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, â€śCalculus: Early Transcendentalsâ€ť, 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.
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).
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
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.
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.
Monday Sept. 10: Integration by
parts (section 7.1), review of substitution rule (section 5.5),
some trigonometric integrals (beginning of section 7.2).
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)
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).
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.
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).