# Math 105-952, Summer 2013

## Integral Calculus with Applications to Commerce and Social Sciences

 Instructor: Cihan Okay Email: okay (at) math (dot) ubc (dot) ca Web Page: http://www.math.ubc.ca/~okay/index.html Lectures: Mon/Thu/Fri 13:00-15:00, Wed 13:00-14:00 MATX 1100 Text: Calculus: Early Transcendentals, third (or second) custom edition for UBC, by Briggs and Cochran Office Hours: Wednesday 14:00-16:00 MLC , LSK 303C

 Webwork TA: Xiaochen Yu (Jason) Email: xiaochen_yu (at) hotmail (dot) com Office Hours: Mon 15:00-16:00, Thu 11:00-12:00 MLC , LSK 301-302

11/08/2013:
• Office Hour: Monday Aug 12, 13:00-14:00, LSK 303D.
08/08/2013:
• quiz 6: There will be a quiz this Friday. There will be one problem on Taylor series of a function and its radius of convergence.
07/08/2013:
• #### Final Exam : Wednesday Aug 14, 12:00-14:30, LSK 201(<--note the location).

• The final exam is cumulative.
• A copy of the formula sheet that will be provided in the final exam.
• Here is a link to an online module that may be helpful in reviewing the material on sequences and series.

Problem set from Math 105, 2012W Term 2.

• Math exam resources wiki is a wiki of solutions to previous final exams prepared by math graduate students. There are currently solutions for most of the April 2011 and 2010 exams, and the Math 101 and Math 103 exams may also be useful.
• Solutions to Sample Final: See Math 105-921, section "Final Info".
• Math 105 2011W final exam.
01/08/2013:
• quiz 5: There will be a quiz this Friday. There will be one problem on convergence of geometric series.
29/07/2013:
• Office hour: Tuesday July 30, 13:00-14:00, LSK 303D.
26/07/2013:
• quiz 4: There is a quiz on Monday, July 29th. There will be one problem on Differential equations and another on Probability. In the probability problem you are expected to remember the relation between PDF and CDF for continuous random variables.
• #### Midterm 2: Wednesday July 31, 13:00-13:50, in class.

• Midterm syllabus: The midterm covers everything in the course syllabus covered in week 3 and week 4 (refer to the week-by-week schedule below).
• Books, notes and calculators are not allowed in the midterm, but this formula sheet will be provided.
• Midterm drafts: 1 , 2 , 3 , 4 , 5 .
• Here are a few review problem sets.
25/07/2013:
• quiz 4: There will be 2 questions: One initial value problem and one probability. In the probability problem you are expected to remember the relation between PDF and CDF for continuous random variables.
18/07/2013:
• quiz 3: There will be 2 questions, the substitution rule and integration by parts.
• Midterm 1 solutions
14/07/2013:
• Office hour: Tuesday July 16, 13:00-14:00, LSK 303D.
11/07/2013:
• quiz 2: Lagrange multipliers; one of the problems in page 31 or 32 (according to the handwritten numbering) in the lecture notes, Week 1 and Week 2.
• quiz 1 solution.
05/07/2013:
• quiz 1: There will be a quiz on Friday at the end of the class.
04/07/2013:
• You are obligated to be here for the entire exam period which runs from Tuesday, August 13th to Saturday, August 17th inclusive. Yes, there are exams on a Saturday. The schedule should be released around July 12th. Students who make plans to leave before the end of the exam period, before the schedule has been released, will not be assisted with an alternate sitting of a Math exam. Anyone with a legitimate conflict can contact me and I'll assess their situation. Those who are legitimate will be asked to go to their Faculty Advising Office to request deferred standing in the course and they will write an exam in a future term's regularly scheduled final exam period. That decision is up to their Faculty. Family vacations or other such optional events will not lead to a deferred exam.

### Course information

• Week 1 and Week 2:
• Planes and surfaces (12.1)
• Graphs and level curves (12.2)
• Partial derivatives (12.4)
• Maximum/minimum problems (12.8)
• Lagrange multipliers (12.9)
• Approximating areas under curves (5.1)
• Definite integrals (5.2)
• Week 3 and Week 4 :
• Fundamental theorem of calculus (5.3)
• Substitution rule (5.5)
• Integration by parts (7.1)
• Trigonometric integrals (7.2)
• Trigonometric substitutions (7.3)
• Partial fractions (7.4)
• Numerical integration (7.6)
• Improper integrals (7.7)
• Introduction to differential equations (7.8)
• Probability
• Continuous random variable
• Mean and variance
• Week 5 and Week 6 :
• Sequences (8.1-8.2)
• Infinite series (8.3)
• The divergence and integral tests (8.4)
• The ratio, root and comparison tests (8.5).
• Approximating functions with polynomials (9.1)
• Properties of power series (9.2)
• Taylor series (9.3)
• Working with Taylor series (9.4)
See the following sections from Math 105, 2012W Term 2
• Need a review of differential calculus?
• Course Outline (Learning Goals)
• Practice problems

### Practice problems

• Week 1&2:
• Section 12.1: 2-4, 11-14, 23-24, 25-28.
• Section 12.2: 1-4, 7, 11-18, 28-33, 36, 38(b) (c), 49.
• Section 12.4: 1-30, 56-73. For problems 72 and 73, show differentiability using Theorem 12.5. You do not need to produce $\epsilon_1$ and $\epsilon_2$.
• Section 12.8: 15-28, 29-36.
• Section 12.8: 37-44, 49-52, 62.
• Section 12.9: 1, 2, 4, 5-10, 20, 21, 38-41, 45-47.
• Section 5.1: 3-8, 17-26, 31-33, 34(i), 49-56.
• Section 5.2: 19-50, 66-69.
• Week 3&4:
• Section 5.3: 12, 17, 18, 19, 22, 25, 30, 32, 37, 39, 51-57.
• Section 4.8: 11, 13, 17, 19, 22, 25, 27, 28,
• Section 5.5: 35, 36, 37, 40.
• Section 7.1: 7-28, 29, 32, 33.
• Section 7.2: 9-32, 40-49.
• Section 7.3: 7-46, 48-55.
• Section 7.4: 5-18, 49, 51-53, 57, 58, 60-62.
• Section 7.6: 7-10, 35-38, 44-47.
• Section 7.7: 5-20, 27-36.
• Section 7.8: 9-20, 23-32, 53-59.
• Probability practice problem set .
• Week 5&6:
• Section 8.1: 6-16, 23--30, 47--58, 60--67.
• Section 8.2: 1--4, 9--26, 35-42, 63, 67, 69.
• Section 8.3: 7-46, 59
• Section 8.4: 9-30, 44-49.
• Section 8.5:
• Section 9.1: 1--46, 53--64.
• Section 9.2: 1--44, 46--49, 52--57.
• Section 9.3: 9--28.
• Section 9.4: 21--26.

### Assignments

There will be weekly homeworks on WebWork. In total there will be 6 assignments, 5 of which will count toward your overall grade.