Calculus IV (MATH 317, 2nd summer term 2015)
Time: Mon/Wed 10:30-12:30, Tue/Thu 12:30-14:00
Place: LSK 201
Office hours: Mon/Tue/Wed 14:00-15:00 in LSK 300C.
Tutoring hours (with a TA): Mon/Wed 12:50-13:50 at the Math Learning Centre LSK 301.
Instructor's e-mail: Replace "nowhere" with "ubc" in ufirst@math.nowhere.ca.
Syllabus
- Textbook: "Multivariable Calculus" by James Stewart, edition 7E
- Topics:
-
Vector valued functions of one variable (Chapter 13):
Parameterized curves, velocity, acceleration, arc length
(includes curvature, normal and binormal vectors, tangential and normal components of acceleration).
-
Vector valued functions of several variables (Chapter 16):
Vector fields, line integrals, conservative fields, fundamental theorem of line integrals,
Green's theorem, gradient, curl, divergence,
parameterized surfaces, suface area, surface integrals,
Stoke's theorem, divergence theorem.
Grading Scheme
The grade is composed of:
- final exam (50%),
- two midterms (30%),
- homework and quizzes (20%),
or the final exam grade minus 10 points
(whichever is higher).
The second option is a safety net --- even if you did poorly during the semester,
you can still have a good grade by doing well on the final exam.
There will be no webwork.
Final grades may be subject to scaling.
Homework and Quizzes
Homework will be published every Monday and Thursday. On the following Monday or Thursday, either
the written homework will be collected to be marked, or there will be a 10-15 minutes quiz based on the homework.
This will be decided randomly in class.
The two lowest homework/quiz grades will be dropped.
- Homework 1 (due on July 9):
13.1: #8, 10, 18, 22, 24, 26, 28, 30, 40, 42, 44.
13.2: #6, 8, 10, 12, 16, 18, 22, 24, 26, 28, 34, 52.
Solution:
A,
B,
C,
D.
- Homework 2 (due on July 13):
13.3: #2, 4, 14, 16, 18, 22, 24, 28, 42.
13.4: #4, 6, 10, 12, 16, 18(a), 20, 26, 38, 42.
Solution:
A,
B,
C.
- Homework 3 (due on July 16):
13.4: 32, 44.
Exercise at the end of Chapter 13 (p. 898): 8, 12, 20.
16.1: 4, 12, 16, 18, 22, 24.
16.2: 2, 4.
16.3: 4, 6.
Solution:
A,
B,
C.
- Homework 4 (due on July 20):
16.1: #26. 16.2: #6, 8, 10, 14, 16, 18, 20, 22, 32(a), 40.
16.3: #8, 14, 16, 20.
Solution:
A,
B,
C.
- Homework 5 (due on July 23):
16.3: 12, 18, 24, 28, 36.
Exercises at the end of chapter 16 (p. 1161): 4, 12, 14.
Solution:
A,
B.
- Homework 6 (due on July 27):
16.4: 2, 4, 6, 10, 12, 14, 18, 28. Exercises at the end of chapter 16 (p. 1161): 16.
Solution:
A,
B.
- Homework 7 (due on July 30):
16.5: #2, 4, 8, 14, 18, 20, 26, 27, 28, 29, 30.
16.6: #14, 20, 22, 24, 26, 34, 36, 40, 42, 44.
Solution:
A,
B,
C,
D,
E.
- Homework 8 (due on August 4):
16.6: #46, 48.
16.7: #6, 8, 10, 16, 22, 24, 26, 30, 38, 48.
Solution:
A,
B,
C.
- Homework 9 (due on August 10):
16.8: #2, 4, 6, 8, 10, 14, 16, 18, 20. Exercises at the end of chapter 16 (p. 1161): 24, 32.
Solution:
A,
B,
C.
- Homework 10 (due on August 12 --- Wednesday!):
16.9: #2, 4, 8, 10, 12, 18 (there is a hint in Exercise 17), 20.
Solution:
A,
B.
Midterms
There will be two midterms, each determining 15% of the final grade.
Please report conflicts and hardships as soon as possible.
Midterm 1
- Time and place: July 21 at 12:30-13:45 (75 minutes), LSK 201.
- Material: Chapter 13: All. Chapter 16: 16.1, 16.2, 16.3 only until page 1100 (including). You also need
to know how to check if a field is conservative and find a potential function.
- Solution: Midterm 1 solution
(Midterm 1 without the solution).
- Practice Midterm: practice midterm
(solution).
- Midterms from previous years:
2015
(solution),
2011
(solution),
2008.
(Notice that the material may be different.)
Midterm 2
- Times and place: August 6 at 12:30-13:45 (75 minutes), LSK 201.
- Material:
Chapter 16, until 16.7 (including). You also need to know Chapter 13, but the emphasis will be
on topics from Chapter 16.
- Solution: Midterm 2 solution
(Midterm 2 without the solution).
- Practice Midterm: practice midterm
(solution).
- Midterms from previous years:
2015
(solution),
2011
(solution).
(Notice that the material may be different.)
Final Exam
Chuck Norris Facts
(This is irrelevant to the course.)
- Chuck Norris can apply Green's Theorem to non-closed curves.
- Chuck Norris can find a potenial function to a non-conservative vector field.
- Chuck Norris knows the anti-derivative of sin(x^2).
- Chuck Norris can use the Divergence Theorem even when the vector field is not defined everywhere
within the solid region.
- Chuck Norris can find the arclength parametrization of any curve.
- Green's Theorem, Stokes' Theorem and the Divergence Theorem are in fact
special cases of the Chuck Norris Theorem. Other special cases of the Chuck Norris Theorem
include Arrow's Theorem
and Hall's Theorem.
Other, almost equally irrelevant, facts:
- Chuck Norris can divide by 0.
- Chuck Norris counted to infinity, twice.
- Chuck Norris knows the last decimal digit of pi.
