# Mathematical Methods for the Physical Sciences

### Syllabus

handouts videos syllabus pdf flier photographs

## Office Hours

Office hours are by appointment: email me and we will find a time for us to meet. I will be glad to answer all of your questions about the course material, go over some problems together with you, check your assignment work, review together for an exam, or discuss any course content you may have questions about.

## Textbook

No textbook required. Handouts with course material and practice problems are on this website. The textbooks used for the class preparation include the following: K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering; J. Stewart, Calculus; S. F. A. Kettle, Symmetry and Structure.

## Topics Covered

1. Line and surface integrals, flux, Stokes' and Divergence Theorems
2. Complex functions and complex integrals
3. Fourier Series Fourier Transform
4. Series solutions of ordinary differential equations
5. Groups, Symmetry Groups of Molecules, intro to Group Representations

Fourier Series and Transform. Students will learn about the Fourier transform and its use in nuclear magnetic resonance and signal processing.

Complex numbers, contour integrals, residues, Divergence and Stokes theorems. These topics represent basics for numerous and widespread applications.

Finding series solutions of ODEs is a method of finding solutions of ODEs with nonconstant coefficients that appear in physics applications.

Groups and Symmetries of Molecules. Group theory is a powerful mathematical theory used in physics and chemistry, in particular quantum mechanics, crystallography and spectroscopy. Students will learn the mathematical definition of a group, basics of the theory of finite groups and point groups and their applications.

For students interested in continuing their education at a graduate level, the course presents some mathematical techniques that certain graduate programs in physics, chemistry and engineering use.

The course emphasizes general ideas, not just mastering various techniques or methods. The underlying theme behind most course topics (Fourier Transform, Groups and Symmetries and Series Solutions) is that it might be easier to solve a certain problem by translating it to a different set up, solve it there and then translate the solution back into the original setting. This general principle of problem solving is often used in various fields and will be a useful concept for the students to acquire.

## Tentative exam dates

Exam 1: during the 4th week of classes.
Exam 2: during the 7th week of classes.
Exam 3: during the 11th week of classes.
Exam 4: during the finals week.

 Exams 1, 2 and 3 18% each Exam 4 22% Assignments 12% Project 12% TOTAL 100%
Grades are computed according to the following system:
 A A- B+ B B- C+ C C- D+ D F grade 93-100 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 60-66 0-59

3

## Prerequisites

Calculus 3 or the permission of instructor.

## Attendance

It is imperative that students attend all classes. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.

## Exams

There will be four semester exams. No makeup exam will be given unless the excuse for missing the scheduled exam is acceptable to the instructor. Any makeup exam must be taken before the next regularly scheduled exam. No exam grade will be dropped.

## Assignments and Project

There will be four assignments and one student project concentrated on applications of mathematics to physics or proofs in mathematics. Sample project topics are on this website. There will be no makeup assignments. Assignments or projects turned in after their due date will receive an automatic reduction in grade. No assignment or project grade will be dropped.

## Response time

The assignments, projects and exams are typically graded in three days after they are turned in. Special circumstances like snow days, school closing or holidays, may occasionally delay the response time. Barring special circumstances, students’ emails are usually responded to within one working day.

## Course Objectives

• Use mathematical methods to develop strategies to solve real world physics and physical science problems.
• Develop mathematical models from physical principles, solve problems using of mathematical techniques covered in the course and verify the validity of the solutions obtained.
• Present the findings in a form of a written report.

## Learning outcomes

Students will:
• develop understanding of various mathematical concepts and techniques required for successful application of mathematics in physics and related sciences;
• be able to model data using the language and techniques of mathematics;
• be able to understand and solve multidisciplinary application problems using mathematical methods;
• demonstrate ability to cover a topic independently and present their results in a written report.