Differential calculus (5 cr)

Evaluation scale

H-5

Content scheduling

There are two teaching sessions weekly excluding week 8.

The first mid exam is held on week 9.
The second mid exam is held on week 15.

Course contents:
- Number systems
- Limit
- Derivative as a limit
- Differentiation formulas
- Solving optimization problems with differentiation

Objective

After completing the course the student:
- operate with mathematical expressions related to technology
- to formulate mathematical model
- understand the concept of a function and recognizes the characteristic properties of different functions
- solve equations involving functions and apply them in practical problems
- use derivatives to analyse graphs
- use differentials to approximate changes and errors
- use matrices and determinants (e.g. for solving linear simultaneous equations),
- use dot and cross products in applications
- give the answer in an expected form

Content

Topics covered in course are (in the order shown):
* functions and graphs
* Pythagoras’ theorem and trigonometric functions
* line and slope
* exponential and logarithmic functions
* function composition
* continuity and limit of a function
* definition of the derivative
* derivatives of basic functions
* derivative rules
* derivative of the composition of functions (chain rule)
* product rule and quotient rule
* tangent and differential
* critical points and extreme values
* finding extreme values by examination of critical points
* functions of several variables
* partial derivatives
* differentials and error estimates
* total differential

Materials

Edita; Insinöörin matematiikka; Ari Tuomenlehto & co.
Itslearning-site and material linked there.

Teaching methods

The teaching is based on contact teaching and exercises.

Exam schedules

The first mid exam on week 9.
The second mid exam on week 16.

There is a possibility of taking a full exam in May and August. A mid exam cannot be redone.

International connections

Teaching sessions consist of theory and examples. The focus on learning is placed on the activity of the student in participation and working on exercises.

Completion alternatives

Finishing the final exam.

Student workload

5 credits = 134 hours of work by the student

24 * 2 h = 48 h contact teaching
2 * 2 h = 4 h exams
82 h personal studying including working on exercises and preparing for exams

Further information

Informing is done during contact teaching, by email or in the ITS-learning site. If you want to contact the teacher, please do it via email.