Warning: this is just a rough outline. For actual schedule with due dates, please go to the schedule page.

# Fall 2018 Outline

Hello! Today is .

Sections of Stewart’s Calculus to be covered:

Main Calc II Topics:

• Chapter 11 infinite sequences and series (Sections 11.1-11.6, 11.8-11.11)
• Chapter 7 integration techniques (Sections 7.1-7.4, 7.7-7.8)

A few additional intro to skills and concepts needed for future STEM courses:

• Chapter 9 modeling with differential equations (9.1, 9.3)
• Chapter 10 parametric equations and polar coordinates (10.1-10.4) + arc length 8.1)
• Optional: 8.2, 6.4, 9.4
• Extra: ordinary generating functions

### Rough Outline

Week_ Date_ Day_ Assessment_ Topics
w1 8/27 Tu   introduction, review Calc 1 Chapters 2-4
Th   Go over questions from review Calc 1 Chapters 2-4, Start 11.1 sequences part 1
F   Finish 11.1 sequences part 1, quiz on 11.1 part 1 from Th.
w2 9/3 Tu   11.1 part 3: epsilon-N definitions and arguments, review L’Hospital’s Rule
Th   Sec 11.1 part 2: geometric sequence, monotonic sequence, bounded sequence.
F   quiz, Practice and quiz on sec 11 part 2, 3 (epsilon-N definitions and arguments) and L’Hospital’s Rule and Monotonic sequence theorem. Review sketching rational functions.
w3 9/10 Tu   Do 11.2 part 1: intro series, geometric series, decimal expansion.
Th   group work on Sec 11.2 HW. Discuss reading HW 11.2 part 2: divergence test and harmonic series; 11.2 part 3 proof of divergence test and harmonic series.
F   quiz, on 11.2 part 1,2 (geometric series, divergence test, harmonic series). 11.2 part 4: tellescoping sum and simplest case of partial fraction decomposition
w4 9/17 Tu   11.4 comparison tests and limit comparison tests (practice).
Th   group work and presentations with practicing Limit Comparison Test and Ratio Test, 11.6 part 1: ratio test, part 2: root test
F   quiz, 11.6 part 3: growth rates lecture, 11.5 alternating series lecture,
w5 5 9/24 Tu   review trig identities, 7.2 trig integrals
Th   7.3 trig substitution
F
w6 10/1 Tu   exam 1 (tentative): sequences, series, series tests, trig substitution and trig integrals
Th   7.1 integration by parts
F   7.1 integration by parts and proof by induction
w7 10/8 Tu   7.8 improper integrals type 1: infinite interval,
Th   7.8 improper integrals type 2: bounded interval
F   quiz, Review 7.8 before quiz
w8 10/15 Tu   11.3 integral test and estimates of sum for positive series
Th   11.5 alternating series estimate, application of 11.5 alternating series estimate: proving e is irrational; 11.8 power series
F   quiz, Continue 11.8
w9 10/22 Tu   11.9 representations of functions as power series
Th   Continue 11.9 representations of functions as power series
F   Explain HW 11.9
w10 10/29 Tu   exam 2
Th   11.10 part 1 Intro to Taylor series.
F   11.10 part 3 Explain Taylor’s Inequality example from Reading HW (part 2). Compute limit of functions using series, other uses of series.
w11 11/5 Tu   11.10 multiplication and long division. 11.10 part 4 Practice Taylor polynomials. Ordinary generating functions, golden ratio, 11.1 continued fraction + silver ratio.
Th   10.1 curves defined by parametric equations, introduce an example of a parametric function for a circle graph,
F   quiz, 10.2 calculus with parametric curves, tangent and area,
w12 11/12 Tu   10.2 practice, 10.3 part 1: Euler’s formula
Th   10.3 part 1: polar coordinates
F   quiz, Sketch polar curves using Cartesian graphs, 10.3 part 2: tangent
w13 11/19     Thanksgiving 2018
w14 11/26 Tu   10.4 areas in polar coordinates,
Th   9.1 Modeling with differential equations
F   quiz, 9.3 separable equations
w15 12/3 Tu   9.4 modeling for population growth (graph sketch only)
Th   exam power series (11.10, 11.11), Calculus with parametric equations and polar coordinates (10.1-10.4), and intro to modeling with differential equations (9.1, 9.3, 9.4).
F   exam mini

## List of Sections

• Sections ordered by how they appear in Stewart.

1. 6.4 work (will not cover)
2. 7.1 integration by parts
3. 7.2 trigonometric integrals
4. 7.3 trigonometric substitution
5. 7.4 integration by partial fractions: will be used in logistic differential equation and calculation of inverse Laplace transforms (MATH 2410 “Elementary Differential Equations,” ECE 3101/ENGR 3101 “Signals and Systems,” ME 3220 ”Mechanical Vibrations,” and ME 3253 ”Linear Systems Theory”). Can involve denominators with a double root!
6. 7.7 approximate integration
7. 7.8 improper integrals
8. 8.1 arc length
9. 8.2 (maybe) area of surface of revolution
10. 9.1 modeling with differential equations
11. 9.3 separable equations
12. 9.4 (maybe) models for population growth
13. 10.1 curves defined by parametric equations
14. 10.2 calculus with parametric curves
15. 10.3 polar coordinates
16. 10.4 arcs and lengths in polar coordinates
17. 11.1 sequences
18. 11.2 series
19. 11.3 integral test, estimates of sums
20. 11.4 comparison tests
21. 11.5 alternating series
22. 11.6 absolute convergence, ratio test
23. 11.8 power series
24. 11.9 representations of functions as power series
25. 11.10 Taylor and Maclaurin series
26. 11.11 applications of taylor polynomials