**Integral Calculus with Applications to Commerce and Social Sciences.**

- When and where: Monday-Wednesday-Friday 8:00am to 9:00am MATX 1100.
- My office: Chemical & Biological Engineering building 437 (here).
- e-mail: rakotonirina@math.ubc.ca
- Office hours: Thursday 12am to 01pm (LSK300C). Or at my office by
**appointment**if you can’t make these hours.

- Final exam (50%)
- 2 midterms (17% + 17% = 34%)
- WebWork assignements (10%)
- Weekly homeworks (given Friday, due: Monday 8am
**before class**) (6%)

**All information about the course is at the common course website**

*These are two links for last year classes (many exam samples): Winter 2015 Term 2 or Winter 2015 Term 2*

**MATH 105 final exam notice**

- 60% of the final exam will consist of the questions which are similar to the questions in the list below.
- the other 40% is a combination of what we’ve taught

**Final: **April 24 from 3:30 pm to 6:00 pm

**Lecture notes and related exercises**

Week 1: Vectors + examples on dot product

- Section 11.1: 9, 11, 15, 31, 33, 37, 41, 45
- Section 11.2: 7, 9, 43, 67, 69
- Section 11.3: 3, 49
- YouTube (external links): vectors in 3D, Length of vectors, Dot product, Dot product and angle between 2 vectors, Addition of 2 vectors, Subtraction of 2 vectors, Multiplication by a scalar

Week 2: Planes + Function 2 variables + Review notes derivatives + Partial Derivatives

- Section 12.1: 1, 3, 11, 13, 29, 31, 33.
- Section 12.2: 1, 3, 7, 11, 15, 17, 19, 31, 33, 35, 37, 53, 65
- Section 12.4: 1, 3, 5, 17, 21, 23, 25, 29, 33, 37, 41, 43, 61, 63

**Homework week 2: Homework + Solutions**

Week 3-4: Min/Max Problems + Absolute Min/Max + Lagrange Multipliers

- Section 12.8: 13, 19, 21, 23, 25, 27, 35, 37, 39, 43, 45, 47, 51, 61
- Section 12.9: 5, 11, 13, 27, 29, 35, 37, 47, 49, 53, 55
- Parametric equation (circle) for abs. min/max

**Homework week 3: Homework + Solutions**

**Homework week 4: Homework **

Week 5: Integrals_1 (corrected) + Integrals_2

- Section 5.1: 5, 7, 21, 23, 27, 31, 33, 35, 39, 41, 55, 57, 59, 61, 63
- Section 5.2: 3, 5, 9, 21, 23, 27, 31, 33, 35, 37, 39, 41, 43, 45, 47, 51, 69, 71
- Youtube: Sigma notation for sums, Sum and sigma notation

Week 6: Integral_2 (continuation) + Substitution + Integration by Parts

- Section 5.3: 5, 9, 11, 17, 19, 21, 23, 25, 37, 39, 45, 61, 63, 65, 67, 69, 75, 85, 99, 101
- Integral Table (from http://integral-table.com)
- Section 7.2: 7, 9, 11, 15, 17, 19, 25, 27, 31, 35, 37
- Lots of examples on substitution: Substitution (Dr. Kouba)
- Youtube: Antiderivatives
- Trigonometric Identities (http://www.sosmath.com): Trig Sheet

**Homework week 6: Homework + Solutions**

Week 7: Trigonometric Integrals

- Section 7.3: 13, 15, 21, 25, 35, 37, 41, 53, 59, 61

Week 8: Trigonometric Substitution + Partial Fractions

- Section 7.4: 7, 9, 17, 25, 27, 35, 37, 47, 59, 63, 65
- Section 7.5: 1, 3 a, 3 b, 15, 19, 21, 27, 29, 63, 65, 67, 71, 77, 79

**Homework week 8: Homework + Solutions**

Week 9: Numerical Integration + Improper Integration + Introduction to Differential Equation

- Section 7.7: 7, 9, 11, 13, 15, 17, 39, 41, 49, 51, 59
- Section 7.8: 9, 11, 15, 17, 27, 43, 45, 71, 73
- Section 7.9: 17, 19, 25, 27, 29, 31, 33, 39, 63, 65, 6

Week 10: Probability + Probability Appendix + Probability (continue)

Week 11: Sequences and Infinite Series + Infinite Series + Geometric Series/Sum

- Section 8.1: 3, 7, 9, 15, 19, 21, 23, 29, 31, 35, 57, 69, 71, 73, 75, 77
- Section 8.2: 3, 5, 9, 11, 17, 29, 45, 47, 49, 75, 79, 81
- Section 8.3: 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 39, 49, 61, 63, 69

**Homework week 11: Homework + Solutions**

Week 12: The divergence and integral tests + The ratio and comparison tests

- Section 8.4: 3, 5, 9, 13, 21, 23, 25, 29, 31, 45, 47, 49, 53, 55, 57
- Section 8.5: 9, 11, 13, 15, 17, 27, 29, 31, 33, 35, 37

Week 13: Power Series + Differentiating and integrating Power Series + Taylor/Maclaurin Series

- Section 9.2: 17, 19, 21, 23, 25, 27, 29, 31, 33, 41, 45, 47, 49, 63, 65, 67
- Section 9.3: 9, 11, 15, 23, 25, 29, 33, 35
- Section 9.4: 25, 27, 29, 31, 55, 61]

*Past finals can be found here and their solutions here*

Dear Students, The MLC is doing two identical review sessions for MATH105 students at 2pm-4pm and 4pm-6pm at April 20th.The location is FDRM153. The facilitator is Abhishek Kumar Shukla.