At the end of this course the students will have an
- An ability to expand functions into Taylor series and related truncation errors, and round-off errors
- An ability to solve first and higher-order initial value ODEs, and coupled set of initial value ODEs with multi-step (Runge-Kutta) methods
- An ability to solve coupled set of initial value ODEs
- An ability to formulate conservation laws in integral and partial differential forms
- An ability to discretize integral forms of governing equations in finite
volumes
- An ability to discretize PDEs in finite differences and perform Fourier stability analysis
- An ability to classify PDEs as elliptic, parabolic and hyperbolic, and make proper choice of numerical methods for their solution
- An ability to write a computer program to solve initial value ODEs in general
- An ability to implement and/or modify finite volume and finite difference
methods in Fortran
- An ability to compile and run Fortran programs on computers and analyze results using graphical tools
- An ability to work on teams
- An ability to report homework solutions in technical form
- An ability to make ethical choices