Advanced Analysis
| Structure Type: | Study unit |
|---|---|
| Code: | IYTS9301 |
| Type: | Optional obligatory / Professional Studies |
| Curriculum: | I-YT 2013 |
| Level: | Bachelor of Engineering |
| Year of Study: | 3 (2015-2016) |
| Credits: | 4 cr |
| Responsible Teacher: | Niemi, Henry |
| Language of Instruction: | Finnish |
Learning Outcomes
During this course a student will deepen the knowledge gained during the courses of differential calculus and analysis. She will learn different methods of integration, solve differential equations efficiently, and to integrate and differentiate multivariable functions. In analytical space geometry she will be made familiar with the properties of curved surfaces, and she will learn to optimize multivariable functions. She will also learn to calculate curvatures of planar curves, which may be applied, for instance, in the construction of gear wheels.
Student's Workload
The total amount of student's work is 108 h
Prerequisites / Recommended Optional Courses
Analysis: Differential- and Integral Calculus basics and Differential equations and series
Contents
Integration by parts and by substitution, inverse trigonometric and hyperbolic functions, curvature of planar curves. Advanced methods of integral calculus, with applications, and numerical methods. Methods of solution of differential equations, applications and numerical methods. Planes, lines and second order surfaces. Linear optimization, with applications. Differential and integral calculus of multivariable functions. Advanced properties of power series expansions, with applications.
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. 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.