Differential Equations and Series
| Structure Type: | Study unit |
|---|---|
| Code: | ISTP0505 |
| Type: | Compulsory / Basic Studies |
| Curriculum: | I-ST 2010 |
| Level: | Bachelor of Engineering |
| Year of Study: | 2 (2011-2012) |
| Credits: | 2 cr |
| Responsible Teacher: | Niemi, Henry |
| Language of Instruction: | Finnish |
Courses During the Academic Year 2011-2012
| Impl. | Study Time | Teacher(s) | Language | Enrolment |
|---|---|---|---|---|
| 1 | 2012-01-09 – 2012-03-02 | Jussi Ojanen | Finnish | 2011-12-07 – 2012-01-15 |
Learning Outcomes
The student knows the concepts of differential equations and how to apply them and series in rough estimates. The student can solve a differential equation using the following methods: separation of variables, methods for solving equations with first and second order linear constant coefficient and Laplace transform. In addition, the student learns to solve differential equations numerically.
The student knows the basics of series and is able to form a power series of a function and modify existing series developments. The student is familiar with the Fourier series and is able to form a fourier series in simple cases. The student knows what a differential equation is and can solve them using z transformation.
Student's Workload
The total amount of student's work is 54 h, which contains 28 h of contact studies.
Prerequisites / Recommended Optional Courses
Integral calculus
Contents
Basic concepts of differential equations, separation of variables and linear differential equation. Differential equations with second order linear constant coefficient. Laplace trasnform and its use in solving differential equations. Sequences of numbers and numerical solutions of differential equations. Arithmetical and geometrical series, power series and their applications, Fourier series and basics od z transformations. Application related to electrical engineering.
Recommended or Required Reading and Other Learning Resources/Tools
Majaniemi: "Matematiikka I, II ja III", Tietokotka Oy; the material prepared by the teacher.
Mode of Delivery / Planned Learning Activities and Teaching Methods
See the description of "integral calculus".
Assessment Criteria
Grade 5: The student is able to apply creatively the contents of the course.
Grade 3: The student is well-abled to utilize the course contents.
Grade 1: The student knows those subjects of the course, which are necessary for the forthcoming studies and working life.
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 by the end of the course.