Math 129 is not coordinated and will take its own final exam. Math 129 has the same basic requirements as Math 126 but typically includes additional topics and applications from Physics and Engineering.
The following table lists the minimum set of topics to be included in this course. The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.
There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.
|5.6 – 5.8||Inverse Functions, L’Hopital’s Rule||4|
|6.1-6.3, 6.5, 6.6||Techniques of Integration||8|
|7.1 – 7.6||Applications of Integration||9|
|8.1 – 8.8||Sequences and Infinite Series||14|
|9.3 – 9.4||Polar Coordinates||3|
OPTIONAL TOPICS (time permitting)
- Section 6.4 on Integration with Tables or CAS
- Section 7.7 on Differential Equations
- Proof by Induction as it relates to Chapter 8
- Section 9.1 on Parametric Curves
- Section 9.2 with more on Parametric Curves
- Other outside topics, readings, videos, or materials the Instructor deems relevant
If all course instructors in a given semester cover a particular topic, they may choose to include that topic in the common final exam.
By the end of this course, students should be able to:
- Understand and apply advanced techniques of integration, including integration by parts, trigonometric substitutions, and partial fraction decomposition.
- Compute integrals via inverse trig functions and hyperbolic functions.
- Evaluate improper integrals and understand their convergence properties.
- Use l’Hôpital’s rule to determine limits of functions.
- Compute the length of curves, surface areas of revolution, and volumes of solids of revolution using integration.
- Apply numerical integration techniques, such as Simpson’s rule and the trapezoidal rule, to approximate definite integrals.
- Explore sequences and series, including the concepts of convergence, divergence, and the relationship between sequences and functions.
- Determine the convergence and divergence of infinite series using various tests, such as the comparison test, ratio test, and integral test.
- Apply power series representations to approximate functions and/or solve differential equations.
- Analyze Taylor and Maclaurin series expansions and use them to approximate functions to a desired degree of accuracy.
- Understand polar coordinates in R2 and apply them to graph curves and evaluate integrals.