Course No: Math-342A Title: Methods
of Applied Mathematics I
Course Prerequisite: Math-252
Vector analysis, divergence and Stoke’s theorem and
related integral theorems. Matrix analysis, eigenvalues and eigenvectors,
diagonalization. Introduction to ordinary differential equations. Computer
software packages for matrix applications, solving ,and graphing differential
equations.
Not open to students with credit in Physics 340A.
1.
Linear Algebra (2 weeks)
· linear sets of equations
· determinants
· vectors
· matrices
· linear combinations.
2.
Revision of multiple integrals (1 week)
· double integrals
· triple integrals
· mass, volume, center of mass, moment of inertia
· change of variables, Jacobian
· surface integrals
3.
Vector analysis (3 weeks)
· applications of vector multiplication
· triple products
· differentiation of vectors
· fields
· directional derivative, gradient
· divergence, curl, Laplacian
· line integrals
· Green's theorem
· divergence theorem
· Stoke's theorem
4.
Complex numbers (1 week)
· Real and imaginary
· complex plane, algebra, series
· elementary functions
· Euler's formula
· powers and roots
· exponential and trigonometric functions
· hyperbolic functions
· logarithms
5.
Ordinary Differential Equations (3 weeks)
· Separation on variables
· Linear first order equations.
· Change of variables
· Integrating factors
· Second order linear equations. (homogeneous and
non-homogeneous)
6.
Coordinate transformations
and tensors (3 weeks)
· Linear transformations
· Orthogonal transformations
· Eigenvalues and eigenvectors.
· Curvilinear coordinates
· tensor analysis (Cartesian, dyadics, general
coordinate systems)
7.
Special Functions (2 weeks)
· Factorial, Gamma function
· Beta Functions
· The simple pendulum
· Error function
· Asymptotic analysis
· Striling's formula
· Elliptic integrals
Recommended Textbook: Mathematical Methods in the Physical Sciences. Mary
L. Boas. Wiley, 1983.
Software recommended: Matlab and
Maple