# Advanced Calculus

**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

#### 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.)

#### Reading

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.

#### Exams and Grading

The grade will be based on the weekly homework and three exams:

Homework | 40% |

Exam 1 | 20% |

Exam 2 | 20% |

Final Exam | 20% |

The exams are two hours long, and will be offered on Fridays. The first two exams are tentatively scheduled for **Friday, October 6** and **Friday, November 10**. The final exam is two hours long, and will be on **Thursday, December 21**.