# MATH1120 - Calculus II, Fall 2018MATH1120, Fall 2018

## Section Materials

While general course materials can be found on the Course Website, materials relevant to my section can be found here:

## Section Schedule

Before every class, make sure to complete the pre-class assignment. These assignments will be turned in at the start of class. During class, we will be discussing the pre-class assignment and working on worksheets. These Problem Sets will not be graded nor required to be submitted. For Homework Assignments, please see the relevant section on Blackboard.

Session Pre-class In-class
24 Aug

27 Aug Read Sections 5.4 and 5.5. Come to class with a short paragraph explaining the relationship between a definite integral and an indefinite integral.
29 Aug Read Section 5.6. Write a small proof of part (b) of Theorem 8. Verify with an odd function of your choice.
31 Aug Read Section 6.1. Make a vocabulary list of words and phrases that are important to understanding this section.

03 Sep No Class -- Labor Day
05 Sep Read Section 6.2. Write a short paragraph explaining why using shells to compute volumes instead of disk/washers might be more appropriate?
07 Sep Read Section 6.3 and 6.4. Explain how one computes the arc length of a smooth curve and the surface area of a solid of revolution. Use $$y = \sqrt{1-x^2}$$ and the corresponding solid of revolution obtained by revolving about the x-axis.

10 Sep Read Section 6.5. Explain how one would go about representing quantities using integrals to solve problems.
12 Sep Read 8.1. Take one of the algebraic techniques discussed in the section and explain how one uses it to compute definite integrals.
14 Sep Read 8.2. Write a paragraph explaining the method of integration by parts.

17 Sep Read 8.3. Summarize the general approach to computing antiderivatives of functions involving algebraic combinations of trigonometric functions.
19 Sep Read 8.4. What is the motivation for Trigonometric Substitution? How do we use this technique? What is its connection to u-substitution?
21 Sep Pick 2 problems from the textbook from any of the sections we've covered and write a full solution to them.

24 Sep Pick 3 problems from the textbook from any of the sections we've covered and write a full solution to them.
26 Sep Read 8.5. Create a vocabulary list for this section and define the terms on your list. Outline the general steps to integrating rational functions.
28 Sep Make a list of the integration techniques we've covered. Write a paragraph describing these techniques and how they are used to compute antiderivatives.

01 Oct Read 8.7. Create a vocabulary list for this section and define the terms on your list. Explain error estimates in the context of the Trapezoidal and Simpson's Rule. Make sure to explain the inequalities given in the textbook.
03 Oct Read 8.8 (up to pg 514). Create a vocabulary list for this section and define the terms on your list.
05 Oct Finish 8.8. Compare and contrast the Direct Comparison Test and the Limit Comparison Test.

08 Oct No Class -- Indigenous People's Day
10 Oct Read 7.2 and 9.1. Create a vocabulary list for these sections and define the terms on your list.
12 Oct Pick a problem from 7.2 and write up a solution for it.

15 Oct Read 9.2. Give a definition for First-Order Linear DEs and rewrite the derivation of the Method of Integrating Factors in your own words.
17 Oct Read 9.3. Show that the family of curves that lie orthogonal to the family of circles centered at the origin consists of lines that pass through the origin.
19 Oct Read 9.4. Create a detailed caption for Figure 9.25 using the vocabulary from the section.

22 Oct Create a flow chart that can help guide a peer to ace a DE problem on the exam.
24 Oct Read 10.1. Explain in your own words what an infinite sequence is and what it means for one to converge or diverge.
26 Oct Prove one of the three first limits of Theorem 5 on page 584.

29 Oct Read 10.2. When we say an infinite series converges, what do we mean? Your response should rely upon sequences.
31 Oct Summarize the the importance of the three subsections on pages 595-597 of 10.3.
02 Nov Read 10.3. Explain the p-series "test" and how it is a corollary of the Integral Test.

05 Nov
07 Nov Read 10.4. What are some common convergent and divergent infinite series you can rely on for comparison tests?
09 Nov Read 10.5. Write a user guide for the Absolute Convergence Test, Ratio Test, and Root Test.

12 Nov Read 10.6. Determine the convergence type of a geometric series.
14 Nov Read 10.7. Determine the interval of convergence for the geometric series $$\sum_{n=0}^\infty x^n$$.
16 Nov Read 10.8. Compute the Maclaurin series for the geometric function $$f(x) = \frac{1}{1-x}$$. For what values of $$x$$ does this Taylor series converge?

19 Nov Read 10.9. Show that the Taylor series generated by $$f(x) = e^x$$ at $$x=0$$ converges to $$f(x)$$ for every real value of $$x$$.
21 Nov No Class -- Thanksgiving Break
23 Nov No Class -- Thanksgiving Break

26 Nov Read 10.10. A special antiderivative of the sinc function $$f(t) = \frac{\sin t}{t}$$ is known as the Sine Integral defined as $$Si(x) = \int_0^x f(t) \, dt$$. Compute the Maclaurin series representation for this antiderivative.
28 Nov Projects Day
30 Nov Finals Review -- Submit questions for Finals Review by 28 Nov.

03 Dec Finals Review -- Submit questions for Finals Review by 28 Nov.