**Course: MATH 31A, Differential and Integral Calculus, Lecture 4, Fall 2015**

**Prerequisite:** Successful completion of Mathematics Diagnostic Test or course 1 with a grade of C- or better.

**Course Content:** Differential calculus and applications; introduction to integration, optimization, Newton's Method, volumes.

**Syllabus:** here.
*Last update:* 15 December 2015

**Instructor:** Steven Heilman, heilman(@-symbol)ucla.edu

**Office Hours:** Mondays, 9AM-12PM, MS 5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
2PM-250PM, Franz 1178

**TA:** Christian, A., archristian(@-symbol)ucla.edu, Hong, P. C.,
philiphong@ucla.edu, Pham, M.
H., minhrose@math.ucla.edu

**TA Office Hours:** Christian, A., Tuesdays and Thursdays,
2PM-3PM, MS 3969, Hong, P. C., Tuesdays 11AM-12PM, MS 6221, Pham
M. H., Tuesdays and Thursdays 1PM-2PM, MS 3955

**Discussion Session
Meeting
Time/Location:**

- 3A, Tuesday, 2PM-250PM, MS 5127, Christian, A. http://www.math.ucla.edu/~archristian/teaching/31a-f15.html
- 3B, Thursday, 2PM-250PM, Boelter 5422, Christian, A. http://www.math.ucla.edu/~archristian/teaching/31a-f15.html
- 3C, Tuesday, 2PM-250PM, MS 5117, Hong, P. C.
- 3D, Thursday, 2PM-250PM, MS 5117, Hong, P. C.
- 3E, Tuesday, 2PM-250PM, PAB 1749, Pham, M. H. http://www.math.ucla.edu/people/grad/minhrose
- 3F, Thursday, 2PM-250PM, PAB 1749 Pham, M. H. http://www.math.ucla.edu/people/grad/minhrose

- My email address for this course is heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.
- Homework questions sent to me by email will be answered altogether in the form of a "digest." I will get to every question, but I cannot reply to every email. This digest will be sent out typically two days before the homework is due.

- Late homework is not accepted.
- If you still want to turn in late homework, then the number of minutes it is late will be deducted from the score. (The estimate of the number of minutes is not guaranteed to be accurate.)
- You may not use the internet to try to find the answers to homework problems.
- The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 8 homework assignments, assigned weekly on Friday and turned
in at the
**beginning**of class on the following Friday. (Exception: in the ninth week, homework is due on Wednesday, and during quiz weeks, homework is not turned in; see the quiz policy below.) - A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
- Collaboration on homeworks is allowed and encouraged.
- All homework assignments must be
**written by you**, i.e. you cannot copy someone else's solution verbatim. - Label your homework with the lecture number and the discussion section number.
- Homework solutions will be posted on Saturday after the homework is turned in.
- Reading the syllabus counts as one homework grade. In order to receive credit for reading the syllabus, you must read the syllabus by October 2, noon, PST.

- There will be four quizzes, administered in the second, third, fifth and sixth weeks of class. In the second, third, fifth and sixth weeks of class, the homework will not be turned in, and instead, the quiz will count for the homework grade. The problems from the quiz will closely resemble or be identical to problems from the homework from that particular week.
- Quizzes will be administered in your discussion section, which is on either Tuesday or Thursday. Each quiz should last about 15 minutes.

- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
- We will use the MyUCLA gradebook.
- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.

** Tentative Schedule**: (This schedule may change slightly during the
course.)

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

0 | Sep 21 | Sep 23 | Sep 25: Introduction, The Calculus Paradigm | ||

1 | Sep 28: 2.3,2.4, Limit Laws, Continuity | Sep 30: 2.5, Evaluating Limits | Oct 2: Homework 1 due. Read the Syllabus. 2.6,2.7, Trigonometric Limits, Limits at Infinity | ||

2 | Oct 5: 2.8, Intermediate Value Theorem | Quiz in section | Oct 7: 3.1, Definition of Derivative | Quiz in section | Oct 9: Homework 2 (ungraded). 3.2, The Derivative as a Function |

3 | Oct 12: 3.3, Product and Quotient Rules | Quiz in section | Oct 14: 3.7, The Chain Rule | Quiz in section | Oct 16: Homework 3 (ungraded). 3.5, 3.6, Higher Derivatives, Trig Functions |

4 | Oct 19: 3.8, Implicit Differentiation | Oct 21: 3.9, Related Rates | Oct 23: Midterm #1 | ||

5 | Oct 26: 4.1, Linear Approximation | Quiz in section | Oct 28: 4.2, Extreme Values | Quiz in section | Oct 30: Homework 4 (ungraded). 4.3, Mean Value Theorem |

6 | Nov 2: 4.4, The Shape of a Graph | Quiz in Section | Nov 4: 4.5, Graph Sketching | Quiz in Section | Nov 6: Homework 5 (ungraded), 4.6, Applied Optimization |

7 | Nov 9: 4.7, 5.1, Newton's Method, Area | Nov 11: no class | Nov 13: Midterm #2 | ||

8 | Nov 16: 5.2, The Definite Integral | Nov 18: 5.3, The Indefinite Integral | Nov 20: Homework 6 due. 5.4, Fundamental Theorem I | ||

9 | Nov 23: 5.5, Fundamental Theorem II | Nov 25: Homework 7 due. 5.7, The Substitution Method | Nov 27: No class | ||

10 | Nov 30: 6.1,6.2, Areas Between Curves, Average Value | Dec 2: 6.3, Volumes of Revolution | Dec 4: Homework 8 due. 6.4, Method of Cylindrical Shells |

**Advice on succeeding in a math class:**

- Review the relevant course material
**before**you come to lecture. Consider reviewing course material a week or two before the semester starts. - When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the
lecture. Also, finish your homework at
least
**two days**before it is due, to alleviate deadline stress. - Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

- (Solutions removed)