MATA218 Advanced Differential Equations 1 (4 cr)

Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

Systems of First-order differential equations;

systems of first-order linear equations; complex eigenvalues, Jordan canonical form, matrix norms and exponential matrix; existence and uniqueness of solutions; stability

Learning outcomes

  • Knows how to solve first order linear autonomic differential equations using exponential function of matrices. 
  • Is familiar with the existence and uniqueness theorem of solutions and is able to apply it as well as the continuous dependence on initial values.
  • Knows how to analyze the behavior of the solutions in the linear case, and near the equilibrium also in the nonlinear case.

Description of prerequisites

Linear algebra and geometry 2, Introduction to mathematical analysis 4, Vector calculus 2

Completion methods

Method 1

Evaluation criteria:
Course exam and exercises
Select all marked parts

Method 2

Evaluation criteria:
final exam
Select all marked parts
Parts of the completion methods
x

Teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish
No published teaching
x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
Finnish
No published teaching