Exam 2 problems and solutions.
Exam 3 problems and solutions.
The Final Exam will be Friday, December 19, in Swain East 240, at 10:15 A.M. It consists of 10 problems worth 10 points each on the material covered on the first three exams and 5 problems worth 20 points each on new material. Good luck, and have a good Christmas Break!
Homework
Due Monday, September 22
- 4.4: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
- 7.1: 3, 6, 7, 9, 18
- Bonus: Express the indefinite integral of sec3x in terms of the indefinite integral of sec x.
Due Thursday, September 25
- 7.2: 5, 10, 15, 20, 25, 30, 35
- 7.3: 5, 10, 15, 19, 23, 30
- Bonus: Find the indefinite integral of x / (1 + sin x).
Due Thursday, October 2
- 7.4: 5, 10, 15, 20, 25, 30, 35, 42
- 7.5: 5, 10, 15, 20, 25, 30, 35, 40, 45
- Prepare for the exam on Friday, October 3. (See trig identities.)
Due Thursday, October 9
- 7.7: 5, 10, 15, 20, 24, 31, 34
- 7.8: 5, 10, 15, 21, 25, 27, 28, 35
- 6.1: 5, 10, 15, 20, 25, 42
- Bonus: Simpson's rule gives an exact answer when applied to polynomials of degree 3 or less. Can you describe a rule which gives an exact answer also for polynomials of degree 4?
Due Thursday, October 16
- 6.2: 5, 10, 16, 21, 35, 40, 55, 59
- 6.3: 5, 10, 15, 20, 25, 30, 35, 40
- Bonus: Count the number of (say) .1 x .1 x .1 x .1 hypercubes in the 4-ball of radius 1 centered at the origin to estimate the volume of the 4-ball.
Due Thursday, October 23
- 6.4: 3, 6, 11, 14, 18, 25
- 6.5: 5, 10, 15, 18
- 8.1: 5, 10, 15, 20, 31
Due Thursday, October 30
- 8.2: 5, 10, 15, 20, 31
- Prepare for the exam on Thursday, October 30.
Due Thursday, November 6
- 11.1: 9, 11, 14, 52, 55, 58, 61
- 11.1: For 10, 13, 16, 21, and 35, find the limit and prove your value is correct by giving a formula for producing N given ε.
Due Thursday, November 13
- 11.2: 15, 20, 25, 30, 38, 45, 49
- 11.3: 5, 10, 15, 20, 25, 32
- Bonus: Without consulting a reference, formulate a definition
of the limit of a function f(x) as x→∞.
Due Thursday, November 20
- 11.4: 5, 10, 15, 20, 25, 30, 38
- 11.5: 5, 10, 15, 20, 25
- Bonus: Give an example of a series with alternating signs and lim an = 0 which actually diverges (because |an| isn't a decreasing sequence).
- Bonus: Give a convincing argument that the series 1+1/2-1/3+1/4+1/5-1/6+1/7+1/8-1/9+... diverges.
Due Monday, December 1
- 11.6: 5, 10, 15, 20, 25, 30, 34
- 11.7: 31, 32, 33, 34, 35, 36
- Prepare for the exam on Tuesday, December 2.
Due Thursday, December 11
- 11.8: 5, 10, 15, 23, 26, 31
- 11.9: 5, 10, 14, 25, 29
- 11.10: 5, 10, 15, 22, 37, 41
- 11.11: 5, 15, 18
Due Thursday, December 18
- Prepare for the final exam on Friday, December 19!
Textbook
- Calculus: Early Transcendentals, Fourth Edition, by James Stewart.
Syllabus
- Inverse functions: 1.6, App. D, 3.6
- L'Hospital's Rule: 4.4
- Techniques of Integration: Chapter 7
- Applications of Integration: Chapter 6; Sections 8.1, 8.2.
- Sequences and Series: Chapter 11
Grading Policy
-
Your grade will be computed from six equally weighted components: homework average,
three hour exams, and a final exam (which counts as two components).
Your lowest component
will be dropped and the rest averaged to produce your score for the course.
From time to time I will assign bonus problems. Bonus problems do not count toward
any homework set grade, but success on these problems indicates mastery of the
material and will have good if unspecified effects on your grade. Failure to solve bonus
problems will not hurt your grade, however.
There will be no make up exams. In cases of hardship, let me know of your absence in advance and I will see what accommodation can be made. In cases of emergency, make sure you can document the justification for your absence.
Calculators are not allowed on exams. They may be used, and may occasionally be useful, on homework; a basic calculator will be enough for this class.
Academic honesty is assumed as a matter of course. Cheating on exams will lead to an automatic grade of zero and other consequences.
Study Groups
- Students are encouraged to form study groups of 2-5 people to discuss the homework. A group size of 3 or 4 is ideal. Study groups are also very important when preparing for exams. While students are strongly encouraged to work in groups on homework, each student is responsible for writing up his or her own solutions in his or her own words.
