Study Guide

Objectives (course unit)

Student is able to:
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations and recognize graphs involving basic functions and apply them in practical problems
- apply the concepts of derivative when solving practical problems
- interpret derivative as rate of change
- determine the derivative using graphical, numerical and symbolical methods
- construct error estimates using the differential method
- understand basic terminology of integral calculus
- determine integral graphically, numerically and symbolically
- calculate areas using definite integral

Content (course unit)

- Basic functions, terminology, graphs and equations (Polynomial, exponential, logarithmic)
- Derivative
- Graphical, numerical and symbolic differentiation
- Applications of derivative
- Error estimation with differential
- Integral function
- Definite integral
- Graphical, numerical and symbolic integration
- Calculation of areas and volumes with integral

Assessment criteria, satisfactory (1-2) (course unit)

Understanding of basic concepts related to course topics. Capability to calculate exercises that are similar to discussed examples. Can interpret derivative as rate of change. Can determine derivatives and integrals using graphical and symbolical methods. Can calculate basic areas and volumes with integrals.

Assessment criteria, good (3-4) (course unit)

In addition, understanding of advanced and most concepts related to course topics. Ability to apply them in basic technical problems.

Assessment criteria, excellent (5) (course unit)

In addition, ability to apply course topics in advanced problems.

Location and time

Dates and times are shown in TuniMoodle.

First lessons on Jan 19th at 11 o'clock

Exam schedules

There will be three exams to be held during the course, i.e., between timeline 19.1.- 30.4.

The initial schedules of the exams will be negotiated with students during the first lessons.

Changes to exam arrangements are possible depending e.g. on the course progress and other teacher's work duties.

Assessment methods and criteria

The final grade of the course will be based on the score from course activity, returned assignments and exam scores.

The maximum score from the returned assignments (all given assignments done with good quality) and course activity (all given lessons actively participated) is 20 .

From each exam, the maximum score is 20.

The total score is calculated from the sum of assigment/activity score and exam scores. In a case where some parts of separate exams cover the same course topics, only the best score from given topic is considered when calculating the total score.

Tthe grading baseline is as follows:

Score / grade
Under 10 points is considered as no participation on the course --> no grade
10-15 points --> grade 0
16 points -> grade 1
21 points -> grade 2
26 points -> grade 3
31 points -> grade 4
36 points -> grade 5

Teacher has a right to revise the score based grade by 1 based on teacher's observations of student's attitude and skills on lessons.

Assessment scale

0-5

Teaching methods

Applying the following teaching methods by teacher's judgement: Contact teaching, Independent learning, Lesson excercises, Videos, Homework, Remote teaching (not recorded), Problem-based learning, Collaborative learning, Group work, Exercise assignments, Question-based teaching, Question-based learning, PC-excercises, Exam

A student solves exercises and saves them in TuniMoodle by given deadlines.

Matlab is used as a technical computation software during the course. Calculators can also be used.

Learning materials

Material, theory and exercises can be found in TuniMoodle. If necessary, a student can use math books he/she has used before and the Internet to search more information about the topics. A student can borrow books in a local library.

Student workload

Contact or remote teaching approx. 45 hours
Independent studying approx. 85 hours
Exam(s) approx. 5 hours

Content scheduling

The course is built around the following main themes:
-Basic functions, terminology, graphs and equations (10%)
-Concept of derivative and its applications (15%)
-Graphical, numerical and symbolic differentiation (20%)
-Concept of differential and its use in error estimation (10%)
- Integral function, Definite integral, fundamental theorem of calculus (15%)
- Graphical, numerical and symbolic integration (20%)
- Calculation of areas and volumes with integral (10%)
The percentages describe the estimated time used in these themes.

Detailed topics are shown in TuniMoodle.

Completion alternatives

To be negotiated with teacher. Teacher is not obligated to grant an alternative way of exectution to a student.