Lecture Notes & Schedule
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. 18-22 | Reading break | |
| 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.
Full text
The FULL TEXT can be downloaded here (5MB), which includes the table of contents as well as an index. The full text is hyperlinked to facilitate navigating the document.
Please alert your instructor regarding typos or errors.
Sections
- Areas, Volumes, and Simple Sums
- Areas, Riemann Sums
- The Fundamental Theorem of Calculus, Definite Integral
- Applications of the Definite Integral to Velocities, and Rates
- Applications of the Definite Integral to Mass, Volume and Arc Length
- Techniques of integration
- Improper Integrals
- Continuous probability distributions
- Differential equations
- Sequences
- Series
- Taylor Series
Note that hyperlinks referencing other chapters only work in the full text of the course notes above.
Hard copies
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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).
