Math 142B Bard College

# Calculus II

Course:  Math 142, Section B (Fall 2017)

Time & Place:  TR 10:10 – 11:30 am in Hegeman 106

Instructor:  Jim Belk (belk@bard.edu)

Office Hours:

• Thursday 7–9 pm (RKC 100)
• Friday 4–6 pm (RKC 100)

Course Tutor:  Alexis Zheng (hz1459@bard.edu)

Math Study Room:  Sun–Thurs, 7–10 pm (RKC 111)

## Announcements

#### Final Exam

The final exam is Thursday, December 21 at the following times:
• 10 am – 12 pm: 3rd floor Albee
• 12 pm – 6 pm: Albee 100
You should make sure to bring a calculator to the exam. You may also bring an 8.5" × 10" sheet of paper with notes written on the front and back.

#### Extra Office Hours

I will be having the following office hours this week.
• Tuesday 7–9 pm (RKC 100)
• Wednesday 3–5 pm (3rd floor Albee)
• Wednesday 7–9 pm (RKC 100)

#### Final Exam Practice Problems

Here are some practice problems for the final exam: Here are the solutions:

#### Quiz Solutions

Here are the solutons to the recent quizzes:

#### Homework Solutions

Here are the solutons to homeworks 6 and 7:

#### Estimating Double Integrals

Here are some practice problems on estimating double integrals numerically: Answers are on the second page.

#### Homework 9 (Revised)

The last written homework assignment is due this Friday, December 15. Here is the assignment: Note that there has been a slight revision to part (b) of the last question.

#### Double Integrals

Here are some practice problems on double integrals over rectangles:
• Section 12.2 # 3, 5, 9, 17, 19, 21
Also, here are some practice problems on double integrals over more general regions:
• Section 12.3 # 1, 3, 9, 21, 23, 25

#### Homework 8

The eighth written homework assignment is due this Friday, December 8. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Areas and Volumes

Here are some practice problems on areas and volumes:
• Section 6.1 # 3, 5, 9, 17, 23
• Section 6.2 # 1, 3, 5, 7, 13, 25

#### Homework 7

The seventh written homework assignment is due this Friday, December 1. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Quiz Tuesday

There will be a long (2 page) quiz this Tuesday, November 21. It will cover integration odds and ends and improper integrals. (See the practice problems below.)

Here are some practice problems on improper integrals Answers are on the second page.

#### Integration Odds and Ends

Here are some problems on some of the aspects of integration that we've been discussing recently:
• Section 5.2 # 35, 37, 41, 43
• Section 5.4 # 7, 9
• Section 5.5 # 49, 50, 59, 60
• Section 6.1 # 1, 13

#### No Homework This Week

There is no written homework due this week.

#### Homework 6

The sixth written homework assignment is due this Friday, November 10. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Advanced Substitution and Integration by Parts

Here are some harder problems on substitution and some problems on integration by parts:
• Substitution: Section 5.5 # 17, 31, 51
• Integration by Parts: Section 5.6 # 1, 3, 7, 11, 19, 25, 27, 29

#### Basic Substitution Problems

Here are the basic substitution problems that you did last week:
• Indefinite Integrals: Section 5.5 # 1, 3, 5, 7, 13, 21
• Definite Integrals: Section 5.5 # 43, 45, 47

#### Midterm Exam Friday

The midterm exam is this Friday from 9 am to 6 pm in RKC 101. Remember:
• • The midterm is designed to be about 2 hours long, but there is no time limit.
• • You should bring a calculator to the midterm.
• • You can bring a 3" × 5" index card to the midterm with anything you want written on the front and back.

#### Office Hours Tonight

I will be having extra office hours tonight (Wednesday) from 7 pm to 9 pm in RKC 100.

#### Midterm Practice Problems

Here are some practice problems for the midterm exam: I've written solutions to these practice problems:

#### Homework Solutions

Here are the solutions to the first four homework assignments:

#### Quiz Solutions

Here are the solutons to the first five quizzes:

#### Paper on Functions without Elementary Antiderivatives

For those students who are interested, here's an expository article from the College Mathematics Journal on the mathematics of proving that certain functions have no elementary antiderivatives:

#### Practice Problems: Integrals and Area

Here are some practice problems on integrals and area. This material will be covered on the midterm exam. Answers are on the second page.

#### Quiz Thursday

There will be a quiz this Thursday, October 19. All of the questions will involve evaluating integrals using the fundamental theorem of calculus (see the exercises below), which is covered in Section 5.3 of the textbook.

#### Practice Problems: Fundamental Theorem of Calculus (with Answers)

Here are some practice problems on the fundamental theorem of calculus: Answers are on the second page.

#### Homework 5

The fifth written homework assignment is due this Friday, October 20. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Homework 4

The fourth written homework assignment is due this Friday, October 13. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Quiz 5

The fifth quiz is this Thursday, October 12th. It covers critical points and the second derivative test. See the practice problems below.

#### Practice Problems: Critical Points

Here are some practice problems on critical points and the second derivative test.
• Section 11.7 # 1, 3, 5, 7, 9, 13
Answers can be found in the back of the book.

#### Quiz 4

The fourth quiz will be this Tuesday, October 3. It will cover higher derivatives, functions of three or more variables, and partial differential equations. See the practice problems below.

#### Practice Problems: Higher Derivatives

Here are some practice problems on second and higher partial derivatives:
• Section 11.3 # 51, 53, 55, 59, 61, 63
Answers can be found in the back of the book.

#### Practice Problems: Functions of Three or More Variables

Here are some practice problems on functions of three or more variables:
• Section 11.3 # 1, 29, 31, 35, 41, 79
• Section 11.4 # 19
Answers can be found in the back of the book.

#### Practice Problems: Partial Differential Equations

If you haven't seen differential equations before, you might want to start with a couple of problems on ordinary differential equations:
• Section 7.1 # 1, 5
Now here are some practice problems on partial differential equations:
• Section 11.3 # 69, 70 (answer)

#### Homework 3

The third written homework assignment is due this Friday, September 29. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Quiz 3

The third quiz was on Tuesday, September 26. It covered partial derivatives. See the practice problems below.

#### Practice Problems: Partial Derivatives

Here are some practice problems on partial derivatives:
• Section 11.3 # 3, 15, 17, 19, 21, 23, 25, 27, 39
• Section 11.4 # 1, 3, 5, 17
Answers can be found in the back of the book.

#### Homework 2

The second written homework assignment is due this Friday, September 22. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Quiz 2

The second quiz was on Tuesday, September 19. It covered cross-sections, contour plots, and equations of planes. See the practice problems below.

#### Practice Problems: Equations of Planes

Since the book doesn't cover equations of planes very well, I've written some brief notes on the subject as well as some practice problems. The answers to the exercises are on the second page of the PDF.

#### Practice Problems: Cross-Sections and Contour Plots

Here are some practice problems on cross-sections:
• Section 9.6 # 18 (answer)
• Section 11.1 # 9, 11, 14 (answer), 19, 23, 35, 37, 45
Answers to the odd-numberd problems can be found in the back of the book.

#### Homework 1

The first written homework assignment is due this Friday, September 15. Here is the assignment: You should feel free to work together with other students on the assignment, but everyone must turn in their own copy of the solutions, and you must acknowledge any collaborators. I will be having office hours this Thursday and Friday to help with the homework.

#### Cross-Sections Animation

Here is the animation of cross sections that I showed in class yesterday:

#### Practice Problems: Multivariable Functions

Here are some practice problems on multivariable functions:
• Section 9.6 # 9, 13, 15, 23
Answers to these problems can be found in the back of the textbook.

Please read sections 9.6 and 11.1, and 11.3 before next Tuesday's class.

#### Derivative Practice Problems

Here are some practice problems on basic derivatives. They are from the Chapter 3 Review on pg. 248. (The exercises start at the bottom, after the “Concept Check” and the True-False Quiz.)
• Chapter 3 Review Exercises: 1, 3, 5, 7, 9, 11, 17, 25, 27, 31, 41
Answers to these problems can be found in the back of the textbook. If you have trouble with any of these problems, you might want to try watching some of the review videos listed below.

#### Review Videos

You might find the following videos helpful for reviewing derivatives:

#### Welcome!

Welcome to Math 142. I will be using this course webpage to post all announcements and documents, including homework assignments, homework solutions, and practice exams.

## Textbook Information

The textbook is Calculus: Concepts and Contexts, 4th edition by James Stewart. You will need a copy of the textbook for reading and homework problems, though you do not need to bring it to class. An electronic version of the book can be rented for \$24 from the publisher, or you can buy the Kindle version for \$105 from Amazon.com. You can also rent a hardcover version from Amazon.com for \$90.

## Course Policies

#### Introduction

Math 142, second-semester calclus, will continue to explore the fundamental ideas of differentiation and integration that you learned in Calculus I. Topics to be covered include functions of several variables, partial derivatives, integrals of single-variable functions, techniques of integration, improper integrals, applications of integration, and multiple integrals.

#### Prerequisites

This course is designed for students who have completed Calculus I (Math 141), or who have taken a calculus course in high school. We will be assuming basic knowledge of derivatives (including the product rule and chain rule) and integrals.

#### Textbook

The text is Calculus: Concepts and Contexts, 4th edition, by James Stewart. We will cover most of the material in chapters 5, 6, 11, and 12, as well as a few topics from elsewhere in the text. You are encouraged to read the text before coming to class, and then again while doing the homework.

#### Written Homework

There will be a weekly written homework assignment due each Friday consisting of a few longer problems, with an emphasis on the conceptual side of calculus. You are encouraged to work with other students in solving the homework problems, but you should write your own solutions, and you must acknowledge anyone that you work with. Your solutions should be written clearly and in complete sentences, with enough detail that another student in the class would be able to follow your reasoning.

#### Practice Problems and Quizzes

Computation is an important component of mathematics, and is a key part of any calculus course. I will often recommend practice problems from the textbook, and you are strongly advised to try at least some of these problems. To make sure your computational skills are progressing, there will be a short (10–20 min.) quiz each Tuesday consisting of a few relatively straightforward computational problems.