Integral Transforms
| Structure Type: | Study unit |
|---|---|
| Code: | IYTS9302 |
| Type: | Optional obligatory / Professional Studies |
| Curriculum: | I-YT 2012V |
| Level: | Bachelor of Engineering |
| Year of Study: | 4 (2015-2016) |
| Credits: | 3 cr |
| Responsible Teacher: | Niemi, Henry |
| Language of Instruction: | Finnish |
Learning Outcomes
Many problems encountered in engineering applications of mathematics become considerably simple, if one studies, instead of the original functions, their integral transforms. When we perform an integral transform for a given function, we transform the function to a new function of a new variable by means of an expression which involves integrals. The most important integral transforms are Laplace- and Fourier transforms. A transform closely related to integral transforms is the so called Z transform, which has many applications, for instance, in telecommunication. During this course a student is made familiar with integral transforms and their applications in differential equations encountered in engineering problems, as well as in a spectral analysis of electromagnetic pulses.
Student's Workload
The total amount of student's work is 81 h, which contains 48 h of contact studies.
Prerequisites / Recommended Optional Courses
Analysis: Differential- and Integral Calculus basics and Differential equations and series
Contents
Fourier series, Fourier transform, Laplace transform, and Z transform. Transfer function. Applications, among other things, in the solution of ordinary and partial differential equations, as well as in the solution of difference equations.
Recommended or Required Reading and Other Learning Resources/Tools
Kreyszig, E: "Advanced Engineering Mathematics", John Wiley & Sons; the material prepared by the lecturer.
Mode of Delivery / Planned Learning Activities and Teaching Methods
The basics of learning constitutes of lectures where the theory is explained and examples are given. An essential ingredient of learning, however, consists of exercises which are gone through during the lectures, and independent homework performed by the student. A mere attending the lectures and listening to the lecturer is not sufficient for proper learning. In practice, an independent pondering of the contents of the course becomes best realized when a student solves independently, at home, the problems given by the lecturer. Solutions to the problems are given during the lectures.
Assessment Criteria
Grade 1: The student knows those subjects of the course, which are necessary for the forthcoming studies and working life.
Grade 3: The student is well-abled to utilize the course contents.
Grade 5: The student is able to apply creatively the contents of the course.
Assessment Methods
Exercises and examination. The student is required to perform at least one quarter of the homework exercises. All the given computer-related exercises must be handed in before the end of the course.