Zooming In on a graph

An experiment with using Desmos on a phone.graph match - big derivative puzzle

The idea is to look at the properties of amount functions (e.g. \(f(x)\)) and their rate functions (the derivative functions, e.g. \(f'(x)\)).

*A note on the puzzle:*

You can make the puzzle task more interesting by scrolling the browser to hide the true/false hints.Circle Area by Concentric Slices Using concentric circles as area elements.

- Kwikis (just below current homework)

**Homework Sources:**

**Next Calculus Test:** Wed April 12, 2017 (generally every other Wednesday)

Due Date | Assignment |
---|---|

Tue 1/3 | WeBWork: WinterBreak-2016Enjoy your break. |

Wed 1/4 | * Finish ladder problem. Kwiki 19065 * Start your journal. Each day spend a few minutes summarizing the concepts we worked on in class and in the homework. You might use the journal to ask yourself questions on concepts. For example, when finding volumes of revolution when is it better to use shells than to use washers?* ( Optional: You might want to review volume by shells by actively watching MIT Volume of revolution via shells.) |

Thu 1/5 | * Carefully read HWS Integration by Parts Introduction * Use Integration by Parts on \[\int x e^{-x} \, dx\] Be sure to check your answer. * TurnIn: A second draft of the appraoch and solution sections of either question 2 (Ladder Problem) or question 4 (Volume of Intersecting Cylinders using rectangular shells) from Kwiki 19066.( Note: You will be doing more work on this writing assignment for Friday.) * Make your journal entry. |

Fri 1/6 | * Determining \(u\) and \(dv\) takes some practice. Actively watch MIT Integration by parts 1 * Finish Kwiki 19067 — (but don’t look up answers and/or solutions) * TurnIn: A third draft of the complete write-up (all four sections and a title) you started yesterday. * Update your journal |

Mon 1/9 | * WeBWorK bic_spring_misc_01 — Note: Only two tries on matching question. * Finish Napkin Ring Problem from Kwiki 19068 * Remember, your journal should include an entry after each class |

Tue 1/10 | * Be prepared (as a group) to put any of the volume problems from today’s Kwiki on the board. * Work on Particle, the dog (question 3 of the Kwiki).* TurnIn: A brief second draft of a write-up of your approach and solution sections for part (a) of the Particle, the dog question — Find an equation for a function, \(P(x)\) that takes the owner’s \(x\) value and produces the distance Particle has traveled along the sine curve since starting at the origin. Be sure to explain how you developed \(dP\), a distance element. Hint: You will ultimately need to use a calulator to get values for \(P(x)\) other than \(P(0)\).Note: If you do not have an equation for \(P(x)\), write question where the answer to that question would help you get closer to a equation for \(P(x)\). Explain how the answer would help you. * Update your journal. |

Wed 1/11 | * Test * Update your journal, print it, and bring it to class. |

Thu 1/12 | * The distance Particle, the Dog travels along a curve is called arc length. Compute the length of the curve \[y=x^{3/2} \, \, \text{ for } \,\, x \in [0,4]\] * Actively watch MIT arclength * Put comments on arc length into your journal. (In preparation for the next test, be sure to start a new page in your journal for this entry.) |

Fri 1/13 | * TurnIn: Demonstrate at least two methods to evaluate \[ \int \cos^2 x \, dx \] * Update your journal with at least three things you learned from taking Wednesdays’s test, working with your group on the redux, and going over questions on the with the class. |

Tue 1/17 | * Work on problems 4-7 on the extended kwiki 19071 * Prepare short write-ups of two problems (4 or 7) and (5 or 6). * TurnIn: Two second draft problem write-ups, each should be on its own page. Each should fit on a single side. * Update your journal. |

Wed 1/18 | * Read about pumping liquids and pulling up a rope using work elements Penn work element * WeBWorK Work-bic-1 * Update your journal. |

Thu 1/19 | * Background on partial fractions can be found in HWS Partial Fractions * WeBWorK partial-fractions-1 * Be sure you are caught up on previous WeBWorK * Update your journal. |

Fri 1/20 | * Do Revisiting Integrals worksheet * Update your journal. |

Mon 1/23 | * Finish Kwiki 19076-with-Homework. Note that there is a third section that contains some homework questions.* Update your journal with comments about: — Revisiting Integrals in light of doing the kwiki in class. Explain why \(f(x)\) needs to be invertible on \([a,b]\) both from a geometric and algebraic point of view.— Question 6 on \[\displaystyle \int_0^\infty f(x) \,dx\] |

Tue 1/24 | * Actively watch MIT Improper Integrals video * WeBWorK Improper-bic * Update your journal. |

Wed 1/25 | * Test * New (or revisited) topics: — partial fractions — Riemann Sums — probability — work — improper integrals * Journals: — Make sure you have comments on Revisiting Integrals — TurnIn: Last two weeks of your journal. |

Thu 1/26 | * WeBWorK Misc_Set_04 * Put in a pagebreak and Update your journal. |

Mon 1/30 | * WeBWorK Misc_Set_05* Be sure to finish all open WebWork before it closes Sunday night (01/30/2017 at 12:01am). * Update your journal. |

Tue 1/31 | * Polar Coordinates: — Read Polar Coordinates — Do sec 10.1 #1,3,5,9,12,13,21 * Improper Integrals Resources:– HWC Improper Integral notes – MIT Improper Integrals video * Update your journal. |

Wed 2/1 | * Polar derivatives: — Read Polar Slopes — Do 10.2 #1, 2, 3, 7, 8 * Improper Integrals: Be prepared to go work with your group to present solutions and comments on questions 2-5 on yesterday’s kwiki 19079.* Update your journal. |

Thu 2/2 | * Polar area: — Read Polar Area — Do 10.3 #12, 21 — Finish #6 on Kwiki 19081 * Update your journal with ideas, diagrams, and questions about: — improper integrals — polar area |

Fri 2/3 | Parametric Curves: * Read Parametric Curves * WeBWorK parametric-intro* Be sure you understand question 2(a) on Kwiki 19082 — See Building a cycloid mathlet * Explore graphing parametric curves using the Desmos Graphing Calculator. * Update your journal with thoughts about parametic curves. |

Mon 2/6 | * Finish WeBWorK parametric-intro by midnight Saturday. You can look at solutions starting on Sunday* Read Parametric Calculus * WeBWorK parametric-bic-ii — TurnIn Solution to problem 6. Use Desmos Graphing Calculator to create a graph of your solution.* Update your journal with thoughts about calculus on parametic curves. |

Tue 2/7 | * TurnIn: A complete, typed write-up of the Coin Toss Problem.– Be sure to address the questions in today’s DoNow * Work on the Nail Drop Problem – See Nail Drop Demo – Think about how you would model the sample space. * Update your journal. |

Wed 2/8 | * Test — TurnIn: Last two weeks of your journal. |

Fri 2/10 | * TurnIn: Second Draft of Clara - CowculusNote: You will be turning in at least one more revision next week. * Update your journal with comments about the test. |

Mon 2/13 | * TurnIn: A third draft of Clara - Cowculus — The key question is the area of the grazing region. You should be able to set-up the area elements (yes, plural) and integrals. — After doing that, you can focus on evaluating the integrals or focus on making an interesting Desmos Graphing Calculator dynamic diagram. — My Moving Cycloid is a working example of a dynamic diagram which contains some comments on how I put it together. * Update your journal with comments on Kwiki 19085 |

Tue 2/14 | * Watch Khan– Differential Equation Introduction * Actively watch Khan– Finding a particular linear solution to a DE * WeBWorK DiffEQ_01_bic (no reopens) * Update your journal with comments on Differential Equations |

Wed 2/15 | * Review Solutions to WeBWorK DiffEQ_01_bic * More on slope fields:— Khan– Creating a slope field — Khan– Slope field to visualize solutions — Khan– Matching Differential Equations and slope fileds * Sequences: — Read Intro to Sequences 11-1 — Do section 11-1 #1-6 * Update your journal with comments on Differential Equations and Sequences |

Thu 2/16 | * Actively watch Khan– Intro Separable DEs * WeBWorK DiffEQ_02_bic * Update your journal with comments on separable DEs, converging geometric series |

Fri 2/17 | * Sequences: — Reread Intro to Sequences 11-1 — Be able to explain: “If a sequence is bounded and monotonic then it converges”— Be able to explain: Example 11.1.15. * Series: — Read Intro to Series 11-2 — Do section 11-2 #1-5 * Update your journal with comments on sequences and series |

Tue 2/21 | * Read about the Integral Test (listed as Theorem 11.3.3). * Actively watch MIT Integral test * Reread Integral Test and do: — section 11-3 #5,6,9 * Update your journal in preparation for Wednesday’s test. |

Wed 2/22 | * Test — TurnIn: Last two weeks of your journal. |

Fri 2/24 | Taylor polynomials are polynomials that can approximate functions where the value of function and the values of all of the derivatives are known for some point \((a, f(a))\). For now let’s assume \(a\) is zero. In this case \(p_1(x)=1+f'(0)x\), our good friend, the tangent in Taylor form. A key idea is that the derivatives of \(f(x)\) and \(p_n(x)\) take on the same values at \(x=a\). The phrase Maclaurin polynomial is used to indicate a Taylor polynomial where \(a = 0\), (we know “all about” \((0,f(0)\)) * Actively watch Khan– Intro Taylor and Maclaurin Polynomials – Part 1 * Do Kwiki 19085 question 3. * Develop an \(11^{th}\) degree Taylor polynomial for \(f(x)=\sin(x)\) at \(a=0\). * Try out your polynomials on Desmos: — [Desmos — first three Taylor polynomials of f(x)=e^x] — [Desmos — Starting Taylor polynomials of f(x)=sin(x)] TurnIn: The journal entry you make on this homework assignment summarizing what your understanding of Taylor polynomials. |

Mon 2/27 | * WeBWorK seq_series_03-bic * Whitman 11-3 11-4 read and do: — section 11-3 #5,6,9 — section 11-4 #1-5 (all) * Explore An Alternating Series: — You can build up points using Demos Start Alternating Series v1 — The first 100 points are plotted at Demos Alternating Harmonic Demo |

Tue 2/28 | * Read and Do —Whitman 11-5 Comparison Tests #1-4 (all) —Whitman 11-7 Ratio Test #1-3 (all) * Actively watch MIT Intro Ratio Test * Finish Kwiki 19093 * Update your journal |

Wed 3/1 | * Read and Do — Whitman 11-6 Absolute Convergence #1-7 (odd) — Whitman 11-8 Power Series #1,2,3 * Actively Watch: MIT Radius of Convergence * Update your journal |

Thu 3/2 | * Read and Do — Whitman 11-9 Calculus with Power Series #1-5 (all) * Actively Watch: MIT Taylor Series of a polynomial * Update your journal |

Fri 3/3 | * Actively Watch: MIT Comparison Tests * WeBWorK Power-Series-bic * Update your journal |

Mon 3/6 | * Do questions 6, 7, 8 on the back of today’s kwiki (19097). * I’ve reopened WeBWorK Power-Series-bic * Read Tips on Using Tests of Convergence * TurnIn convergence-tests-worksheet * Update your journal |

Tue 3/7 | TurnIn: A unit circle (\(C_1\)) fits snuggly into a 2 by 2 square. Find the radius of the largest circle (\(C_2\)) that fits snuggly in the region of the lower left hand corner of the square outside the unit circle.* Spend 30 minutes on this problem. (Start by sketching a good diagram.) * Spend 5 minutes planning an organized write-up. You might not have a complete solution, but you should have things to say about the problem. * Spend 15 minutes writing (it need not be typed, but you will be turning in a revision on Thursday) an organized Four Sections write-up. * Update your journal |

Wed 3/8 | * Test — TurnIn: Last two weeks of your journal. |

Thu 3/9 | TurnIn: a full write-up to the Snuggly Circle problem. * Update your journal |

Fri 3/10 | * Actively Watch MIT Graphing DE with IVC * Assume the power series \[p(x)=x-4 x^3+16 x^5-64 x^7+256x^9+...\] is a Maclaurin series for some function \(f(x)\). Write an equation for \(f(x)\). * Update your journal |

Mon 3/13 | * Turn-in: Bacteria Growth Problem * Update your journal |

Tue 3/14 | * The MAA Mean Policeman is a fun introduction to the Mean Value Theorem from the 1960’s. * Watch Khan– Mean Value Theorem * Update your journal on MVT |

Wed 3/15 | * WeBWorK MVT-intro (Just one problem) * Watch Five Unusual Proofs. Put comments on the video in your journal |

Thu 3/16 | * Finish both sides of Kwiki 19103 * WeBWorK DiffEQ_06_bic * Update your journal. |

Fri 3/17 | * Actively watch Khan– Intro Eulers Method * (Today’s Slides on Eulers Method can be reviewed.) * Finish WeBWorK DiffEQ_06_bic * Update your journal on Euler’s Method and our discussion of the symmetric difference quotient from today’s class. |

Mon 3/20 | * WeBWorK DiffEQ_05a_bic* Finish question 1 on Kwiki 19104. (You might find this Video on Using a Google Spreadsheet for Euler’s Method to be of value. Let me know.) * (WeBWorK DiffEQ_06_bic is still open) * Update your journal. Wednesday’s test is coming. |

Tue 3/21 | * TurnIn Questions 8 and 9 on the back of today’s Kwiki 19105. A Handwritten second draft of responses is fine. * Update your journal. e.g. Average Value, Logistic Growth, Euler’s Method |

Wed 3/22 | * Test (possible recent items)–+ Separable Differential Equations –+ Modeling Logistic Growth –+ Euler’s Method –+ Average Value of a function –+ Working with data, e.g. approximating derivatives and Riemann sums * You may use a non-graphing calculator. I will have a few to lend. * TurnIn: Last two weeks of your journal. |

Fri 3/24 | * Look at Numerical Integration demo * TurnIn: WeBWorK find_parabolaWhen you are done with this problem, write a brief write-up including: –* Problem –* Solution –* Graph –* Final Thoughts (e.g. See an example Desmos ) to show the parabola and your three points. |

Mon 4/3 | * Prep Set 1 Set aside 90 minutes to do the six questions. You can use your TI on the first three questions. Write out your solutions as if you were really taking the test. After that you can use resources (e.g. books, the internet, friends) to get a better understanding of any questions that you did not immediately ace. Feel free to email me with any questions over the break.* Prep Set 1 Quiz Monday * (Optional) Send me email if you have made any progress on the infinite product from today’s kwiki 19107 Have a good break. |

- Kwiki 19100 Misc problems to revisit
- Kwiki 19101 Misc problems to revisit, Bacterial Growth
- Kwiki 19102 \(\pi\)-day and Euler’s approach to the Basel Problem
- Kwiki 19103 Using data to get a DE, Logistic Growth
- Kwiki 19104 Euler’s Method
- Kwiki 19105 Average valuse, and homework on back

- Kwiki 19091 misc
- Kwiki 19092
- Kwiki 19093
- Kwiki 19094
- Kwiki 19095 Taylor and MacLaurin Series
- Kwiki 19096 Taylor and MacLaurin Series, finding some limits
- Kwiki 19097 Taylor and MacLaurin Series: new series from old
- Kwiki 19098 Power Series convergence tests
- Kwiki 19099 More on Taylor series

- Kwiki 19085 DoNow parametric line segment; (polynomial approximations of functions
*will not*be on Test 4S) - Kwiki 19086 differential equations
- Kwiki 19087
- Kwiki 19088
- Kwiki 19089 Fibonacci Fun
- Kwiki 19090 Integral and Sums, Fibonacci Fun

- Kwiki 19078 improper integrals, repeating decimals
- Kwiki 19079
*DoNow*, improper integrals (we did not get past the*DoNow*in class but you should finish the kwiki at home.) - Kwiki 19080 playing with polar 1
- Kwiki 19081 playing with polar 2
- Kwiki 19082 rolling a circle, parametric curves
- Kwiki 19083 Nail Drop problem
- Kwiki 19084 Nail Drop problem

- Kwiki 19071 more on napkin ring, \(\theta\)-substitution, arc length
- Kwiki 19072 Work, \(\cos^2(x)\)
- Kwiki 19073 partial fractions, work
- Kwiki 19074 \(\cos^2(x)\)
- Kwiki 19075 Riemann sums, probability
- Kwiki 19076 revisiting integrals, probability, misc homework questions
- Kwiki 19077 improper integrals

- Kwiki 19065 Ladder problem, sphere volume by shells
- Kwiki 19066 DoNow: \(u\)-substitution and chain rule, ladder problem, intersecting cylinders revisited
- Kwiki 19067 Integration by parts
- Kwiki 19068 Napkin rings problem
- Kwiki 19069 Setup up volume elements – washers and shells; begin
*Particle, the Dog*.

- Copies of Stewart
**Calculus**are available if you want to read a Calculus text with worked examples.

As in previous math clases some homework assignments will come from the [Whitman Calculus] text, but other assignments will be done on-line using WeBWorK , an on-line math homework system.

You need to fill out this form To get a set up an *WeBWorK* account. Be prepared to give a (and remember) a password for your account. (Yes, the submit button says “Never submit passwords through Google Forms.” Your WeBWorK password is not a high level security item.) Details about using *WeBWorK* will be available soon. If you can't wait, you can sign-in as a *guest*.

- Bring your calculator to class starting Monday, August 24.
- For most of you, here are basics of TI-83, notes on using the TI-83/4 (a pdf file), and/or a TI-83/84 On-Line Tutorial. This might also help.
- For the computing hungry, here are basics of TI-89, notes on using the TI-89 (a pdf file), and/or a TI-89 On-Line Tutorial
- And if you have been given a free TI-86, here is a TI-86 On-Line Tutorial

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