# MATH 172 - Weekly Schedule

## Textbook:

Calculus Early Vectors, Stewart

## Suggested Schedule

• Week 1
• Sections 6.1–6.5
Except for Section 6.5 this material has been covered in 171, and will be a review.
• Week 2
• Sections 6.6, 7.1–7.2
• Week 3
• Sections 7.3–7.5
Section 7.5 contains the mean value theorem for integrals, a result we expect students to know. Rather than relegate its proof to the exercises, it is suggested that the intermediate value theorem for continuous functions be used to prove this result. Note: In the applications sections of Chapters 7 and 9, it is important for students to see the integrals derived from their underlying Riemann sums.
• Week 4
• Section 8.1–8.4
Students should be able to derive the integration by parts formula. Do not spend a great deal of time in Section 8.2. Students should learn how to integrate the following standard forms for small values of n
$$\int\sin^{n}{x}, dx$$ $$\int\cos^{m}{x}, dx$$ $$\int\sin{mx} cos{mx}, dx$$

Students are expected to know the anti derivatives of all 6 trig functions, but don't get bogged down with all of the myriad possibilities. In particular don't worry about the sec-1 substitution in Section 8.3. In Section 8.4 don't ask students to do much more than

$$\int\frac{dx}{(x-a)(x^{2}+1)}$$
Students of course should be able to transform integrals into the above or an equivalent form.
• Week 5
• Exam 1 (through Section 8.4), then Section 8.9, improper intergrals.
• Week 6
• Sections 8.8, 9.1–9.2
Section 8.8 is on numerical integration. Cover the trapezoidal rule and the error estimate. Simpson's rule does not have to be covered, and in the interest of time probably should not be.
• Week 7
• Sections 9.3 and 9.6
• Week 8
• Section 10.1
Give Exam 2 about now. It should cover the material through Section 9.6.
• Week 9
• Sections 10.1–10.2
Spend some time in Section 10.1. Be sure to prove some of the limit theorems, and show how the monotone convergence theorem is used. Students are expected to be able to state this theorem. The summation formulas, e.g., the series of a sum is the sum of the series, and similar algebraic properties of convergent series should be proven, and students held accountable for these proofs. Students are expected to know the summation formula for a geometric series, be able to derive it, and know where it is valid.
• Week 10
• Sections 10.3–10.4
The text discusses four tests for the convergence of a positive term series, comparison and limit comparison, integral, and ratio. Students should be able to state these tests in writing, and be able to use them. The same comments apply to the Alternating Series test. Students should know that the harmonic series diverges, and the alternating harmonic series converges, and be able to explain why.
• Week 11
• Sections 10.5–10.6
• Week 12
• Section 10.7 and 10.9
Students should be able to use Lagrange's formulas for the remainder (error) term when approximating a function with its nth order Taylor polynomial. The integral form for the remainder term could also be derived.
• Week 13
• Section 10.8
Can be covered at the instructors discretion. In the Fall semester, Thanksgiving break occurs in week 13.
• Week 14
• Exam 3 and review.