Differential Calculus
| Structure Type: | Study unit |
|---|---|
| Code: | IITA0101 |
| Type: | Compulsory / Professional Studies |
| Curriculum: | IT 2014 |
| Level: | Bachelor of Engineering |
| Year of Study: | 2 (2015-2016) |
| Credits: | 2 cr |
| Responsible Teacher: | Mäkelä, Jarmo |
| Language of Instruction: | English |
Courses During the Academic Year 2015-2016
| Impl. | Group(s) | Study Time | Teacher(s) | Language | Enrolment |
|---|---|---|---|---|---|
| 5 | I-IT-2N | 2015-10-26 – 2015-12-31 | Jarmo Mäkelä | English | 2015-08-14 – 2015-10-30 |
Learning Outcomes
Differential calculus is one of the most important branches of mathematics. The fundamental problem of differential calculus is the following: If two quantities depend on each other in a certain manner, then in which way do the changes of these quantities depend on each other, if those changes are very small? The quotient of the small changes of two quantities depending on each other is known as a derivative. The petrol consumption of an automobile, for instance, will increase together with the speed of the automobile, and the change in the petrol consumption divided by the change in the speed is the derivative of the petrol consumption with respect to the speed. Differential calculus is based on the concept of derivative. During this course a student is made familiar with the concept of derivative, she will learn to calculate a derivate of a given function, or differentiate, and to use differential calculus in practical applications. These include, among other things, estimation of the errors made in the measurements, and finding the most economic form of industrial products.
Student's Workload
The total amount of student's work is 54 h, containing 28 h of scheduled contact studies.
Prerequisites / Recommended Optional Courses
Analytic Geometry and Linear Algebra.
Contents
Limit and derivative, differentiation of basic functions, composite function, study of the properties of functions. Partial derivative, differential, extreme values of a single-variable function and of multi-variable functions. Applications specific to degree programme.
Recommended or Required Reading and Other Learning Resources/Tools
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. At the end of the course, students may be 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 tpo apply creatively the course contents.
Assessment Methods
An examination, homework exercises and tutored exercise sessions. The student is required to actively take part in exercise sessions, in the same way as in Physics laboratory exercises. All the given computer-related exercises must be handed in by the end of the course.