SF1633 Differential Equations I 6.0 credits

• Educational level

  First cycle

• Academic level (A-D)

  C

• Subject area

  Mathematics
  Techonology
  

• Grade scale

  A, B, C, D, E, FX, F

• Link to homepage

• Course page on KTH Social

Learning outcomes

To give the students

• acquaintance with the fundamental theory of ordinary differential equations.
• ability to solve certain types of (systems of) ordinary differential equations using standard methods.
• ability to analyze (systems of) ordinary differential equations using geometric and qualitative methods.
• ability to compute Laplace transforms.
• ability to compute Fourier series.
• ability to solve separable partial differential equations and to find solutions to boundary value problems using Fourier methods.
• the possibility to gain deeper insights into areas relevant for their education.
• ability to use suitable computer software for symbolic as well as graphic investigations of the problems mentioned above.
• ability to attack modeling problems.

Course main content

• First order ordinary differential equations: Fundamental theory and concepts. Modeling. Directional fields and solution curves. Autonomous equations. Stationary solutions. Stability. Separable equations. Linear equations.
• Linear ordinary differential equations of higher order: Fundamental theory. Methods of solution for constant coefficient equations. Vibrational phenomena.
• Systems of linear ordinary differential equations: Fundamental theory and concepts. Solving linear systems with constant coefficients using eigenvalue methods and variation of parameters.
• Autonomous systems of ordinary differential equations: Fundamental concepts. Stationary solutions and their stability. Global phase portraits. Modeling.
• The Laplace transform and its applications.
• Fourier series with applications.
• Linear partial differential equations: Separation of variables. Solution of classical boundary value problems (wave equation, heat equation, Laplace's equation) using Fourier methods.

Eligibility

Basic knowledge of linear algebra and calculus, as presented 

SF1624 Algebra and Geometry

SF1625 Calculus in One Variable

SF1626 Calculus in Several Variables

Literature

Zill-Cullen/Differential Equations with Boundary-Value Problems

Råde-Westergren/Mathematics Handbook for Science and Engineering.

Examination

• TEN1 - Examination, 6.0 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

Oral and/or written exam, plus continuous examination (TEN1; 6 hp).

Offered by

SCI/Mathematics

Examiner

Hans Tranberg <tranberg@kth.se>

Version

Course plan valid from: Autumn 10.
Examination information valid from: Autumn 07.