Calculus III: Calculus with Several Variables
Course: Math 32, Spring 2018
Time &h; Place: MW 1:15 pm — 2:30 (Fletcher Hall 110)
Instructor: Jorge Basilio (jorge_basilio@pitzer.edu)
Office: Avery 220
Office Hours:
- M 10:30-11:30, W 2:30-3:30, F 8-9
Office Phone: 909.607.7961
Math Tutoring (Free!)
Where: Atherton 103- Sundays: 8:00-10:00 pm
- Tuesdays: 8:00-10:00 pm
- Thursdays: 8:00-10:00 pm
Handouts
Good vs Bad Cheat Sheets
Exam Preparation — Notes
- Exam Study Guide: Math32-CalcIII-Notes.pdf
- Update: 5/1 @ 8 am (through Final Exam material)
- Update: 4/20 @ 9 pm (through Exam 3 material)
- Update: 3/16 @ 3 pm (through Exam 2 material)
- Update: 2/1 @ 8 pm (through Exam 1 material)
Prereq Review Sheets
- Calc I/II Review Sheet - Complete Version (from Paul's Online Math Notes).
- Calc I/II Review Sheet - Reduced Version (from Paul's Online Math Notes).
On Reading Mathematics
Announcements
Cheat Sheets for Final Exam
I forgot to mention this in class this morning, but I will allow a cheat sheet on the final exam under certain rules.
Please read the document "GoodvsBad" Cheat Sheets. It was written for a different school but the info obviously is school independent.
The key to making a Good Cheat Sheet (GCS) is that it has to be done by hand and well-organized. Printing one out from the internet will not be allowed.
I will collect your cheat sheets at the beginning of the exam and will check them individually to see if they satisfy the requirements of a GCS. If they pass, it will be returned to you and you can use it for the remained of the text (approximately 15-20 minutes after the exam begins). However, if it's a bad cheat sheet then I will not return it and you will not be able to use it on the exam. Please follow the following rules/requirements:
REQUIREMENTS FOR GCS:
- Must be hand-written & NEAT & written by YOU
- SIZE: using a regular 8.5" x 11" piece of white printer paper (no other paper allowed, no lined paper, graph paper etc)
- CHEAT SHEET NOTES ARE ONLY ALLOWED ON ONE SIDE of the page
- The other side of the page must include: Your name, Course, Instructor, Date and nothing else
- You may include an unlimited number of definitions, theorems, graphs of standard functions, and formulas
- You are allowed to have AT MOST TWO example problems with complete solutions. These must be clearly indicated with a box around them so that I can find them and check that no more than two worked out problems are on your cheat sheet.
- Must follow the principles outlined in the GCSvsBCS document discussed in class and available on Sakai
- This is completely subjective and up to my discretion
- If I don't think you followed the spirit of the document or if you failed to follow any of the above directions then I reserve the right to not allow you to use your cheat sheet
- ***BONUS*** if your cheat sheet is beautiful & complete (meaning it has the main ideas from all the chapters we covered) you can earn 3% extra credit on your final exam.
If you have any questions, you can email me or ask me during the final exam review session on Friday.
Final Exam Review
I noticed that Friday is a designated reading day so there will not be office hours on Friday morning.
Instead, we will have an optional final exam review session on Friday from 2-4 pm. Just find us in our of the classrooms near my office.Exam 3 — Take-Home Instructions
Here is Exam 3. DUE: Monday at 5pm in my office (Avery 220).
>>Directions:
- Once you open/download/print the exam, you are not allowed to consult any textbook, notes, other people, or the internet.
- You must work entirely on your own! No tutors, working with classmates, using the textbook, online sources, or other outside help. Students suspected of cheating will be given a zero for this exam and reported to the appropriate office.
- Please print this exam and write your answers in the space provided. All work must be shown to receive credit. You may chose to do some scratch work on another page, but be sure to write any relevant calculations on your printed exam copy.
- Include:
- a cover page (including: title, your name, course, my name, date due),
write on the front side of each page only,[removed: doesn't make sense since you'll print and write on the exam directly]- staple your work.
- No calculator is allowed on this exam.
Good luck!
PS. I will be traveling all day and will not be able to check my email until the evening (hopefully by 6pm or so). Just keep that in mind if you email me questions. I will be happy to reply and answer questions when I have internet access again.
Exam 2 Extra Credit
For our second exam, instead of test corrections I would like to offer everyone the opportunity to retake the exam to increase your grade. If you would like to retake the exam, please email me to schedule a date and time (during regular office hours would be preferable).This will not be done during the regular class time.
More details:- It will be exactly the same exam as Exam 2
- You will have 50 minutes to complete it (instead of 60)
- No calculators, show work, and the same test directions as usual.
- I will be grading it a bit tougher than the first time (because it's a retake and you'll have an opportunity to study from it and also read my comments). In particular, if you didn't simplify all the way on the exam but got full credit on the retake you might not get full credit. Why? Because I would like this to be a learning opportunity.
- How it will change your score: I will take the average of your two scores.
- If you perform worse on Exam 2 then it WILL NOT negatively effect your grade, and we'll keep the first score only.
- If you have any questions, please email me. Have a nice weekend.
Exam 2 Extra Credit
There is an opportunity to increase your Exam 2 score by doing "test corrections:"Instructions for Test Corrections:
- Due: Wednesday, April 11 (in-class).
- Write test solutions to every question. Your work can contain at most one incorrect solution. More than that and you will not qualify for extra credit.
- If your score was 94 or higher, then you only have to redo the problems where you missed points (but the problem needs to be re-done from beginning to end).
- For True/False questions, on the test corrections please include a brief justification with your answer. On the test, you don't need any justifications but for the test corrections I would like to see them.
- Follow the same directions as for Exam 1 extra-credit
- New grade = [Exam 2 score] + 35 % * [110 - Exam 2 score] (rounded up to the nearest whole number).
Exam 1 Extra Credit
There is an opportunity to increase your Exam 1 score by doing "test corrections:"Instructions for Test Corrections:
- Due: Wednesday, February 28 (in-class).
- Write test solutions to every question. Your work can contain at most one incorrect solution. More than that and you will not qualify for extra credit.
- If your score was 90 or higher, then you only have to redo the problems where you missed points (but the problem needs to be re-done from beginning to end).
- Must have a cover page (including: title, your name, course, my name, date due)
- Write on the front side of each page only
- Box answers, make sure problems that require units have the correct units, etc
- You must work entirely on your own! No tutors, working with classmates, using the textbook, online sources, or other outside help
- Only help allowed is me. Come to office hours or schedule a meeting. I am more than happy to explain these questions in person!
- New grade = [Exam 1 score] + 10 % * [100 - Exam 1 score] (rounded up to the nearest whole number).
Exam Preparation
I posted the document Math32-CalcIII-Notes.pdf under the hand-outs. This document has tons of helpful info to help you prepare for our upcoming exam. It explains basic test info, sections covered, notes that summarizes the key points of the sections covered, and at the end it has practice exam problems from the textbook. The answers to odd problems are available via the ebook on WebAssign and the even numbered problems are provided in the document itself. Happy studying!Online Graphing Calculator for 3D Plotting
As I showed in class, "CalcPlot3D", is a very useful tool to help you visualize 3D plots of curves, functions etc.You can use this on some of the tougher WebAssign questions as an aid.
Hope you find it helpful and straightforward to use :-)Math Lunch!
This semester the Pitzer Math faculty: Jemma Lorenat, Jim Hoste, and myself will be hosting MATH LUNCH every Monday from 12-1 pm in the dinning room (look for the cheesy hand-written "Math Lunch" sign). What is MATH LUNCH? It's an informal way to come and chat with us. We can talk about math, or not about math….that pretty much covers everything! See you there!New Office Hours!
These are my updated hours for this semester:- Monday: 10:30-11:30 am
- Wednesday: 2:30 pm - 3:30 pm
- Friday: 8-9 am
Office Hours Poll
Using the google doodle link, https://doodle.com/poll/zm2bcpbs7tvrwmh9, please select ALL the times that fit into your schedule where you can attend office hours. I will select the THREE times that have the largest number of selections at the end of the week and begin holding these hours next week. In the meantime, I'm sticking to the hours posted on the Syllabus: MW 10:45-11:45 am, F 11-11:50 am Hope this helps :-)Section Key
Sections marked with a "*" = Optional sections to be read but no RP. Students who plan to take more advanced courses using calculus (e.g. econ, physics) are encouraged to read these.WebAssign Access and Class Key
Jan 16 2018 Here is the "Class Key" to register and access WebAssign, which is the online homework system that we will use.
- Class Key: pitzercollege.ca 5915 4397
Hello!
Welcome everyone to Calculus III! I'm excited to begin the new semester and to meet all of you tomorrow. I'll post important information here. I posted the course syllabus below--for students who have not taken a course with me please read it carefully. More info coming soon...
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| 5 | Exam 1 (60 min) | {M} 2/12 @ 1:30 — 2:30 pm |
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| 10 | Exam 2 (60 min) | {M} 3/21 @ 1:30 — 2:30 pm |
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| 16 | Exam 3 (Take-home) | {W} 5/2 @ 5 pm |
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| 17 | Final Exam (3 hrs) | {M} 5/7 @ 9 am — 12 pm |
Course Policies
Please consult the Course Syllabus for a more detailed description.
What is this class?
This course extends the thread of mathematical inquiry of the dual topics of differentiation and integration for functions of several variables. Whereas functions of one variable may be visualized as curves on the plane, we may visualize a real-valued function of two-variables as a surface in three-dimensional space. But what does it mean to take a derivative or a defnite integral of a surface? We will address this question and more in this course. Like in Calculus I &p; II, we will see that there is a beautiful geometry associated with functions of several variables.
Our frst task will be to develop a useful language for easily describing geometric objects in two and three dimensions using vectors. Then we will continue to study vector-valued functions, partial derivatives, the gradient vector, Lagrange multipliers, double and triple integrals and line integrals, culminating with the fundamental theorems of Green, Stokes, and Gauss. We will also apply these ideas to a wide range of problems that include motion in space, optimization, arc length, surface area, volumes, and centers of mass, time permitting.
The students should be able to interpret the concepts of Calculus algebraically, graphically and verbally. More generally, the students will improve their ability to think critically, to analyze a problem and solve it using a wide array of tools. These skills will be invaluable to them in whatever path they choose to follow, be it as a mathematics major or in pursuit of a career in one of the other sciences.
Prerequisites
Completion of Math 31 (or equivalent experience with college-level Calculus II), a suitable score on the mathematics placement exam, or permission of the instructor.Online Homework via WebAssign
Computation is an important component of mathematics, and is a key part of any calculus course. I will select problems from the textbook to be done and checked online via the platform WebAssign.Textbook
The textbook is Calculus: Early Transcendentals, 8th Ed., by James Stewart. We will cover most of the material in Chapters 12 – 16. You should read the relevant section of the text before we cover the material in class, and then again while doing the homework.The textbook comes with access to the WebAssign system. So if you are ok with studying from an ebook then you DO NOT have to buy a hard copy of the textbook.
You can buy an earlier edition for cheaper if you plan to use it as a future reference or resource. Since the HW is done online you will not need the textbook for the homework, only to read the book and study.
Additional Textbooks and Resources
- Paul’s Online Math Notes. Free and online. The notes are simple and to the point. Excellent for extra examples.
- MIT’s OCW Calculus III course with video lectures and notes. Free and online. Haven’t really watched the videos so check them out and let me know if you like them.
- Calculus III, by Jerrold Marsden and Alan Weinstein. Free and online. A more advanced textbook that is geared towards future engineers and physicists. They are excellent but can be very challenging. Some topics and notation choices are unusual.
- Vector Calculus by Marsden and Tromba A more refined and theoretical version of the Calc III book by Marsden and Weinstein referenced above. It covers more topics at a higher level. It has wonder sections on history and also more sophisticated mathematical notation. Worth reading for students who plan to major in mathematics. Available at the library.
Grading
The grade will be based on the following:| Participation | 5% |
| Online Homework | 20% |
| Exams (3 @ 15% each) | 45% |
| Final Exam | 30% |
Exams
The in-class exams are one hour long, and will take place on
- Exam 1. Monday, 2/12/2018
- Exam 2. Monday, 3/21/2018
- Exam 3. Friday, 4/30/2018
The final exam is three hours long, and will be on Monday, May 7, in our usual classroom from 2-5 pm.