Math 21A, Differential Calculus, Sections C01-C06
Fall 2016
MWF 10-10:50AM, 2205 Haring Hall
Welcome to the course webpage for Math 21A, Sections C01-C06. Here you will find some general info about the course. This is also the place to look for homework assignments, occasional course notes, and other things that might interest you.
TA Information Calculus Room Textbook Exams and Grading Homework Assignments Material by Day Various Notes
ANNOUNCEMENT: the final will be on Monday, Dec. 5, 8AM-10AM, in our usual classroom. It will be cumulative with no intended bias towards any particular part of the course. It will cover chapters 2, 3, and all of 4 except the last two sections: Newton's method and antiderivatives. Here is a practice final. We will have a review session on Wednesday in 2 Wellman, 6-7:30PM. I will post the notes from the review and solutions to the final exam, as well as all course notes (this will complete the incomplete set on canvas) after this. You can find the audio for the review session (video did not record, alas) on canvas. Here are the notes from the review, followed by full practice final solutions.
Here is the list of formulas and theorems that will come with your final.
Office hours this week are as follows: Tuesday, 3-5PM and Thursday, 2-4PM in MSB 3236. There will be office hours run by graduate students on Saturday and Sunday (Dec 3 and 4), 10AM-3PM. This is a fundraising effort by the graduate math club, and it will cost $10 per person per day (you do not have to stay the full 5 hours, however). NOTE: THESE OFFICE HOURS WILL NOT BE IN THE CALCULUS ROOM, AS PREVIOUSLY ANNOUNCED: THEY ARE IN 1147 MSB, not too far from the Calculus room.
Also, if between Thursday's office hours and Saturday at 7PM you come up with any questions for me, email them to efuchs@math.ucdavis.edu and I will answer them all and post the answers on this webpage (your identities will be kept anonymous).
Course syllabus
Professor: Elena Fuchs
Office: MSB 3109
Email: efuchs at math dot ucdavis dot edu
Office hours: MF 2:15-3:30PM.
TA Information
Lead TA: Nathaniel Gallup
Please email any administrative questions about the course to Nathaniel Gallup,our lead TA, at npgallup at math dot ucdavis dot edu
Discussion sections:
C01, T 4:10-5PM, Yuanyuan Xu in Roessler 55
C02, T 6:10-7PM, Henry Kvinge in Olson 207
C03, T 8:10-9PM, Carson Rogers in Olson 207
C04, T 7:10-8PM, Henry Kvinge in Roessler 55
C05, T 5:10-6PM, Yuanyuan Xu in Roessler 55
C06, T 6:10-7PM, Carson Rogers in Roessler 55
Calculus Room and Additional Resources
The Calculus Room is a great resource for our class. It is staffed with 21ABCD TA's MTWR 1PM-7PM, F 1-6PM, and is located in MSB 1118, on the ground floor of the Mathematical Sciences Building.
There are also 21A workshops and daily drop-in tutoring available at the Student Academic Success Center. Please go to http://success.ucdavis.edu/academic/dropin.html for more information.
Textbook and Prerequisites:
The textbook we'll be using is "Thomas' Calculus, Early Transcendentals" by Weir and Hass, 13th Edition. If you have the 12th edition, it is your responsibility to figure out the differences to the 13th. Most relevant are the problems at the end of each section. For a useful guide to where there are differences in problems between the 12th and 13th edition, see this useful guide of Professor Gravner's.
The prerequisite for this course is two years of high school algebra, plane geometry, plane trigonometry, and analytic geometry, as well as the Math Placement Requirement. You will be DROPPED from this course if you have not met the Mathematics Placement Requirement which is a total score of 35 or more on the Math Placement Exam, with a trigonometry subscore of 3 or more.
Homeworks, Exams, and Grading:
Your grade for the course is determined as follows:
- 10% for weekly quizzes in discussion.
- 25% for Midterm 1
- 25% for Midterm 2
- 40% for the Final.
The exams will be closed book and closed note. A sheet of some useful formulas will be included in each exam, and it will be posted ahead of time on this website. Electronics of any kind (calculators, phones, laptops, etc) are prohibited. Anyone seen to be using a cellphone during an exam will receive a 0 on the exam. There will be no make up exams.
Homework (along with occasional supplementary notes) will be posted here every Wednesday. The homework will not be collected, but some of the problems will be discussed in your discussion section. The way these problems will be chosen will be via a doodle poll that your TA will send out each week. I strongly urge you to do the homework, even though it is not collected: it is unlikely that you will pass the course without doing so.
Quizzes consisting of one problem each will be given weekly in discussion section and will be a variant of some homework problem from the week before. Our first quiz will be on Tuesday, October 4th. There are no make-up quizzes but your lowest two quizzes will be dropped. Note that you have to take quizzes in your registered section.
Our midterms will be in class on Friday, October 21st and Friday, November 18th. More details about these exams will be announced in class and posted here closer to the dates.
Our final exam code is A. It will take place in our classroom on Monday, December 5th, 8-10AM.
If you need special accomodations for the exams, these accommodations must be documented through the Student Disability Center in order to be valid.
Basic Plan:
We will cover roughly the first four chapters from the textbook. For a detailed syllabus as suggested by the department of mathematics, please click here.
Our goal, in a nutshell, is to learn differential calculus which can be thought of as the study of rates of change of motion. This topic is at the core of many facets of science and engineering, and one goal for the course will be to understand how to model a variety of real world scientific problems using a mathematical model which follows a set of simple laws which at first seem quite separate from the problems themselves.
Detailed Plan:
The following is a rough outline of what we will be doing in lecture every day, along with the relevant sections in the book (note that the reading for a given lecture should be taken to mean the relevant section of the mentioned chapter). In reality, we may move faster or slower. It will be updated on a regular basis.
- 9/21: Introduction to the course; rates of change, tangents to curves. Reading: section 2.1.
- 9/23: Continuing rates of change from last time, beginning limits. Reading: Sections 2.1 and 2.2.
- 9/26: Limit laws, precise definition of a limit. Reading: Sections 2.2 and 2.3. You may find it interesting at this point to look at and compare the precise definiton of a limit that involves infinity, rather than just real numbers: this is section 2.6 and we will get to it later.
- 9/28: Proofs about limits. Reading: Section 2.3
- 9/30: Finishing up definition of a limit, beginning one-sided limits. Reading: Sections 2.3 and 2.4.
- 10/3: Finishing up one-sided limits, beginning the notion of continuous functions. Reading: Sections 2.4 and 2.5
- 10/4: Quiz 1 in discussion, based on Homework 2
- 10/5: Continuing continuous functions, Intermediate Value Theorem. Reading: Section 2.5
- 10/7: Revisiting limits: limits involving infinity, asymptotes of graphs. Reading: Section 2.6
- 10/10: Limits involving infinity, asymptotes of a graph. Reading: Section 2.6
- 10/12: Derivatives at a point and as a function. Reading: Sections 3.1 and 3.2
- 10/14: Beginning talking about some differentiation rules: sum, product, quotient rules. Reading: Section 3.3.
- 10/17: Differentiation rules, including the chain rule. Lots of examples. Reading: Section 3.3 and 3.6.
- 10/19: Differentiation rules continued. Derivatives of trigonometric functions. Reading: Section 3.5 and 3.6.
- 10/21: Midterm 1. Covers Chapter 2 and relevant information from Chapter 1. Here are the solutions.
- 10/24: Chain Rule continued, derivative of ln(x) and a^x. Reading: Section 3.6 and 3.8.
- 10/26: Derivative of inverse functions, nth derivatives and their meaning. Reading: Section 3.4 and 3.8, some of 3.9.
- 10/28: Derivative as a rate of change, implicit differentiation. Reading: Section 3.4 and 3.7
- 10/31: Derivative as a rate of change, using derivative to find limit. Reading: Section 3.4 and 3.8
- 11/2: Finishing derivative as a rate of change, implicit differentiation, related rates. Reading: Section 3.7 and 3.10.
- 11/4: Related rates, linearization. Reading: Section 3.10 and 3.11.
- 11/7: Linearization and approximations using derivatives. Reading: Section 3.11.
- 11/9: Finishing approximations using derivatives, beginning minima and maxima, optimization. Reading: Section 3.11 and 4.1.
- 11/11: Veterans' Day, no class.
- 11/14: Optimization continued, starting Mean Value Theorem. Reading: Section 4.1, 4.2.
- 11/15: Review Session in Med Sci 180, 6:10-7:30PM.
- 11/16: Finishing Mean Value Theorem, beginning talking about how derivatives help us sketch graphs. Reading: Sections 4.2, 4.3.
- 11/18: Midterm 2. Here are the solutions.
- 11/21: Monotonic functions and sketching graphs. Reading: Section 4.3.
- 11/23: Concave up/down: what the second derivative tells us about the behavior of the function. Reading: Section 4.4. Notes from this lecture.
- 11/25: Thanksgiving break.
- 11/28: Curve sketching continued. Reading: Section 4.4.
- 11/30: Optimization problems and L'Hopital's rule. Reading: Section 4.5 and 4.6
- 12/2: Optimization and L'Hopital's rule continued.
- 12/5: FINAL EXAM, 8AM-10AM in usual classroom.
Some supplementary notes:
Homework assignments: