# Schedule

Week Topic Notes
Jan. 2-4 Areas and simple sums
Jan. 7-11 Areas and Riemannian sums
Jan. 14-18 The Fundamental Theorem of Calculus
Jan. 21-25 Applications of the definite integral
Jan. 28 - Feb. 1 Volumes and Length
Feb. 4-8 Techniques of Integration
Feb. 11-15 Techniques of Integration, Improper Integrals
Feb. 25 - March 1 Continuous probability distributions
March 4-8 Differential Equations
March 11-15 Sequences
March 18-22 Series
March 25-29 Series, Taylor polynomials
April 2-5 Taylor Polynomials, Review

## Topics & Learning Goals

Please check out the comprehensive syllabus of the course.

# Lecture notes

The course notes were written by professor Leah Keshet and are based on material taught in Math 103 over several years and are constantly being updated.

© Leah Keshet. Not to be copied, used, distributed or revised without explicit written permission from the copyright owner.

## Sections

Note that hyperlinks referencing other chapters only work in the full text of the course notes above.

## Hard copies

You can buy a printed paper copy of this material from Copiesmart on University Boulevard for \$25 including taxes.

Address: Copiesmart, #103 5728 University Blvd. Tel: 604-222-3189, 604-222-3194.

# Errata

Please report typos and errors to your instructor. All corrections are listed below and fixed at the end of term for the benefit of future installments of MATH 103.

### Course Notes

• p.69: Table 3.1, the last column with anti-derivatives should include an integration constant.
• p.195 bottom: The solution includes repetitive information for finding an upper bound: "by noting that for all $$x>0$$

$0 \leq\frac{x}{1+x^3}\leq\frac{x}{x^3}=\frac1{x^2}."$

can be deleted. Identical information is provided in the following sentence.
• p.213: In the integral immediately following Figure 8.2, a factor of $$\pi/12$$ is missing in front of the integral.
• p.229 middle: Note, the statement "If the distribution is non-symmetric, a long tail in one direction will shift the mean toward that direction more strongly than the median." is a very useful rule of thumb to visually assess features of a (probability) distribution. However, it is just a rule of thumb and is not mathematically rigorous.

### Exercises

• p.368: Solution 2.14 (d) should be 81/4 (not 182.25).
• p.368: Solution 10.4 (d) should read monotonically increasing, bounded (and not monotonically decreasing, bounded).