PY/MA 370 Mathematical Methods for the Physical Sciences I
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 Covered1. 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 datesExam 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|
Number of credits
PY212 and Calculus 3 or the permission of instructor.
AttendanceIt 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.
ExamsThere 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.
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.
- 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 outcomesStudents 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.