AME 60611: Mathematical Methods I (JMP)

AME 60611

"Multidimensional calculus, linear analysis, linear operators, vector algebra, ordinary differential equations. (Every fall)"

The course is directed at first year graduate students in engineering. It is open to undergraduates who wish to become better prepared for graduate studies or become more proficient in the techniques of applied mathematics.

Next: ?
Current: Fall 2015
Previous: Fall 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2007, 2008, 2009, 2011, 2013

Multi-variable calculus
- Implicit functions
- Functional dependence
- Coordinate transformation
- Maxima and minima
- Lagrange multipliers
First-order differential equations
- Separation of variables
- Homogeneous equations
- Exact equations
- Integrating factors
- Bernouilli equation
- Riccati equation
- Reduction of order
- Uniqueness
- Clairaut equation
Linear differential equations
- Linearity and linear independence
- Complementary functions for equations with constant coefficients
- Complementary functions for equations with variable coefficients
- Particular solutions
Series solution methods
- Power series
- Perturbation methods
- Functional equations
Special functions
- Sturm-Liouville equations
- Representation of arbitrary functions
Vectors and tensors
- Cartesian index notation
- Cartesian tensors
- Algebra of vectors
- Calculus of vectors
- Line and surface integrals
- Differential operators
- Special theorems
- Orthogonal curvilinear coordinates
Linear analysis
- Sets
- Differentiation and integration
- Vector spaces
- Operators
- Equations
- Method of weighted residuals
Linear algebra
- Determinants and rank
- Matrix algebra
- Orthogonal and unitary matrices
- Matrix decompositions
- Projection matrix
- Method of least squares
- Matrix exponential
- Quadratic form
- Moore-Penrose inverse
Dynamical systems
- Paradigm problems
- Iterated maps
- High order scalar differential equations
- Linear systems
- Nonlinear equations
- Fractals
- Bifurcations
- Lorenz equations

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