Course syllabus - Differential Equations for Teachers

Objectives

The objective of the course is to introduce to the fundamental qualitative and quantitative methods used for analysis of ordinary differential equations and difference equations, and associated applications. The course is primarily for prospective teachers in secondary schools.

Learning outcomes

At the end of the course the student is expected to be able to
- analyse and solve ordinary differential equations of first order including concepts/methods as existence, uniqueness, phase portrait, stability, separability, linearity, exactness and substitution techniques.
- model dynamical courses of events for which rates can be specified matematically by ordinary differential equations of first order.
- analyse and solve linear differential equations including concepts/methods as fundamental set of solutions, particular solution, techniques involving reduction of order, and substitutions.
- analyse and solve linear difference equations with constant coefficients.

Course content

Ordinary differential equations of first order. Qualitative methods for analysis of autonomous differential equations. Modelling with first-order differential equations. Ordinary linear differential equations. Difference equations. Existence and uniqueness.

Tuition

Teaching is done involving lectures, assigned problems, classes, and quizzes.

Specific requirements

30 hp in mathematics including Vectors and matrices 7.5 credits, Discrete Mathematics with Didactics 7.5 credits, Mathematical modeling with analysis 7.5 credits, and Analysis, a second course 7.5 credits, or equivalent.

Examination

Exercises and tests (INL1), 2.5 credits, marks Pass (G)
Written and/or oral examination (TEN1), 5 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass, Fail