# Edwin O'Shea

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## Description, Syllabus and links for Math 235, Spring 2015

• Math 235 intends to provide a first proper insight into one of the great achievements of humankind, the Calculus. This course will be an introduction to differential and integral calculus of functions of one variable, culminating with the ``Fundamental Theorem of Calculus'' which says (and says why) that differentiation and integration are inverses of one another in a welll defined sense.
• A detailed syllabus is here.
• A schedule for the semester is here.
• A guide to the semester is here.

## Homework

• For 1/14: Reading: Sections 0.1 and 0.2 (exclude transformations but include symmetry), including Exercises 1 and 2.
Audio guides for these sections: 0.1 and 0.2.
• 0.1: 3,4,7,10,16,17,18, 33-38, 48-50, 57-64.
• 0.2: 6-8,16,20,51-56, 57-60, 67-70, 71-74, 75,77,78.
• For 1/15: Reading: Sections 0.3 and 0.4 (only log and exp on 0.4), including Exercises 1 and 2.
Audio guides for these sections: Powers and Polys and Rational and Absolute..
• 0.3: 8,11,12,15,16,19,22,23,24,28,43,45,46,52-54,73-80,83,84.
• 0.4: 3,8,10, 27-29,33-36,45-47,79,80.88.
• For 1/16: Reading: Section 0.4 including Exercises 1 and 2.
Audio guides for these sections: Trig and Inverse Trig.
• 0.4: 15,16,17,18,23,25,26,30-32,42,43,51,54,57-60,96.
• For 1/19: Reading: Section 0.5 including Exercises 1 and 2.
Audio guides for these sections: 0.5(Logic).
• 0.2: Transformations: read ``transformations and symmetry'' and example 2 of section 0.2. Do exercises 4,5,9,10,40-42 of 0.2. Read example 3 of 0.4 and do exercise 13 of 0.4.
• 0.5: 1,2,6,7, 26, 32, 34, 55-57, 63, 66, 67-71, 83, 88. (many of these are for pure enjoyment).
• Review: Not required BUT it will really help to look over all review problems at the end of Chapter 0.
• For 1/21: Reading: Section 1.1 including Exercises 1 and 2.
Audio guides for these sections: 1.1 Informal Limits.
• 1.1: [This looks like a lot but most of them are very quick] 0--7,14,17,21--40,63,64,66,76,77.
• For 1/22: Quiz at the end of class. All topics up to and including 1.1 are covered.
• For 1/23: Reading: Section 1.2 including Exercises 1 and 2.
Audio guides for these sections: 1.2 Finite Limits.
• 1.2: 1-8,12,16,18,19-26,43-46, all evens from 48-54 (do the odds too for practice),66.
• For 1/26: Reading: Section 1.2 including Exercises 1 and 2.
Audio guides for these (other) sections: 1.2 "Infinite" Limits.
• 1.2: Same exercises as last day. Plus: 9,10,11, 27-42, all evens from 55-64 (do the odds too for practice),67.
• Ask yourself if you know the topics in the rough schematic, starting today and every day from here on.
• For 1/28: Reading: Section 1.4 (continuity and holes only) including Exercises 1(a-c only) and 2.
Audio guides for these sections: 1.4 Continuity and Holes.
• 1.4: 1 (a-c only), 2, 3,4,8-12, 23-32,39-44.
• For 1/29: Quiz at the end of class. All topics covered since last quiz.
• For 1/30: Reading: Section 1.4 (remainder of section on EVT and IVT and root finding) including Exercises 1(d-h only).
Audio guides for these (other) sections: 1.4 Applications of Continuity.
• 1.4: 1 (d-h only), 18-22, every third question in 49-66, 75-80.
• For 2/2: Reading: Section 1.5 including Exercises 1 and 2.
Audio guide: 1.5 Limit Properties.
• 1.5: 1,2,5,6,12,16-18,20,21,24, every third problem of 29-70 inclusive (being careful in the manner of Example 1), 71,74-78, 79-86.
• For 2/4: Reading: Section 1.6 including Exercises 1 and 2.
Audio guide: 1.6 Infinite and Indefinite Limits.
• 1.5: 24.
• 1.6: 1-10, 15-20, 24,27,29-34. Try as many as possible from 35-80. 81, 94.
• For 2/5: Quiz at the end of class. Don't forget one sided 3x5 index card. All topics covered since last quiz.
• For 2/6: Reading: Section 2.1 including Exercises 1 and 2.
Audio guide: 2.1 Informal Derivatives.
• 2.1: 1,2,3,8,9,11-14,21-24,25,26,30,31-33, 35-38,43,44,45-48, 54.
• For 2/9: Reading: Section 2.2 (derivative at a point, as a function, and tangent lines + local linearity, Liebniz) including Exercises 1 (a-e).
Audio guide: 2.2 Derivatives I (Formally).
• 2.2: 1(a-e),3,4,5,6, 23-28,31-38,39-46,51-54,55,56,59-64.
• For 2/11: Reading: Section 2.2 (derivatives involving roots, piecewise fns, continuity-v-differentiability, Newton's Method) including Exercises 1 and 2.
Audio guide: 2.2 Derivatives II (Formally).
• 2.2: 1,2,7,8,12,21,22,29,30,47-50,65-68,69-74,81-86.
• For 2/13: Reading: Section 2.3 including Exercises 1 and 2.
Audio guide: 2-3 Basic "Rules".
• 2.3: 1,2,7,11--14,21,22,23--26,29,30, every fourth question from 36 to 64 inclusive, 67--70,73,74,80.
• For 2/16: Reading: Section 2.4 (all except implicit differentiation) including Exercises 1 and 2.
Audio guide: 2-4 Chain.
• 2.4: (chain rule) 1(a-e),2(a only), 3-8, 9-12, every fourth question from 22 to 46 inclusive, 47-50, 59,60, 63,64,67,68,85,86.
• For 2/18: Reading: remainder of Section 2.4 (implicit diff.) and 2.5 (exp and log, not log. diff.) including Exercises 1 and 2.
Audio guide: 2-4 Implicit and 2-5 Exp and Log.
• 2.4: (implicit differentiation) 1,2,17,53-58,69-84.
• 2.5: (exponential and log) 1(a-f), 2(a-b),3,4,5,8, 12,13, 14, all evens from 18--48, 64--67.
• For 2/20: Reading: remainder of Section 2.5 (logarithmic diff.) including Exercises 1 and 2.
Audio guide: 2-5 Log. Diff..
• 2.5: 1,2,49-58, 59-63.
• For 2/23: Reading: 2.6 (not hyperbolic trig) including Exercises 1 and 2.
Audio guide: 2-6 Trig.
• 2.6: [Ignore parts on hyperbolic sin, cos, etc] 1,2,3,4,5,7,8, every fourth question from 18--50.63--71.
• For 2/25: Reading: (Consequences of Local Linearity) 3.6 and Exercise 21 of 2.2 including Exercises 1 and 2.
Audio guide: 3-6 + Local Linearity.
• 2.2: Using local linearity, similar to Exercise 21, approximate the following. For each case "check" your answer using a calculator.
• The square root of 9.1, using local linearity close to x=9.
• The cubed root of 9 and 10, using local linearity close to x=8 in both cases.
• The sine of 5 degress, i.e. sin(π/18), using local linearity close to x=0.
• The square root of 2, using local linearity close to x=1.5.
• The cosine of 50 degrees...
• Why is the tan of 89 degress hard to compute using local linearity?
• 3.6: Read Examples 1,2 and 3, then do 10,11, 31--34,40,42,48.
• For 3/2 and 3/4: No new reading. Review days for Thursday's midterm.
• For 3/5: Midterm 1. All topics since beginning of semester are covered.
• For 3/18: Please read topics on 3.2 and 3.3 in Schematic again.
Reading: 3.2 including Exercises 1 and 2.
• 3.2: 4-7, 9,10, 17,18, 19-26, 29-34, 51-56, 66-70, 75,78,79.
• For 3/19: Please read topics on 3.2 and 3.3 in Schematic again.
Reading: 3.3 including Exercises 1 and 2.
• 3.3: 3-6,9, 15-20, 25--28, 42,44,47,48,53-62,65,66,75,78.
• For 3/20: For the first 25 minutes of class you will do examples of curve sketching on the board, from Sections 3.2 and 3.3.
Please read the first section of 3.4, on finding global extrema, and read example 1, and do exercises 1 and 2.
• 3.4: 1--20.
• For 3/23: Please read the rest of 3.4.
(Sorry for the absense of an audio file - I've come down with cough and sore throat and am not up to making a recording. )
• 3.4: 21--42.
• For 3/25: Please read the rest of 3.4.
• 3.4: 43--62.
• For 3/26: Quiz will only cover 3.4. For many questions, you will be asked only to set up the optimization questions. i.e. Give an equation in one variable with an interval and say how you would find (but not actually find) the best solutions.
• Some pictures of solutions from today: 1, 2 , 3 , 4 , 5 , 6 , 7 , 8 .
• For 3/27: Read first two subsections and examples 1, 2, and 3.
• 3.5: 1-8,12,13,17,18, 19-23, 27-30, 37-45.
• For 3/30: Read the remainder of the section and the examples.
• 3.5: 7,8, 25,26, 46-61.
• For 4/3: Read 4.1 and 4.2, being sure to look at the examples.
In 4.2, ignore all things about upper and lower sums.
• 4.1: 4,5,12,30,31,39,40.
• 4.2: (Be sure to draw pictures. Lots of pictures!) 17-20,27,28,31,34-38,39-42.
• For 4/6: Read 4.2 again and read 4.3, being sure to look at the examples.
Ignore all things about upper and lower sums.
• 4.2: (Be sure to draw pictures. Lots of pictures!) 1,2,17-20,27,28,31,34-38,39-42.
• 4.3: 1-12,20,21-26,29-34,41-44,47,49,50.
• For 4/8: Read 4.4 (Antiderivatives, aka Calculus Jeopardy!)
Just to convey how important these sections are, read 4.2 and 4.3 again, being sure to look at the examples.
Ignore all things about upper and lower sums.
• 4.4: 1,2, 4, as many as possible between 21-58.
• 4.2: (Be sure to draw pictures. Lots of pictures!) 1,2,17-20,27,28,31,34-38,39-42.
• 4.3: 1-12,20,21-26,29-34,41-44,47,49,50.
• For 4/9: Quiz on Sections 3.5, 4.1, 4.2, 4.3 and 4.4. Read the remainder of the section and the examples.
• For 4/10: Setting up the FTC I.
Read Section 3.1, paying special attention to Rolle's Theorem and the Mean Value Theorem. Worry mostly about the intuition of the statements and note that it does not tell you where the desired point is, only that it exists.
• 3.1: 41,46,47,49-52,53,54,57, 61.
• 4.5: (note, no reading of 4.5 for today) 15. It will help to write out each sum for the first and last few values of k. Why do you think these are called telescoping sums?
• For 4/13: Read 4.5.
• 4.5: 1,2,3,5,7,8,13, as many as you can of 19-64.
• For 4/15: Read 4.6.
• 4.6: 1,2,8,9,11,12,13,14, as many as you can of 26-37, 38,39,40, as many as you can of 41-52, 77.
• For 4/16: Quiz on Sections 4.4, 4.5 and 4.6.
• For 4/17: Read first two subections of 4.7, and examples 1,2, and 3.
• 4.7: 0,1,2,4,5,6,17-20,27,28,31,32,35-48,49,50,60,62.
• For 4/20: Read rest of 4.7, defining the logarithm function as an area accumulation function, including examples 4 and 5.
• 4.7: 21-23, 55-58, 70-78.
• For 4/22: Last quiz, on 4.7 only.
• For 4/23 + 4/24: Review all topics from chapters 3 and 4 covered since last midterm.
• For SUNDAY 4/26: Midterm 2. 5-8pm in Roop 129. One-sided 5x8 cheat sheet allowed.
• For 4/27-5/1: Review all topics for Final on SUNDAY 5/3.
• For SUNDAY 5/3: Final Exam. 5-8pm in Roop 129. One-sided 5x8 cheat sheet allowed -- anything larger will be confiscated.