Alexander Paulin 

Department of Mathematics
796 Evans Hall
University of California, Berkeley

me  |  research  |  teaching  |  CV

Analytic Geometry and Calculus 16A (001 LEC) Fall 2017

Lectures: MWF, 9am-10am, 105 Stanley Hall.
Office hours : MTWTF 3pm-5pm, 796 Evans Hall.
Discussion sections:One and a half hours every Tuesday. Here is a link with further details. You may only attend the discussion section for which you are enrolled.
Enrollment: For question about enrollment contact Thomas Brown.


Welcome to Math 16A! If you're a freshman, welcome to UC Berkeley! If you're not, welcome back! This course is a gentle introduction to one of great achievements of human thought: Calculus. Calculus is everywhere. It governs the motion of the planets and the stars; It tells us how to maximize profits when selling a product; It tells us how much trouble we'll be in if we take out an ill-adivsed loan! In this course everything will be done from scratch, so don't worry if don't know a thing about it yet. By the end of the course you'll understand the beauty and power of the subject.

Everything related to the course will be on this website. We will not be using bCourses. There will be weekly homework (posted below) and a quiz in discussion section every two weeks. I have office hours everyday of the week so there should always be an opportunity to get my help if you need it. If you can't make any office hours, e-mail me and we'll find another time to meet. In addition to this I will be posting my own lecture notes on this website at the end of each week. You'll be able to link to them directly from the detailed syllabus below. There will also be video recordings of the lectures posted at the end of Monday, Wednesday and Friday. Again you'll be able to link to them directly from the syllabus below.

Discussion sections will begin on Tuesday the 29th of August. That's in week 2.

Make sure to read the course policy and the detailed syllabus below.

I've posted a homework 0 below. You do not need to submit this during discussion section. It is predominantly a diagnostic test to warm up your algebra skills. The first official homework will be posted on Monday next week. It will not be due until discussion section in week 3.


Calculus with Applications by Lial, Greenwell, Ritchey, 11th Edition, ISBN: 9780133886832.

We've just changed the textbook so there may be conflicting info on older university websites. This is the textbook.

We won't be using the online math lab stuff so you just need to buy the textbook itself. Do not buy this textbook from a random bookstore if possible. We've negotiated the price down substantially so you should buy it from either the official Cal student store ($95 for the hardcover textbook. If they tell you otherwise you're at the wrong bookstore) or directly from the publisher. Here's the link:

Pearson Textbook Website Enter Username: berkeley and Password: math

You will also be able to rent the new textbook for $50 a semester from the university bookstore. To access the university bookstore click on the Cal textbook link on the 16A Calcentral website. I don't think you can buy it just yet. They'll have copies quite soon I think.

This book will cover both 16A and 16B. If you're only going to be doing 16A you'll certainly be able to sell if after the semester is done. I know these things are expensive. If it's any comfort, it's a widely used hardcover textbook so it will have excellent resale value.


The Student Learning Center provides support for this class, including an adjunct course, review sessions for exams, and drop-in tutoring. This is a fantastic resource, I definitely recommend you take advantage of it.

Grading and course policy

Homework 10%
Quizzes 10%
First Midterm 20%
Second Midterm 20%
Final Exam 40%

If the lowest (curved) midterm score is less than the (curved) final score, then it will be replaced by your final score. This grading policy allows you to miss one midterm without serious consequences. For example, if you scored 100% on everything except the second midterm, which you missed, then you would still get an overal score of 100%. You must, however, sit the final exam. It is your responsibility to make sure you have no schedule conflicts in exam week. Unless there are truly exceptional circumstances, there will be no make-up exams.

For more detailed information make sure to read the course policy.


Homework assignments are due each week in section. They will be posted here along with solutions. Your two lowest homework scores will be dropped. For more detailed information see the course policy.

Homework 0. This is an algebra diagnostic test. You do not need to submit this in discussion section. It's for you to warm up your algebra skills after a summer (or more) away from mathematics.

Homework 1 and Solutions 1

Homework 2 and Solutions 2

Homework 3 and Solutions 3

Homework 4 and Solutions 4

Homework 5 and Solutions 5

Homework 6 and Solutions 6

Homework 7 and Solutions 7

Homework 8 and Solutions 8

Homework 9 and Solutions 9

Homework 10 and Solutions 10

Homework 11 and Solutions 11

Homework 12 (Not to be submitted) and Solutions 12


Quizzes will take place roughly every two weeks in discussion section. They will last about 15 minutes, be of a similar difficulty to the homework and cover material from the preceding two week. Your lowest score will be dropped from your grade. Here is the quiz schedule:

1 Week 3 (9/4 - 9/8)
2 Week 5 (9/18 - 9/22)
3 Week 8 (10/09 - 10/13)
4 Week 10 (10/23 - 11/27)
5 Week 13 (11/13 - 11/17)
6 Week 15 (11/27 - 12/1)

For more detailed information see the course policy


There will be two midterms, the first on Wednesday September 27 and the second on Monday November 6. The final exam will be on Monday December 11 (7pm - 10pm).

For more detailed information see the course policy

First Midterm (Practice 1) and solutions, First Midterm (Practice 2) and solutions, First Midterm (Practice 3) and solutions

Midterm 1 Solutions and statistics.

Second Midterm (Practice 1) and solutions, Second Midterm (Practice 2) and solutions, Second Midterm (Practice 3) and solutions

Midterm 2 Solutions and statistics. Midterm 2 Solutions and statistics.

Final(Practice 1) and solutions, Final (Practice 2) and solutions, Final (Practice 3) and solutions

Syllabus and Schedule

Here is the lecture schedule for the course:

WhenWhat Where
Week 1 (8/23 - 8/25) Practical Stuff (video)
Slopes and Equations of Lines (video 1, video 2) 1.1
Linear Functions and Applications (video 1, video 2) 1.2
Week 2 (8/28 - 9/1) Properties of Functions (video 1, video 2) 2.1
Core Functions and Operations (video) 2.2/2.3
Exponential Functions (video) 2.4
Logarithmic Functions (video) 2.5
Week 3 (9/6 - 9/8) Limits (video) 3.1
Failure of Limits to Exist (video) 3.1
Week 4 (9/11 - 9/15) Limits at Infinity (video) 3.1
Continuity (video) 3.2
Rates of Change (video) 3.3
Week 5 (9/18 - 9/22) The Derivative (video1, video 2, video 3) 3.4
Graphical Differentiation (video) 3.5
Week 6 (9/25 - 9/29) Review
Midterm 1 (on 9/27)
Techniques for Finding the Derivative (video)4.1
Week 7 (10/2 - 10/6) Derivatives of Products and Quotients (video) 4.2
The Chain Rule (video) 4.3
Week 8 (10/9 - 10/13) Derivatives of Exponential Functions (video) 4.4
Derivatives of Logarithmic Functions (video) 4.5
Increasing and Decreasing Functions (video 1, video 2) 5.1
Week 9 (10/16 - 10/20) Relative Extrema (video) 5.2
Higher Derivatives and Concavity (video) 5.3
Curve Sketching (video) 5.4
Week 10 (10/23-10/27) Absolute Extrema (video) 6.1
Applications of Extrema (video) 6.2
Week 11 (10/30 - 11/3) Further Business Applications (video) 6.3
Implicit Differentiation (video) 6.4
Week 12 (11/6 - 11/8) Midterm 2 (on 11/6)
Antiderivatives (video) 7.1
Week 13 (11/13-11/17) Substitution (video) 7.2
Areas and the Definite Integral (video) 7.3
Week 14 (11/20 - 11/24) Areas and the Definite Integral (continued) (video) 7.3
Week 15 (11/27 - 12/1) The Fundamental Theorem of Calculus (video) 7.4
The Area Between Two Curves (video 1, video 2) 7.5
Week 16 (12/4 - 12/8) Review
Week 17 (12/11 - 12/15) Final Exam (7pm-10pm) on Monday 12/11