HMC MATH 115 SPRING 2013

COURSE OVERVIEW

Math 115 is designed to teach some mathematical techniques used to find solutions to the ordinary and partial differential equations that describe the physical world around us.

Objective: By the end of this course, I hope that

you will understand how partial differential equation arise in some classical problems in math and physics;
you will be familar with complex variables, complex functions and contour integrals;
you will know how to use integral transforms, such as Fourier and Laplace transforms, to solve some differential equations;
when faced with a problem involving a linear partial differential equation, you will be able to select and carry out an appropriate solution strategy;
you will understand why linear differential equations are essentially solved once the eigenvalues and eigenvectors of the appropriate differential operators are known, and to be able to identify those operators;
you will be comfortable using special functions such as Bessel functions.

Topics covered (tentative): Complex variables and residue calculus, Laplace transforms, Fourier transforms, Separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, Bessel functions, orthogonal polynomials, the heat equation, wave equation, and Laplace's equation.

Class Time: Class will meet MW from 2:45-4:00 PM in Beckman B126.

Prerequisite: Math 65 or permission of the instructor.

INSTRUCTOR

Andrew Bernoff
Office: Olin 1260 (Chair's Office - in the Math Departmental Office)
E-mail: ajb @ hmc.edu
Office Hours: Friday 3-4, Monday 4-5, Tuesday 11-12

TEXTBOOK & LECTURE NOTES

The textbook for this course is an electronic textbook by the professor; for most lectures a chapter of notes will be made available in addition to your class notes.

If at any time you want a supplemental textbook, come see me. I will either lend you one or recommend one you can get out of the library

The textbook is provided for your personal use only. Please do not share or duplicate it.

MAPLE

Some of the homework requires the use of Maple; Harvey Mudd College has a site license or you can purchase a copy of the software from Huntley Bookstore or online. Maple worksheets will be archived here.

HOMEWORK

Written homework will generally be due weekly, on Monday in class. You are encouraged to discuss the homework with other members of the class, but you will be expected to write up your solutions without any assistance. It is appropriate to acknowledge the assistance of others. I will reserve the right to refuse to accept late homework for any reason. Assignments may be found here.

Homework should be formatted in accordance with the Math Department Homework Policy.

Consulting homework solutions, exams or exam solutions, and other materials from previous semester of Math 115 or Math 180 is strictly prohibited; any violation of this policy will be considered a violation of the honor code and will be dealt with accordingly.

PIAZZA

As an experiment we will be using Piazza, a social media site (think Facebook for Fourier), to answer all questions. Note you can post a question anonymously or send a question just to the instructor.

EXAMS & GRADING

There will be two midterm exams and a cumulative final. The exam dates will be given in class.
Review sheets will be provided for the exams listing the topics covered.

Course grades will be based on the following percentages:

Class Participation (including Piazza)	5%
Homework:	30%
Midterm I: Complex Variables & Laplace Transforms Available 3/6 - Due 3/11	20%
Midterm II: Fourier Series, Separation of Variables, & Fourier Transforms Available 4/24 - Due 4/29	20%
Final Exam: Available 5/9 - Due 5/15 at 4PM	25%

The Final Exam is optional - you will be offered a letter grade for the course based on your performance on the two midterms and the homework. Note that if you choose to take the final exam there is a chance your grade will be lower than the grade offered.

All the exams will be take home.

The date and time for the Final Exam is a hard deadline. I reserve the right to refuse late exams.

If you are a freshman you will receive a letter grade for this course.

OFF-CAMPUS STUDENTS

All students (including CGU students) will be graded on the same scale. Note that the median grade for classes at Harvey Mudd College is a B+ (a detailed analysis is here). Typically, the lower quarter of the class may receive grades of C or below. More information about HMC grades may be found here. All students are expected to abide by the HMC Honor Code.

DISABILITIES

Students who need disability-related accommodations are encouraged to discuss this with me as soon as possible.

HONOR CODE

The Harvey Mudd College honor code applies in all matters of conduct concerning this course.