Mathematical Methods in Physics and Biology

Recommended Prerequisites

Knowledge of Differential and Integral Calculus, Linear Algebra and Differential Equations.

Teaching Methods

Classes are expository and include examples and exercises for applying the acquired knowledge. As homework the students solve analytical problems that involve the application of the methods studied.
During the semester students may use tutorial time to clarify their difficulties in grasping the theory and in gaining practical knowledge, as well as in the development of the necessary skills for homework assignment.

Learning Outcomes

The course is designed to develop modelling skills - in Physics and Biology - and analytical knowledge within linear and quasi linear partial differential equations. Laplace, diffusion and wave equations will be studied. Diffusion reaction will deserve some attention, namely pattern formation and chemotaxis.

Work Placement(s)

No

Syllabus

  I - Differential equations in the modeling of physical and biological phenomena.

 II - Partial differential equations (PDEs) of second order. Analytical methods to construct solutions.

III - Quasi-linear PDEs. Qualitative properties. Travelling waves.

IV - Reactive fluids and   biological movements: dispersion and invasion.

Head Lecturer(s)

José Augusto Mendes Ferreira

Assessment Methods

Continuous assessment
During the semester there are two mid-term exams (80% of the final grade) and a set of homework assignments (20% of the final grade: 100.0%

Final assessment
The final exam option consists of a single exam (100%).: 100.0%

Bibliography

L. Debnath, Non Linear Partial Differential Equations for Scientists and Engineers, Birkauser, 1997.

E. DiBenedetto, Partial Differential Equations, Birkhauser, 1995.

N.F. Britton, Essential Mathematical Biology, Springer 2003.

F. John, Partial Differential Equations, quarta edição, Springer, 1978.

J.D. Murray, Mathematical Biology I - An Introduction, Springer, 2002.

J.D. Murray, Mathematical Biology II – Spatial Models and Biomedical Applications, Springer, 2003.

I. Rubinstein, L. Rubinstein, Partial Differential Equations in Classical Mathematical Physics, Cambridge University Press, 1993.

D.W. Trim, Applied Partial Differential Equations, PWS-Kent Publishing Company, 1990.

E. Zauderer, Partial Differential Equations of Applied Mathematics, John Wiley Sons, 1993.