Basics of Analysis
| Structure Type: | Study unit |
|---|---|
| Code: | ITTP0307 |
| Type: | Compulsory / Basic Studies |
| Curriculum: | TT 2014V |
| Level: | Bachelor of Engineering |
| Year of Study: | 3 (2016-2017) |
| Credits: | 2 cr |
| Responsible Teacher: | Mäkelä, Jarmo |
| Language of Instruction: | Finnish |
Learning Outcomes
This course is a direct continuation of the differential calculus course. A student will learn the basics of integral calculus, differential equations, and series. Integral calculus may be used, for instance, to calculate areas of planar regions and volumes of three-dimensional bodies. Differential equations, in turn, have a very large range of applications. They may be used, for instance, when we try find the best possible form for a bridge or investigate the changes of electric current and voltage during the course of time in an electric circuit. As a matter of fact, most equations used in applied mathematics are actually differential equations. Series and power expansions, in turn, are needed when the behaviour of a given function becomes hopelessly complicated, and we want to find a practical approximation for the behaviour of the function within a certain small domain. During this course the student will learn to integrate, solve differential equations, and write the power expansion of the given function.
Student's Workload
The total amount of student's work is 54 h, which contains 20 h of contact studies and 34 h of individual studies.
Prerequisites / Recommended Optional Courses
Differential Calculus.
Contents
Definite and indefinite integrals, formulas of integration, area and volume, numerical integration. Basic concepts of differential equations. Separation of variables and a linear differential equation. Differential equations of the second order with constant coefficients. Sequences, numerical solution of differential equations. Arithmetical and geometrical series. Power series and their applications. Applications specific to degree programme.
Recommended or Required Reading and Other Learning Resources/Tools
Majaniemi: "Matematiikka I, II ja III", Tietokotka Oy; opettajan valmistama materiaali; 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. 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. Students are given exercises which are to be solved with a computer.
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 by the end of the course.