Mathematics III - Ordinary Differential Equations
7.5 credits cr.
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Differential equations, i.e. equations of one or more functions and their derivatives, are an indispensable tool for understanding the world: they appear in the modeling of numerous processes in physics, biology, technology, social sciences, and economy.
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This course provides an introduction into ordinary (i.e. one-variable) differential equations, their analytical and numerical solution techniques and the underlying theory, such as statements on the existence and uniqueness of solutions or their stability. In addition, a few examples of partial differential equations will be treated.
Linear differential equations with constant and variable coefficients, existence and uniqueness theorems, boundary value problems, Green's function, plane autonomous systems, stability and classification of critical points, examples of second order partial differential equations, separation of variables, transformation methods for differential equations, numerical solutions.
The contents of the course may be applied in modelling in a number of fields, as for example Physics and Economy.
The course consists of three elements, where one (theory) is compulsory and the student chooses one of the other two elements (project - theory, or project - numerical calculations) to complete.
Instruction is given in the form of lectures and exercise sessions.
Examination for the course is done with a written (and, for higher grades, oral) examination, and written and oral presentation of the project (whether theory or numerical calculations).
To pass the course, you must pass the theory element and one of the two project elements. The grade is decided by the grade on the theory element.
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Course literatureNote that the course literature can be changed up to two months before the start of the course.