Math 2414: Calculus II
Here are some extra homework assignments and some other study sheets you might find useful during the course. They are all available in Adobe Acrobat format (go here if you need to download the free Acrobat reader; most computers will have it on them already) or in RTF format (can be read in Microsoft Word or Wordpad). I may add to this during the semester; I will try to announce in class when I do so, however.
Methods of Integration
- Homework assignment 1 on trig integrals. Problems / Answers
- Practice worksheet on integration - Here is the set of practice problems I assigned in class (due-date will be announced in class). Problems / Answers
- Review sheet on integrating products of trigonometric integrals - A former student (Damon Bohls) drew this up to review the "rules" for multiplying products of trig functions. Feel free to use this to study if you find it useful. RTF
- Review sheet on methods of integration - A former student (J LWeiss) wrote up the big review of methods of integration (and how to know which to use) that I give each semester and produced this review sheet. The one thinng I should mention on this is that, despite the numbered order of methods on the left, you really shouldn't go by that. First, try straight substitution. If that doesn't work, look at the form of the integral to decide which method to use. (So, for example, if you are trying to integrate a rational function, i.e., a polynomial divided by another polynomial, you should skip all the intermediate methods and skip straight to partial fractions.) pdf
- Practice problems on integration using Tables - Here are the problems I promised in class to practice using tables to solve integrals on some trickier problemms. Problems / Answers (formula number refers to the table included in your book)
- Practice problems on applications - Here is the set of practice problems I assigned in class, along with the answers. Problems: pdf / html. Answers: pdf / html (If you have problems with fonts in the pdf file, try the html version.)
Sequences and Series
- Extra series homework 1 - This provides some extra practice in deciding which convergence test to use. Thanks to Derrick Rosiles for writing this up and sharing it. pdf / Word document.
- Flowchart on how to decide whether a sequence or series converges or not - A former student (Damon Bohls) typed up a flowchart I drew on the board to make this useful summary of how to choose which of the many tests to use to determine convergence/divergence. pdf / Word document.
Extra credit computer projects
You may choose either one of the following to do for extra credit. (If you are feeling particularly industrious, you could do both. That won't get you double credit, but it will be worth more than just one.) Before you submit this, be sure to check out my Lab Submission Guidelines.
- Extra credit lab
Finding Taylor series expansions of a function and the error introduced by using a finite Taylor polynomial. (html / Mathematica notebook)
- Numerical Integration and Error Approximation
This lab investigates the simpler methods of approximating a definite integral numerically (left-hand sum, right-hand sum, Trapezoid Rule, Midpoint Rule, and Simpson's Rule) and the errors in these methods as a function of the number of subdivisions. (html / Mathematica notebook)
More will be coming later...