Featured Programs
Experiential Learning Opportunities
Claim up to $500 in flight credits!
Get up to $500 in flight credits or grants toward study or internship programs abroad when you apply by March 15, 2025. See our Official Rules for full details.
Mathematical Methods II
University of Galway - Engineering & Computer Science Program
Galway, Ireland
Dates: 1/7/20 - 5/9/20
Mathematical Methods II
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Other Subject Area: Physics
Instruction in: English
Course Code: MP346
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
This is a mathematical methods course, and amongst the topics considered are the heat equation, Laplace's equation, Sturm-Liouville theory, the Fourier transform, and the numerical solution of partial differential equations using finite difference techniques.
Learning Outcomes
1. Solve the 1-dimensional heat equation subject to different boundary conditions and initial conditions
2. Prove orthogonality of eigensolutions and reality of eigenvalues of a Sturm-Liouville system
3. Calculate eigenvalues and construct corresponding eigenfunctions for some simple Sturm-Liouville problems
4. Solve the 2-dimensional Laplace equation subject to different boundary conditions in a rectangular or a rotationally symmetric region
5. Solve the 1-dimensional heat equation on an infinite region by use of the Fourier transform
6. Solve the 1-d heat equation numerically by use of the finite difference method
Learning Outcomes
1. Solve the 1-dimensional heat equation subject to different boundary conditions and initial conditions
2. Prove orthogonality of eigensolutions and reality of eigenvalues of a Sturm-Liouville system
3. Calculate eigenvalues and construct corresponding eigenfunctions for some simple Sturm-Liouville problems
4. Solve the 2-dimensional Laplace equation subject to different boundary conditions in a rectangular or a rotationally symmetric region
5. Solve the 1-dimensional heat equation on an infinite region by use of the Fourier transform
6. Solve the 1-d heat equation numerically by use of the finite difference method