PY/MA 370 Mathematical Methods for the Physical Sciences I


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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.


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.


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.


Exams 1, 2 and 318% each
Exam 422%
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



PY212 and Calculus 3 or the permission of instructor.


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.


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

Academic integrity is at the center of the educational experience at the SJU. Students are therefore expected to uphold the highest standards of academic integrity and not engage in nor tolerate academic dishonesty. Academic dishonesty includes, but is not limited to, fabrication, cheating or plagiarism, and unauthorized collaboration. Any violation of academic integrity will be investigated and, where warranted, the student will receive appropriate sanctions through the University's Student Conduct Process. Please familiarize yourself with the current Student Handbook. In particular, adherence to the Student Conduct Policy and Academic Integrity Policy will help to ensure that your learning and living experiences are founded on integrity.

Americans with Disabilities Act (ADA) Compliance Statement

SJU supports the educational endeavors of all students, including students with disabilities. ADA defines a disability as a mental or physical impairment that substantially limits one or more major life activities. If you believe that you have a disability that may impact your ability to fulfill your course or degree requirements, and you would like more information on applying for an accommodation under ADA, please contact the Program Coordinator of Student Accommodations who serves as 504 Coordinator.

Mental Health Wellness Statement

SJU encourages students to recognize that academic success requires students to be emotionally and physically well. If you are having difficulty coping with stress associated with the classroom or are experiencing other personal issues, please go to Student Health and Counseling (SHAC) located on the first floor of Whitecar Hall or call 215.596.8536. Additional emotional support is available 24/7 and can be obtained by contacting the National Suicide Prevention Hotline at 800.273.8255 or by texting “Go” to the Crisis Text Line 741-741. The services listed above are all free and confidential.

COVID-19 Syllabus Statement

As we continue to navigate the COVID-19 pandemic it is important to remember that:
· All individuals, regardless of vaccination status, are required to wear masks indoors on campus.
· SJU mandates that all students, faculty, and staff are vaccinated against COVID-19.
· Practice good hygiene by frequently washing hands.
· Conduct a daily health check before coming to campus.
Check the COVID-19 Return to Campus Guidelines regularly for updates. If we all follow the rules, we will help to ensure that our learning environment is as safe as possible.
Students who are ill, regardless of symptoms, vaccination status or or diagnosis, should not come to campus for classes or activities and should contact SHAC. If students are ill, but able to virtually participate in courses they may do so. Students should not contact the Office of Student Health for “sick notes.”
The COVID-19 pandemic has refocused the need for both mental and physical personal wellness. The University encourages students who are ill to take the time to focus on their health. Additionally, if needed students may reach out to their college dean’s office to inquire about leave of absence options including: short-term leave of absence (up to 10 business days), a personal leave of absence, or a medical leave absence. We firmly believe to learn you must be healthy.