PY/MA 370 Mathematical Methods for the Physical Sciences I

Syllabus

handouts videos syllabus pdf flier photographs

Office Hours

Office hours in Spring 2022 will be by appointment. Please feel free to make an appointment whenever you have a question, no matter if it is a longer or a quick one, or when you would like to work on a problem together with me.

Textbook

No textbook required. Handouts with new material and practice problems will be distributed for each teaching unit. 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.

Technology

Matlab will be used extensively. All students are also recommended to have a calculator.

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.

Series solutions of ODEs covers a method of finding solutions of ODE 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.

These mathematical topics will be related to specific problems in various areas of physics and physical science such as fluid dynamics, electricity and magnetism, quantum mechanics, thermodynamics, biophysics, and mechanics. 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.

Grading

Exams 1, 2 and 318% each
Exam 422%
Assignments12%
Project12%
TOTAL100%
Grades are computed according to the following system:
A+ A A- B+ B B- C+ C C- D+ D D- F
grade 97-100 93-96 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 63-66 60-62 0-59

Number of credits

3

Prerequisites

PY212 and 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 will be distributed. 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.

Academic integrity

Saint Joseph’s University encourages the free and open pursuit of knowledge; we consider this to be a fundamental principle and strength of a democratic people. To this end, SJU expects its students, its faculty, its administrators, and its staff to uphold the highest standards of academic integrity. The University expects all members of the University community to both honor and protect one another’s individual and collective rights.

Student with Disabilities Statement

Reasonable academic accommodations may be provided to students who submit appropriate documentation of their disability. If students have need of assistance or questions with this issue, they are encouraged to contact the Office of Student Disability Services (SDS) at sds@sju.edu or by phone at 610.660.1774. The Office of SDS also provides an appeal/grievance procedure for complaints regarding requested or offered reasonable accommodations. More information can be found at: www.sju.edu/sds.

Health and Wellness Statement

Saint Joseph's University recognizes that physical and mental health strongly impact one's ability to do well in school and in life. As a result, there are many helpful campus resources designed to help students to care for their physical, mental, and spiritual health. Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressure and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. All of us benefit from support during times of struggle and challenges. If you are experiencing concerns, seeking assistance sooner rather than later is a courageous thing to do for yourself and those who care about you. The resources at https://sites.sju.edu/counseling/ can help you to cope with stress and to achieve your academic and personal goals.

COVID-19 policy

SJU's Covid-19 policy is available at: https://www.sju.edu/hawk-hill-ahead/health-and-safety/monitoring . In particular, it states that all faculty, staff, students and visitors are asked to carry a mask at all times while on campus and that they should wear it if asked to. Since my office is relatively small, please note that I ask you to wear a mask when you are in my office.