40, 53(a).
Apr 20: 17.7 Surface Integrals
Homework: Section 17.7: 5, 6, 7, 11, 13, 15, 17, 18

Week 15:

Apr 23: 17.7 Surface Integrals
Homework: Section 17.7:

Exam3 solution

PracticeFinal1

PracticeFinal2

Apr 25: 17.7 Surface Integrals of Vector Fields
Homework: Section 17.7: