APPLIED MATHEMATICS FMA022

Higher education credits: 4,5. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in Swedish. FMA022 overlap following cours/es: FMA021, FMA020, FMA021, FMA020 och FMA021. Compulsory for: F2. Optional for: D3, E2, M3, N3, N3nel, N3nf. Course coordinator: Director of Studies, Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Recommended prerequisits: FMA036 Linear Analysis. Assessment: Written test comprising theory and problem solving. Computer work. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The course treats mathematical concepts and methods for partial differential equations. The intention is to make the student acquainted with the whole chain from the drawing up of a model, the theoretical analysis of the model up to a numerical solution. One aim is also to give the students ability to read and judge mathematical reasoning, to give ability in problem solving and training in accounting of mathematical discussions. The main stress is on calculations with paper and pencil, but also on providing via computer exercises acquaintance with mathematical and numerical software.

Knowledge and understanding
For a passing grade the student must

be able to show capability to draw up mathematical models for phenomena in heat conduction, diffusion, wave propagation, and stationary heat conduction/diffusion/electrical fields.

be able to show capability to physical interpretation of mathematical models with different boundary conditions, such as the heat equation, the wave equation and Laplace' or Poisson's equation.

be able to show capability to identify Sturm-Liouville operators and in simple cases to find the corresponding eigenfunctions and eigenvalues.

have some experience and understanding of mathematical and numerical software.

Skills and abilities
For a passing grade the student must

be able to show capability independently to choose appropriate methods to solve the three "central" types of partial differential equations, och to carry out the solution essentially correct.

be able to show capability to use theoretical tools from areas such as special functions and Fourier and Laplace transforms to solve the three "central" partial differential equations in simple cases.

with proper terminology, in a well structured way and with clear logic be able to explain the solution to a mathematical problem within the course.

Contents
Physical models. Fourier's method, series expansions. Applications in heat conduction and wave propagation. Sturm-Liouville operators and special functions. Transform methods. Somewhat about numerical solving of partial differential equations.

Literature
Sparr, G & Sparr, A: Kontinuerliga system. Studentlitteratur 2000. ISBN 91-44-01355-8