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
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
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 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.
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):
For additional review problems, check out Randolph Knoche's page for
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.
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).
Monday November 12: Root and Ratio test for non-negative series
(Section 11.6), p-series, and started the Integral Test (Section
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).