Special topics in calculus for physics majors and engineers. Topics include vector calculus, linear algebra, power series, Taylor's series, complex analysis, and differential equations. The mathematical ideas and techniques are presented in the context of how and where they appear in the laws of physics, and the physical significance of the mathematics is discussed.
Athena Title
Mathematical Methods in Physic
Prerequisite
PHYS 1212-1212L or PHYS 1312-1312L
Pre or Corequisite
MATH 2270 or MATH 2500 or MATH 3500 or MATH 3500H
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Student Learning Outcomes
Students should be able to apply vector differential operators (gradient, divergence, curl, Laplacian) to physically-relevant mathematical problems.
Students should be able to solve systems of linear equations using matrix methods, including computing the eigenvalues and eigenvectors of a matrix, and apply these techniques to physical problems.
Students should be able to expand functions using Fourier series, and apply Fourier analysis techniques to the solution of differential equations in physics.
Students should be able to use power series / Taylor series for finding the approximate behavior of functions and for solving differential equations.
Topical Outline
Infinite Series: Power series, Maclaurin and Taylor series, other methods of series calculation, convergence tests, series solutions of differential equations
Vector Analysis: Scalar and vector products, scalar and vector fields, vector differential operators, line and surface integrals, divergence and Stokes theorems
Linear Algebra: Linear vector spaces, matrix multiplication, determinants, matrix inverse, eigenvalues and eigenvectors
