Mathematical Physics I(2.0 credits)
|Course Type||:||Basic Specialized Courses|
|Starts 1||:||2 Autumn Semester|
|Lecturer||:||John A. WOJDYLO Designated Professor|
|This course is a companion course to Mathematical Physics II. Students master analytical techniques for problems
that arise in physics, engineering and chemistry. This course introduces first order and second order ordinary
differential equations and their solution methods. Questions of uniqueness of solutions and convergence are also
discussed. Students are also introduced to Fourier series, the Fourier transform, convolution, Laplace transform, and
the Dirac delta function. Students will find this mathematical methods course helpful in other units such as Quantum
Mechanics, Analytical Mechanics, Electricity and Magnetism, as well as in Automotive Engineering and other
engineering courses. This course has dual aims: 1) to convey mathematical principles; 2) to improve students’
technical ability ‒ i.e. ability to express intuition in mathematical terms and ability to solve problems.
|Calculus I; Calculus II; Linear Algebra I; Linear Algebra II, or Consent of Instructor
Mathematical Physics Tutorial I, Mathematical Physics II
|• First order ordinary differential equation (ODE) initial value problems. Integration factor; separable equations;
systems of ODEs (Hamiltonian systems); phase plane, flow. Uniqueness and existence theorems. Some differences
between linear and nonlinear ODEs.
• Second order linear ODE initial value problems. Homogeneous solution. Proving linear independence (Wronskian).
Method of Undetermined Coefficients; Variation of Parameters. Series solutions: ordinary point, regular singular
point; convergence tests; Method of Frobenius. Examples from physics and engineering.
• Fourier series. Dirichlet conditions. Role of symmetry. Gibbs phenomenon. Effect of jump discontinuity on speed of
convergence. Integration and differentiation of Fourier series.
• Fourier transform, convolution, Dirac delta function. Laplace transform.
|Boyce W., DiPrima R, Elementary Differential Equations, 7th ‒10th Ed., Wiley.|
|1.Boas M.L., 2006, Mathematical Methods in the Physical Sciences, 3rd ed., John Wiley & Sons.
2.Strang, G., Introduction to Linear Algebra, 4th Edition, Chapter 6.
3.Arfken G.B. & Weber H.J., 2005, Mathematical Methods for Physicists, 6th ed., Elsevier Academic Press. (Copies
are available in the library.)
|Attendance: 5%; Weekly Quizzes and Assignments: 25%; Mid-term exam: 35%; Final Exam: 35%
The “Absent” grade is reserved for students who withdraw by November 16. After that day, a letter grade will be
awarded based on marks earned from all assessment during the semester.
|Office: Science Hall 5F 517