Calculus II

MATH 1272: Calculus II (Section 20)

Instructor: Paolo Codenotti
Lectures: 020 LEC: 9:05 - 9:55 AM, MWF, Anderson Hall 210
Final Week Office Hours:
Lind Hall 351, Tue 12:00-2:00pm, Wed 3:30-5:30pm
Lind Hall 305, Thu 3:00-5:00pm
Email: pcodenot (at) umn (dot) edu
Textbook: Stewart, “Calculus: Early Transcendentals”, 7th Ed, Vol 1.
- on reserve at the Mathematics Library, 310 Vincent Hall

Index:

Announcements
Resources
Homework
Review and Extra Problems
Lecture Notes and Topics
TAs and office hours

Announcements:

Final Week Office Hours:
Lind Hall 351, Tue 12:00-2:00pm, Wed 3:30-5:30pm
Lind Hall 305, Thu 3:00-5:00pm
Final review page , common to all sections of Calculus 2.
All students must have their official University I.D. card with them at the time of the final exam and must show it to one of the proctors when handing in their exam. The proctor will NOT accept a final exam from a student without an I.D. Card
Homework 11 solutions
Problems for vectors (not to be turned in):
- 12.1: 5, 7
- 12.2: 13, 19, 27
- 12.3: 5, 19 (exact only), 29
- 12.4: 5, 15, 31(a)
- 12.5: 33
Solutions to midterm 1, midterm 2, and midterm 3 posted.
Homework 11 Due THURSDAY December
Homewrk 10 solutions
Homework 9 solutions

Resources:

Syllabus (in pdf format)
Moodle log in for grades and other information.
Undergraduate Mathematics . Check out the math department webpage for information about classes, registration, and other resources.

Homework:

All homework are due at the beginning of the discussion session.
No late homework will be accepted, however, your lowest two scores will be dropped.

Homework 11 : solutions
Homework 10 : solutions
Homework 9 : solutions.
Homework 8 : solutions.
Homework 7 : solutions .
Homework 6 : solutions There are 2 issues with the solutions:
- Problem 9.3.46: It is easier to model the amount of carbon dioxide, instead of the percentage. We will talk about this more in class, but the resulting differential equaiton doesn't correctly model the problem. One quick check is the constant solution, which should be the same as the concentration of the air coming in.
- Problem 9.6.4: The frogs and crocodiles should be inverted: Q(t)=number of crocodiles, R(t)=number of frogs.
Homework 5 : solutions
Homework 4 : solutions
Homework 3: Not to be turned in Solutions; I highly suggest to (attempt to) solve the problems before looking at the solutions.
Section 7.3: 16, 24, 32(a);
Section 7.4: 16, 26;
Section 7.5: 60, 68;
Chapter 7 Review: 18, 36.
Homework 2: (Due September 18) Solutions.
Homework 1 : (Due September 11) Solutions .

Review and extra practice problems:

Final review: see the common page to all the sections.
Midterm 3 study guide .
solutions part 1 (Polar and Sequences) , solutions part 2 (Series).
Review Session: Monday November 26 6-9pm in Vincent 16.
Instructor extra office hours: Monday November 26 2:30-4:30pm.
More resources:
- Flow chart for series convergence/divergence tests on Randolph Knoch's webpage (This includes Taylor Series, which we have not yet done).
- Extra practice problems below (they are also in the study guide).
- Old tests (as usual, we did not cover exactly the same material as in previous years, so these may be different).
  The Fall 2011 midterm is available (look at Midterm 3 and 'Exam 3 key') here: http://math.umn.edu/~knoc0004/docs/1272%20Lecture%20S%202011/Midterm%20Exams/
  The Spring 2012 midterm is available here: http://www.math.umn.edu/~daristof/1272_mid3.pdf
Midterm 2 study guide ( solutions )
If you want additional practice, you can look at old tests, although we did not cover exactly the same material:
The Fall 2011 midterm is available (look at Midterm 2 and 'Exam 2 key') here: http://math.umn.edu/~knoc0004/docs/1272%20Lecture%20S%202011/Midterm%20Exams/
The Spring 2012 midterm is available here: http://www.math.umn.edu/~daristof/1272_mid2.pdf
Midterm 1 study guide . It includes practice problems and the formula sheet you will be given in the exam.
Study guide solutions: part 1 (substitution, approximate integration, and integration by parts), part 2 (trigonometric integrals and trigonometric substitution), part 3 (partial fractions), part 4 (more partial fractions), part 5 (improper integrals).
Review Problems (choose the ones in the topics you remember least, do more of the end of chapter review problems if you need it and have time):

Limits: Chapter 2 Review problems: 3, 9, 15, 23, 29;
Derivatives: Chapter 3 Review problems: 13, 19, 27, 51, 87;
Integrals: Chapter 5 Review problems: 5, 11, 29, 33, 43.

For additional review problems, check out Randolph Knoche's page for MATH 1271 here.
The website has solved homeworks, lectures, exams, and more. Week 2: To review u-substitution, practice with problems from section 5.5 in the book. To see the solution to many of these problems (some of the numbers don't quite match up, because it's an old version of the book), look at Randolph Knoche's page here
Week 1 Extra Practice Problems:
Section 7.7: 11, 15, 21, 31, 33.
Section 7.1: As many of the odd numbered problems 3-36 as you can stand.
Weeks 2-4 See the review for the first midterm.
Week 5
Section 8.1: 11, 13, 37
Section 8.2: 5, 9
Section 8.3: 27, 31, 33
Section 8.4: 5, 7, 17, 19
Section 8.5: 7, 8, 11
Week 6
Section 9.1: 3, 5, 7, 9
Section 9.2: 19, 23
Section 9.3: As many of the odd numbered problems 1-21 as you want.
Week 7
Section 9.3: 45
Section 9.6: 2 (plus find equilibrium solutions), 3
Section 9.Review: 17, Concept Check and T/F quiz (except 6 in CC, and 5, 6 in T/F)
Section 10.1: 7, 9, 15
Section 10.2: 11, 33
Week 8 (and monday of week 9)
Section 10.2: 31, 41
Section 10.3: 5, 11, 17, 25, 57
Section 10.4: 7, 9, 27, 41
Week 9 (WF)
Section 11.1: 71; 25-54 (as many odd problems as you want, they will come in handy).
Week 10
Section 11.2: 5, 15, 23, 31, 43, 73, 79 (we did this in class), BONUS (FOR FUN): 87
Section 11.4: 3, 7, 9, 15, 17, 19, 29, 31 (we did this in class), 41.
Week 11
Section 11.3: 11, 13, 19, 25
Section 11.5: 11, 15, 17
Section 11.6: 9, 21, 31, 35
Section 11.7: any of the odd ones.
Week 12
Section 11.8: odd ones 3-27
Week 13 and monday week 14
Section 11.9: 7, 25
Section 11.10: 1, 7, 15, 33, 43, 49
Weeks 14-15 (vectors)
12.1: 5, 7
12.2: 13, 19, 27
12.3: 5, 19 (exact only), 29
12.4: 5, 15, 31(a)
12.5: 33

Lecture Slides:

After every lecture I will post the slides here.
These are not a good substitute for notes, as they will be quite sparse, but they may come in handy to remember the topics discussed.

Week 1 (September 5-7)

Wednesday Sept. 5: review of sections 5.1-5.3, section 7.7
Friday Sept. 7: end of section 7.7, beginning of section 7.1.

Week 2 (September 10-14)

Monday Sept. 10: Integration by parts (section 7.1), review of substitution rule (section 5.5), some trigonometric integrals (beginning of section 7.2).
Wednesday Sept. 12: Integrating cos^m sin^n (Section 7.2), beginning of trigonometric substituion (section 7.3).
Friday Sept. 14 : Integrating tan^m sec^n (Section 7.2), more trigonometric substituion (section 7.3).

Week 3 + Monday-Wednesday of Week4 (September 17-26)

Monday Sept. 17: Finished trigonometric substitution (section 7.3), and started partial fractions (section 7.4).
Wednesday Sept. 19: More on partial fractions (section 7.4). The most important (and general) example we went over was the integral of 1/(x^2 - a^2) (example 3 from the book section 7.4)
Friday Sept. 21 and Monday Sept. 24 : Finished partial fractions (section 7.4), started improper integrals (section 7.8)
Wednesday Sept. 26: Finished improper integrals (section 7.8) and midterm review.

Friday of Week 4 (September 28): Arc Length (Section 8.1).

Week 5 (October 1-5):

Monday October 1: Review of differentials (Section 3.10), Surface Area (Section 8.2), Center of mass (Section 8.3), Consumer Surplus (Section 8.4).
Wednesday October 3: Cardiac output (Section 8.4), Probability (Section 8.5)
Friday October 5: Probability (Section 8.5).

Week 6 (October 8-12)

Monday October 8: Models of Population Growth (Section 9.1); some specific examples of Euler's method (Section 9.2), although we did not use that name yet; finding all solutions to a separable differential equation in a specifc case (Section 9.3).
Wednesday October 10: Modelling using differential equations (Section 9.1) and Separable differential equations (Section 9.3).
Friday October 12: Two examples of separable differential equations: a mixing problem (Section 9.3) and logistic population growth (Section 9.4).

Week 7 (October 15-19)

Monday October 15: Finished mixing problem example (Section 9.3), Euler's method (Section 9.2)
Wednseday October 17: Predator-Prey models (Section 9.6).
Friday October 19: Midterm Review (see the study guide), parametric curves (Section 10.1)

Week 8 and Monday of Week 9 (October 22-29)

Monday October 22: Cycloid (Section 10.1), tangents and the beginning of area for parametric equations (Section 10.2).
Wednesday October 24: Midterm review, area and arc length for parametric equations (Section 10.2).
Friday October 26: arc length of the cycloid (Section 10.2), polar coordinates (Section 10.3).
Monday October 29: more on polar coordinates: intersections (Example 3 from Section 10.3), tangents (Section 10.2), and area (Section 10.3).

Week 9 Wed-Fri (Oct 31-Nov 2)

Wednesday October 21: Sequences (Roughly the first half of Section 11.1)
Friday October 21: More on sequences (Section 11.1, except the Monotnic Sequence Theorem.)

Week 10 (Nov 5-9)
Thanks to Brendan Ames for the slides from Monday.

Monday November 5: Monotonic Sequence Theorem (Section 11.1), definition of infinite series and their convergence, and power series (Section 11.2)
Wednesday November 7: More on series: finding closed form expressions for partial sums, e.g. by telescoping sums; linearity of series; the vanishing condition and divergence test (Section 11.2)
Friday November 9: More on the divergence test (Section 11.2), Comparison Theorem and Limit Comparison Theorem (Section 11.4). We showed that sum of 1/n diverges and sum of 1/(n squared) converges.

Week 11 (Nov 12-16)

Monday November 12: Root and Ratio test for non-negative series (Section 11.6), p-series, and started the Integral Test (Section 11.3).
Wednesday November 14: Integral test (section 11.3), and alternating series (Section 11.5). We also talked about general strategy for testing the convergence of series. The book talks about such strategy in section 11.7. The book is somewhat more systematic than what we did in class, so it might be good to read.
Friday November 16: Alternating series test (Section 11.5), absolute convergence, conditional convergence (Section 11.6).

Week 12 (Nov 19-21)

Monday November 19: review of Ratio and Root test for absolute convergence (11.6), power series (11.8).
Wednesday November 21: Why Series + Series review.

Week 13 (Nov 26-30)

Monday November 26: Midterm Review.
Wednesday November 28: Approximating functions by Taylor Polynomials (Sections 11.10, 11.9).
Friday November 30: Derivatives and Integrals of power series (Section 11.9), Taylor Series and Taylor's Theorem (Section 11.10)

Week 14 (Dec 3-7)

Monday December 3: Recap of Taylor series so far, manipulation of series, when is the taylor series equal to the function? (Sections 11.9, 11.10).
Wednesday December 5: Using Taylor's theorem to approximate functions, e is irrational (11.10). 3D-coordinate systems (12.1).
Friday December 7: Vectors (12.2), Dot product (12.3).

Week 15 (Dec 10-12)
- Monday December 10: Cross product (12.4), planes (12.5).
- Wednesday December 12: Review (see the final study guide for topics).
Teaching Assistants:
- Heidi Goodson (email: goods052 (at) umn (dot) edu)
  Office Hours: Vincent Hall 552, Monday 11:30-1:00, Wednesday 3:30-4:30, Thursday 11:30-1:00
  Sections 021 and 026.
- Randolph Knoche (email: knoc0004 (at) umn (dot) edu)
  Office Hours: Vincent Hall 262,
  Mon 12:20-1:10, Tue 8:00-8:50 and 10:10-11:10
  Thu 8:00-8:50, Fri 10:10-11:00 and 12:20-1:10
  Section 022.
- Mary Sylvia Agwang (email: agwan003 (at) umn (dot) edu)
  Office Hours: Vincent Hall 456,
  Mon 1:30-4:30pm
  Wed 1:30-2:30pm
  Fri (by appointment only) 1:30-2:30pm
  Sections 023 and 025.
- Alanna Hoyer-Leitzel (email: hoyer025 (at) umn (dot) edu)
  Office Hours: M 2-4pm, W 10am-12pm
  Sections 024 and 027.