# Differential Equations

• ECTS credits10
• Teaching semesterSpring
• Course codeMAT131
• Number of semesters1
• LanguageNorwegian
• Resources

Spring

### Objectives and Content

Objectives:

The course introduces the theory and solution methods for ordinary and partial differential equations.

Contents:

Solution methods for scalar and linear systems of differential equations, and stability of nonj-linear systems. The course also includes solution of different partial differential equations by means of Fourier series.

### Learning Outcomes

On completion of the course the student should have the following learning outcomes defined in terms of knowledge and skills, and general competence:

Knowledge and skills

The student has the ability to:

• Identify and solve first-order differential equations that are separable, linear or exact.
• Identify different processes that are described by one or more differential equations.
• Explain the theory of existence and uniqueness for second-order differential equations, and master solution methods in special cases.
• Use methods from linear algebra to solve linear systems and give a qualitative description of the solution curves in the phase plane.
• Find critical points for first-order non-linear systems and classify their stability properties.
• Work with simple predator-prey models.
• Use separation of variables and Fourier series to solve the wave equation and the heat equation.

General competence

• The student has a good command of the theory behind the above methods

### Recommended Previous Knowledge

MAT111, MAT112 and MAT121. (MAT112 and MAT121 can be taken together with MAT131.)

Excercises

### Forms of Assessment

Written examination: 5 hours

Available aids: None

Due to the measures taken to avoid the spread of SARS-CoV-2, UiB is closed for teaching and assessment. As a consequence, the following changes is made to assessment spring semester 2020:

• Written home examination instead of written examination

M117: 10 ECTS

## Exam information

• For written exams, please note that the start time may change from 09:00 to 15:00 or vice versa until 14 days prior to the exam. Autumn 2020 written exams will be arranged either at home or on campus. Please see course information on MittUiB.

• ### Type of assessment: Written examination

Date
24.09.2020, 09:00
Duration
5 hours