Alexander Paulin 

Department of Mathematics
796 Evans Hall
University of California, Berkeley

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Analytic Geometry and Calculus 16B (001 LEC) Spring 2017

Lectures: MWF, 12pm-1pm, 155 Dwinelle Hall.
Office hours : MTWTF 2pm-4pm, 796 Evans Hall.
Discussion sections:One and a half hours every Thursday. 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 Calculus 16B! This fantastic course is a continuation of 16A, which introduced the basic concepts of Calculus: differentiation and integration. This course applies these techniques to a number of important applications, from optimization of functions of several variables to probability theory. As we shall discover, all these new techniques have significant applications in economics, architecture, business, the social sciences and beyond.

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 Thursday the 19th of January.

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


The textbook for this course is:

Goldstein, Lay, Schneider, Asmar, Calculus and it's Applications, 2nd custom edition for math 16B at UC Berkeley.

This is just chapters 7,8,9,10,11 and 12 from the 13th edition of the non-custom version. As such, the 13th edition of the non-custom version is acceptable. It is important though, to have the correct version of these textbooks because homework will be taken from them. Different version may have different numbering.


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 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 2 (1/23 - 1/27)
2 Week 4 (2/6 - 2/10)
3 Week 7 (2/27 - 3/3)
4 Week 9 (3/13 - 3/17)
5 Week 13 (4/10 - 4/14)
6 Week 15 (4/24 - 4/28)

For more detailed information see the course policy


There will be two midterms, the first on Wednesday February 15 and the second on Friday March 24. The final exam will be on Wednesday May 10 (3pm - 6pm).

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 andMidterm 1 Statistics.

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

Midterm 2 Solutions and Midterm 2 Statistics.

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

Syllabus and Schedule

Here is the lecture schedule for the course:

WhenWhat Where
Week 1 (1/16 - 1/20) Practical Stuff
Functions of Several Variables (video 1, video 2) 7.1
Week 2 (1/23 - 1/27) Partial Derivatives (video 1, video 2) 7.2
Maxima/Minima (video) 7.3
Week 3 (1/30 - 2/3) Lagrange Multipliers (video 1, video 2, video 3 ) 7.4
Double Integrals (video 1, video 2, video 3) 7.6
Week 4 (2/6 - 2/10) Trigonometric Functions (video 1, video 2) 8.1-8.4
Week 5 (2/13 - 2/17) Review (video)
Midterm 1 (on 2/15)
Integration by substitution (video ) 9.1
Week 6 (2/20-2/24) Integration by Parts (video) 9.2
Definite Integrals (video) 9.3
Week 7 (2/27-3/3) Some Applications of Integration (video 1, video 2) 9.5
Improper Integrals (video) 9.6
Week 8 (3/6-3/10) Solutions of Differential Equations (video) 10.1
Separation of Variables (video 1, video 2) 10.2
First-Order Linear Differential Equations (video) 10.3
Week 9 (3/13-3/17) Graphic Solutions (video 1, video 2) 10.5
Applications (video 1, video 2) 10.4/10.6
Week 10 (3/20-3/24) Review (video 1)
Midterm 2 (on 3/24)
Week 11 (3/27-3/31) Spring Break!
Week 12 (4/3-4/7) Taylor Polynomials (video 1, video 2) 11.1
Infinite Series (video) 11.3
Week 13 (4/10-4/14) Series with Positive Terms (video 1, video 2) 11.4
Taylor Series (video 1, video 2) 11.5
Week 14 (4/17 -4/21) Random Variables (video 1, video 2) 12.1/12.2
Expected Values and Variance (video 1) 12.3
Week 15 (4/24-4/28) Exponential and Normal Random Variables (video 1, video 2) 12.4
Poisson and Geometric Random Variables (video) 12.5
Week 16 (5/1-5/5) Review (video 1, video 2,video 3)
Week 17 (5/8-5/12) Final Exam (3pm-6pm) on Wednesday 5/10