PHY510 Mathematical Methods of Physics I

Course Information

Professor: Dr. Peter Nightingale
Semester: Fall of odd years
Credits: 3
Prerequisites: permission of chairperson.

Catalog Description: Topics designed to include applications in physics: linear algebra;
determinants, matrices, eigenvalues; properties of finite and infinite bases; basics of numerical linear algebra; probability and statistics; Monte Carlo methods

Course Goals & Outcomes

By the end of the semester students will be able to:

  • Use mathematical methods presented in this course to solve numerical problems
  • Strengthen their understanding of mathematical methods used in physics and medical physics
  • Application of Monte Carlo methods

Course Syllabus

This course meets two times per week for lecture. Topics covered in this course include:

  • Vector and Tensor Analysis
  • Linear Algebra
  • Coordinate Systems
  • Determinants and Matrices
  • Infinite Series
  • Complex Analysis
  • Analytic Properties
  • Conformal Mapping
  • Calculus of Residues
  • Fourier Analysis
  • Laplace Transforms
  • Singular value decomposition
  • Probability theory and statistics
  • Markov chains
  • Monte Carlo Integration
  • Metropolis algorithm

Grades are based on the following criteria:

  • Exams (3-4)
  • Computational Project
  • Final Exam

About the Professor

http://www.phys.uri.edu/people/nightingale.html

Reasons To Take This Course

The mathematical methods presented in this course will enhance students’ ability to solve numerical problems relating to physics. It is important for students to have knowledge of the various methods used in analysis, since medical physicists use sophisticated data analysis techniques.

Cool Links

http://mathworld.wolfram.com/ConformalMapping.html
http://demonstrations.wolfram.com/XFT2DA2DFastFourierTransform/