Math 312 Bard College

Course:  Math 312, Fall 2017

Time & Place:  TR 3:10 – 4:30 pm in RKC 102

Instructor:  Jim Belk (belk@bard.edu)

Office Hours:

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

## Announcements

#### Final Exam

The final exam is this 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 up to three sheets of paper with anything you like 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)

#### Quiz Solutions

Here are the solutions to the quizzes:

#### Practice Final Questions (with Solutions)

Here are some practice questions for the final exam: Here are the solutions: When studying for the final, make sure you also take a look at the practice problems on integration on manifolds and on quick integration (see below).

#### Integration on Manifolds

Here are some practice problems on integration on manifolds, which we covered on Thursday. Answers can be found on the second page.

#### Quick Integration

Here are some practice problems on integration using geometric methods. You ought to be able to solve most of these in your head: Answers can be found on the second page.

#### Quiz 2 Tuesday

There will be a quiz on Tuesday covering integration on curves and surfaces. The quiz will count as much as a single homework assignment. The problems on the quiz will be very similar to the practice problems below.

#### Integration on Curves and Surfaces

Here are some practice problems on integration on curves and surfaces: Answers can be found on the second page.

#### Quiz Tuesday

There will be a quiz on Tuesday covering integration in curvilinear coordinates. The quiz will count as much as a single homework assignment. The problems on the quiz will be very similar to the practice problems below.

#### Integration in Curvilinear Coordinates

Here are seom practice problems on integration in curvilinear coordinates: Answers can be found on the second page.

#### Homework 7

The seventh homework assignment is due next Tuesday, November 21. 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 6

The sixth 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.

#### Practice Midterm Questions

Here are some practice questions for the midterm: Here are the solutions:

#### Homework Solutions

Here are solutions to the first three homework assignments:

#### Homework 5

The fifth homework assignment is due this Friday, October 20. Here is the assignment: Here are some brief notes on Kantorovich's theorem that should be helpful for the homework:

#### Homework 4

The fourth homework assignment is due next Friday, October 13 (after break). 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.

#### First Exam

The first exam is postponed until after fall break.

#### Homework 3

The third 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.

#### Homework 2

The second 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.

#### Homework 1

The first 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.

#### Picture from Class

Here is the picture I showed in class of the decomposition of a cube into six tetrahedra of equal volume: You can decompose any parallelepiped in a similar way. Of course, there's also a slightly simpler way to decompose a cube into five tetrahedra, but they don't have equal volume.

#### Practice Problems: Vectors and Matrices

Here are some suggested practice problems from the book that should help you to review vectors and matrices. These are mostly review, so you should feel free to skip over ones that you know how to do:
• Section 1.1 # 6
• Section 1.2 # 4, 12
• Section 1.3 # 2, 3, 4, 7, 10, 12
• Section 1.4 # 16, 21
(Note: For those with the first edition, see §1.1 #5; §1.2 # 3, 12; §1.3 # 2, 9, 10, 13; §1.4 # 13, 20.)

Please read through Chapters 0 and 1 of the textbook as soon as possible.

#### Welcome!

Welcome to Math 312. 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 Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 5th edition by John Hubbard and Barbara Burke Hubbard. You will need a copy of the textbook for reading and homework problems, but you do not need to bring it to class. You can purchase the textbook as either an e-book or in print form from the Matrix Editions website. The e-book is \$74 and works on up to two devices, while a hard copy is \$87.

## Course Policies

#### Introduction

This course treats the differential and integral calculus of several variables from an advanced perspective. Topics may include the derivative as a linear transformation, change of variables for multiple integrals, parametrizations of curves and surfaces, line and surface integrals, Green's theorem, Stokes' theorem, the divergence theorem, manifolds, tensors, differential forms, and applications to probability and the physical sciences.

#### Prerequisites

The prerequisite is Vector Calculus (Math 241) or the Mathematical Methods sequence (PHYS 221–222). We will be assuming a good foundation in linear algebra and vector calculus, including vectors and matrices, partial derivatives, multiple integrals, directional derivatives, the gradient vector, and so forth.

#### Homework

There will be a written homework assignment due each Friday. 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.