Notes

Welcome! Today is .

Week 1 Wed

• Review l’Hopital’s Rule Sec 4.4
• Sect 1.1 sequences part 1

Week 1 Fri

• Sect 1.1 sequences part 2 only geometric sequence
• Math fun fact: Article: Romance, Continued Fractions, and You did not discuss

Week 2 Wed

• Sect 1.2 intro to series part 1: geometric series and repeating decimal expansions
• Sect 1.2 repeating decimals fun - you don’t need to memorize the pattern unless you enjoy remembering patterns

Week 2 Fri

• Sec 11.1 Def 2, Epsilon-N definition and examples.
  • Example for choosing N if epsilon is given: Example for choosing N
  • Watch these Khan Academy videos: Formal definition for limit of a sequence and Proving a sequence converges using the formal definition

• Sect 1.1 sequences part 2 Example 13 and Monotonic Sequence Theorem (Thm 12)

• Sample quiz week 2

Week 3 Mon

• Sect 11.2 intro to series part 2: telescoping sum, divergence test, harmonic series, properties of convergent series everything but harmonic series

Week 3 Wed

• Explain this joke
• Sect 11.2 intro to series part 2: telescoping sum, divergence test, harmonic series, properties of convergent series harmonic series
• Sec 11.1-11.2 worksheet (practice for week 3 quiz)

• Reading homework sec 11.4 limit comparison test reading HW due Friday

• Problems A: problems A and answer key

Week 3 Fri

• Sample quiz week 3

Week 4 Mon

• Sect 11.4 comparison tests reading homework
• Sec 11.6 part 1: ratio test reading homework

Week 4 Wed

• Sec 11.6 part 2: root test reading homework
• Desmos growth rates demo
• Sec 11.6 part 3: growth rates blank and filled in
• Sec 11.6 part 4: growth rates application blank and filled in
• Strategy for series with positive terms (Sec 11.1-2, 11.4, 11.6) reading homework

Week 4 Fri

• Sec 11.5 part 1: alternating series optional reading hw

• Worksheet: old and new basic skills worksheet and answer key homework

• Quiz week 4: Sample quiz, answer key, extra hw

• Sec 7.2 part 0: trig identities reading homework due Mon

Week 5 Mon

• Sec 7.2 part 1: integrate products of sine and cosine
• Sec 7.2 part 2: integrate products of tangent and secant reading homework due Wed
• Learning Activity Worksheet Sec 7.2 part1, part2 and answer key part1, answer key part2 - homework due Wed
• Worksheet 7.2 trig integrals from 1132 NOT homework
• Sec 7.3 part 2: inverse trig substitution book examples reading homework due Wed

Week 5 Wed

Handed out:

• Sec 7.3 part 1: inverse trig substitution strategies
• Worksheet 7.3 trig substitution from 1132 not homework

• Learning Activity Worksheet Sec 7.3 worksheet and answer key not homework

• Homework Sec 7.2 and 7.3: hw and key homework due Friday
• Reading homework Sec 7.1: integration by parts due Friday

Week 5 Fri

Handed out:

• Homework Sec 7.1 hw and key homework due Monday

• Learning Activity Worksheet Sec 7.1 worksheet and answer key
• Worksheet 7.1 integration by parts from 1132 NOT homework

List of problem presentations

Week 6 Mon

Math fun fact: (Reviewing Integral, cosine, natural log, and e) Is this limerick accurate?

Handed out:

• Exam 1: Ch 11 list of topics + questions + key
• Exam 1: Ch 7 list of topics summary + questions + key
• Exam 1 Sample: questions and key
• Factsheet which you will get on the test

Week 6 Fri

Handed out:

• Sec 7.8 improper integrals part 1: infinite interval
• Sec 7.8 improper integrals part 2: infinite discontinuity and comparison theorems
• Learning Activity Worksheet Sec 7.8 part 1: infinite interval worksheet and answer key not homework
• Learning Activity Worksheet Sec 7.8 part 2: infinite discontinuity and comparison theorems worksheet and answer key reading HW due Monday (last two pages)

• Sec 7.4 partial fraction reading HW due Monday

• Problems B problems due next Friday

One-sided bridge bonus activity

Extra (not printed):

• Worksheet 7.4 partial fractions questions 1 and 2 only from 1132

Week 7 Mon

Handed out:

• Sec 11.3 part 1: Integral Test

• Learning Activity Worksheet Sec 7.8 part 3

• Reading homework sec 7.5 strategy for integration reading HW due Wed

Week 7 Wed

No handouts. Extra practice (not handed out):

• Learning Activity Worksheet Sec 7.4 partial fraction decomposition worksheet and answer key

Week 7 Fri

• Sample quiz week 7

Handed out:

• Sec 11.3 part 2: Estimates of Sums
• Sec 11.5 part 2: alternating series estimation theorem
• Sec 11.8 power series reading homework due Mon
• Sec 11.9 representations of functions as power series reading homework due Mon

Week 8 Mon

Math fun fact: e is irrational and sum of alternating series sum (-1)^k/k!

Handed out:

• Homework Sec 11.8 homework due Wed

Extra practice (not handed out):

• Worksheet 11.8 power series from 1132

Week 8 Wed

Handed out:

• Learning Activity Worksheet Sec 11.9: applying composition and term-by-term integration theorem for power series
• Homework Sec 11.9 blank and anwers/guide homework due Friday

Week 8 Fri

Group work handouts:

• Board work 11.8 power series
• Board work 11.9 power series manipulations
• Pay attention to the True/False question at the end Worksheet 11.9 representation of functions as series from 1132

Week 9 Mon

• Sample quiz week 8 postponed to week 9 Monday

Handed out:

• HW Sec 11.10 part 1 homework due Wed
• Sec 11.10 part 1
• Learning Activity worksheet Sec 11.10 part 1 didn’t have time to do

Math fun fact: Application of Taylor series

• What is the shape of a suspended rope? Images of simple suspended bridges: Austria and Finland. Robert Hooke. St. Louis arch.

• For future civil engineers and architects, How the Gateway Arch Got its Shape: YouTube video and article

• St. Louis arc Desmos approximation activity: move the slides to approximate the St. Louis arch with quadratic and ellipse equations. (See a future problem, Sec 8.1, problem no. 42, pg 550). Homework due Wed (upload a link of your Desmos or a screenshot on HuskyCT)

Week 9 Wed

Handed out:

• Sample quiz week 9 hw due Fri

Math fun facts (generating functions):

• (In class) the power series related to the silver ratio. See also:
  • Jim Fowler video: Fibonacci numbers as power series coefficients
  • silver ratio, the metallic means, taffy-puller machines

Week 9 Fri

Handed out:

• Stapled together in green paper
  • Sec 11.10 part 2 reading homework due Wed next week (not Monday)
  • HW Sec 11.10 part 2 homework due Wed next week (not Monday)

• Worksheet 11.10 Taylor Series from 1132 not homework.

• Problems C Problem set due next Friday

Week 10 Mon

Handed out:

• Learning Activity worksheet Sec 11.10 part 1 previously handed out but didn’t have time to do
• Learning Activity worksheet Sec 11.10 part 2: blank and key for second problem

Math fun facts:

• Taylor-made Pi team activity
• Warm-up for Chapter 10 polar coordinates: complex number multiplication, rotation, and Euler’s Formula using Taylor series

Week 10 Wed

Continue with complex number multiplication and Euler’s formula warm-up, introduce a parametric function.

Week 10 Fri

Handed out:

• Worksheet 11.11 application of taylor polynomials from 1132, see an answer

• Volumes

Approximating stuff: Article: Continued fractions are objectively the best in approximation technology

• Tutorial: Graphing parametric functions with Desmos

Week 11

Exam 2 Study Guide:

• Exam 2: Ch 7 list of topics + questions + key
• Exam 2: Ch 11 list of topics + questions + key
• Problem presentations starting from Week 7 + selected student problems If a problem was presented but not typed in, you don’t have to worry about it.
• More Exam 2 questions (True/False and more): questions and key
• Factsheet which you will get on Exam 2 Let me know if there are missing facts.

Week 11 Friday

Handed out:

• Notes Sec 10.1, Desmos parabola
• Worksheet 10.1 curves defined by parametric equations from 1132
• Visualizing paramatric equations on Desmos:
  • no 2 Linear parametric equation
  • no 4 A circle oriented counterclockwise starting at (0,16)
  • no 5 A circle centered at (-2,-3) oriented clockwise
  • no 6 A circle oriented counterclockwise
• Homework Sec 10.1 HW due Mon

Week 12 Mon

• Trigonometry/Geometric explanations number 4 and 6 in last week’s Worksheet 10.1 Curves defined by parametric equations from 1132 are the same using geometry

Handed out:

• Notes Sec 10.2 part 1
• Notes Sec 10.2 part 2 HW due Wed

Week 12 Wed

Cycloid animation: Desmos 1, Desmos 2 and Wikipedia gif

Handed out:

• Worksheet 10.2 Calculus with parametric curves from 1132 Especially figuring out orientation of a parametric curve without plotting points.
• Learning Activity Sec 10.2 part 1 questions+key and (not printed) part 2
• (distributed but didn’t have time to do during class) Learning Activity Sec 10.1
• (Not printed) HW Sec 10.2 questions and key HW due Fri

Week 12 Fri

• Start Notes Sec 10.3 part 1, see Desmos examples

Week 14 Mon

• Continue Notes Sec 10.3 part 1, see Desmos examples
• Start Learning Activity Sec 10.3 part 1 submit on Wed

• Start Notes Sec 10.3 part 2 plus Learning Activity Sec 10.3 part 2

• HW Sec 10.3 HW due Wed

Week 14 Wed

• Start Notes Sec 10.4 plus Learning Activity Sec 10.4

• Worksheet 10.3 polar coordinates from 1132 HW due Fri

• (not printed) HW Sec 10.4 and key HW due Fri

Week 14 Fri

Bonus student presentations on applications of the divergence of harmonic series

• Worksheet 10.4 areas in polar coordinates from 1132

• Notes Sec 8.1 arc length green, to be collected on Mon

• Application of polar coordinates: drawing a heart with cardioid

Week 15 Mon

Worksheet 9.1 Modeling with Differential Equations from 1132 pink, hw for Wed

Week 15 Wed

• Worksheet 9.3 Separable Equations from 1132
• Orthogonal trajectories def and pictures

Week 15 Fri

• Sample final Sec 9.3 (board work): question and key

• Not used: Worksheet 9.4 Models for Population Growth from 1132

Final Exam Study Guide

• Final Sample and Key to Final Sample
• Fact sheet provided during the exam
• Sec 11.7 strategy for series tests
• The final exam will only cover the following:
  • Chapter 11 infinite sequences and series (Sections 11.1-11.6, 11.8-11.11)
  • Chapter 7 integration techniques and improper integral (Sections 7.1-7.4, 7.7-7.8)
  • Chapter 10 parametric equations, polar coordinates, areas (10.1-10.4)
  • Chapter 9 modeling with differential equations (9.1, 9.3)

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Content credit: Uconn and MAA publications and MAA members, especially S. Chao, T. Chumley, M. Rabideau, F. Tabing, used with thanks