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Solutions to final exam
Here is the final exam, the challenge final exam, and solutions.
- In pdf: final.pdf.
- In pdf: final_answers.pdf.
- In pdf: challengefinal.pdf.
- In pdf: challengefinalanswers.pdf.
Have a great Summer!
Solutions to take home exam 2, info for the final exam
Here are my solutions to the second take home exam.
- In pdf: exam3_answers.pdf.
In addition to the material that appeared on the take home exams and the midterm, be sure you've studied the material on complex numbers (Say 9.1-9.7 in the text) and sequences of functions (chapter 11, except section 11.12).
Solutions to 2005 math 158 final
Here are solutions to the math 158 in-class final exam I gave in in a few years ago: 2005final/finala.pdf.
Take home exam 2
Here's the second take home exam. try to turn it in on Tuesday, May 13. I will accept it until Thursday, May 15.
- In pdf: exam3.pdf.
Homework for the week
Here's an outline for studying over the next two weeks.
- I recommend taking the math 158 in-class final exam I gave in in a few years ago: 2005final/final.pdf. You'll have to read ahead into chapter 11 for the definition of pointwise convergence and uniform convergence (go ahead!) to do problems 3, 4, and 7a. Otherwise, we've covered all the material needed. If you've been studying a lot, try to sit down and take the exam in 2 hours as a diagnostic practice final. If you haven't been studying much, treat the old exam as a problem set and solve the problems open-note, open-book to catch up.
- What's missing from the final exam is the large number of straightforward practice you should do determining whether particular series converge or diverge. For that, do Exercises 1-48 in Section 10.20 (pages 409-410). Pick a few, at least, and write your solutions in detail, carefully stating which convergence tests you use, etc...
- Remember the challenge: to come up with an infinite series for which you cannot determine whether it converges.
- I also like exercises 1-5 and 18 in the miscellaneous review in Section 10.22 (pages 414-416) and exercise 11 in Section 10.124 (page 420).
Homework for the weekend
Carefully read through section 10.13 in chapter 10 (up to page 398). Here are some exercises.
- Exercises in Section 10.9 (page 391). Here are some problems that involve "tricks" with power series. Have fun with them and don't worry to much about justifying every step: 2, 3, 4, 6, 10, 11, 12, 15, 20, 22, 23, 24.
- Exercises in Section 10.14 (pages 398-399). Here are some problems about infinite series that involve tests for convergence. For these, carefully justify your answers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 16, 17, 18, 19.
We'll have a short quiz at the beginning of class on Tuesday.
Homework for the weekend
Carefully read through section 10.3 in chapter 10 (pages374-381).
Here are some exercises from section 10.4 (pages 382-384). I urge you to do them all.
- Computing limits of sequences: exercises 1-19 (for 19, remember that i^2=-1).
- Working with epsilon-N definition: exercises 23-28
- Short theoretical proofs: exercsies 29, 30, 31.
- Sequences that are like integrals: exercises 34, 35.
Midterm and solutions
Here's the midterm exam and my solutions:
- In pdf: exam2.pdf.
- In pdf: exam2_answers.pdf.
- For LaTeX and pictures, check the directory exam2/
Solutions to take home exam
Here are my solutions to the take home exam.
- In pdf: exam1_answers.pdf. For LaTeX and pictures, check the directory exam1/
For those of you that are interested, here's the Mathematica notebook with the animation of the related rates: relatedratesanimation.nb.
Notes and exercises
Here are some notes about limits and some exercises to work on.
- In pdf: limits.pdf. For LaTeX and pictures, check the directory limits/
Take home exam
Here's the first take home exam. Due Tuesday, March 11.
- In pdf: exam1.pdf.
Mathematica
Later in the course, I'll find some ways to use Mathematica in interesting ways. For now, I encourage you to check it out. In addition to being installed in all OCT computer labs, CUNY has purchased licenses so that CUNY students can download copies of Mathematica onto their own computers. To do so, go to Wolfram's User Portal and create an account using your email address (it's important to use your qc.cuny.edu email address). You should be able to download and install the sofware. After that, you need to request an Activation key from Wolfram. Feel free to contact Wolfram for help if you need it.
To get started using it, I recommend the following screencasts from Wolfram's learning center:
Reading and problems for the weekend
Remember there's no class on Thursday, February 19. Over the next week, practice integration by substitution and integration by parts.
Homework 4: Due Tuesday, February 25
- Carefully read sections 5.6, 5.7, 5.9
- Do exercises 1, 3, 5, 6, 10, 11, 12, 23 in section 5.8 (page 216-217
- Do exercises 1, 2, 3, 7, 10a, 11a, in section 5.10 (page 221-222)
- Do exercises 1, 10, 11, 17, 34, 35 in section 5.11 (page 222-224)
Homework 2 solutions
I wrote solutions to (most) of the problems on homework 2.
Reading and problems for the weekend
Homework 3: Due Tuesday, February 18
- Carefully read sections 5.1-5.7 (pages 201-215)
- Do exercises 2, 3, 7, 10, 11, 20, 21, 22, 26, 28 in section 5.5 (page 208-210)
- Do exercises 1, 3, 5, 11, 12, 23 in section 5.8 (page 216-217)
Homework for the weekend
Here are some problems to work on over the weekend.
Homework for the week
You have a week to study and get a good mastery of the techniques of differentiation and practice applying them. Read sections 4.1 - 4.13 carefully and do plenty of exercises (I suggest some below). Then, to get a little bit ahead, read through section 4.14 about the mean value theorem. I'll cover the mean-value theorem in class on Thursday, February 6.
Here are some suggested exercises. I think you'll have fun with these!
- In section 4.9 (page 173): 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16.
- In section 4.12 (page 179): 2, 3, 7, 8, 11, 17, 18, 20, 22, 24, 34
- Exercise 3 in section 4.15 (page 186).
CUNY Mathfest at The Graduate Center
As I mentioned in class CUNY Mathfest will take place at The Graduate Center on Tuesday, February 4. See the schedule for a list of the activities. You are invited to come to part or all. There's a link on the event's front page to register. Because of the time of the event, there will be no class on Tuesday, February 4.
CUNY Math Challenge
You should know about The CUNY Math Challenge. I encourage all of you to take the challenge. The first round begins on Monday, February 10. See the webapge for more information.
Welcome to Math 158
Hope everyone had a great break!
The new piazza page is https://piazza.com/qc.cuny.edu/spring2014/math158.
Homework 1: Due Thursday January 30
- Read sections 4.1-4.5 (pages 156-166)
- Do exercises 1, 2, 3-12, 16-13, 25-35, 36 in section 4.6 (page 167, 168)