TATA57 · 4 credits · Basic level (G1F) · Matematik, Tillämpad matematik
Transform Theory
Active · next start VT 2027
55%
passed the latest ordinary exam
TEN1 · 5 Jun 2026 · 22 students
56%
passed the ordinary exams, all sittings over the last 5 years
TEN1 · 126 students
82%
Harder than 82% of courses at basic level
Compared with 874 courses at the same level, ordinary exams over the last three academic years. 36 students.
Part of 1 programme
Exam
TEN1 Written examination
- 5
- 4
- 3
- U
Ordinary exams
56% passed · 126 students
- 55%22
- 64%14
- 59%27
- 52%33
- 53%30
Re-exams
61% passed · 90 students
- 64%11
- 50%10
- 67%15
- 50%8
- 60%10
- 77%13
- 57%23
- Pass the re-exam: 61% (90 students), compared with 56% (126 students) on the ordinary exam
- Get 4 or 5: 23% (216 students)
Show small sittings (4)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
- 33%3
- 67%3
- 100%2
- 33%3
About the course
Aim
After completing the course, the student should be able to
- choose and apply methods to problems in all parts I-IV of the course, as they are described in the course content
- present and justify solutions to tasks within the course content using relevant concepts and clear reasoning
Content
In this course we study some important linear transformations, with the help of which linear problems (differential-, integral- ,difference equations) can be translated into more manageable algebraic problems, the solutions of which are then translated back into solutions to the original problems.
The following are studied:
Part I: Fourier series and convergence Convergence of function sequences. Uniform convergence. Periodic functions. Fourier series. Pointwise and uniform convergence of Fourier series. Bessel's inequality and Parseval's theorem. Convergence in means. Applications include periodic solutions to differential equations.
Part II: The Fourier Transform The Fourier transform of absolutely integrable functions. Properties and calculation rules. Folding. Inversion of the Fourier transform. Plancherel's theorem. Applications include differential and convolution equations.
Part III: The Laplace Transform The one-sided Laplace transform of exponentially bounded functions. Properties and calculation rules. Solving initial value problems. Folding. The beginning and ending value rate.
Part IV: The Z Transform The one-sided Z-transform. Properties and calculation rules. Solving difference equations. Folding.
- Examiner
- Johan Thim
- Scheduled hours
- 46 h
- Main field of study
- Matematik, Tillämpad matematik