Mathematics 2 (5 op)

Osaamistavoitteet (Opintojakso)

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

Sisältö (Opintojakso)

- 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

Arviointikriteerit, tyydyttävä (1-2) (Opintojakso)

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.

Arviointikriteerit, hyvä (3-4) (Opintojakso)

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

Arviointikriteerit, kiitettävä (5) (Opintojakso)

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

Aika ja paikka

Dates and times are shown in TuniMoodle.

Tenttien ja uusintatenttien ajankohdat

There are two partial exams (part 1, Differential Calculus and part 2, Integral Calculus). The schedule of the first partial exam will be announced in course Moodle pages. The second partial exam and final exam are to be held tentatively on April 27th. Changes to exam arrangements are possible depending e.g. on the course progress and other teacher's professional duties.

The two retake exams are for full final exams and are held on
1. May 18th 2022 (Only for those who have received grade 0)
2. June 8th 2022

Arviointimenetelmät ja arvioinnin perusteet

The final grade is based on the both partial exams or final exam and the grading baseline is as follows:

Score / grade
40 % -> grade 1
52,5 % -> grade 2
65 % -> grade 3
77,5 % -> grade 4
90 % -> grade 5

Teacher has a right to upgrade a grade based on the course activity (including homework). The baseline for homework bonus is as follows:

Homework percentage / Score effect
30% -> +1 point
50% -> +2 points
70% --> +3 points
90% --> +4 points

All the grades (including grade 0) require active participation (over 70% participation on lessons and regularly done homework) on the course. Grade 0 gives a right to participate in the re-sit exams. Grades 1-4 give right to participate in the second re-sit exam. The homework bonus points apply only in the partial exams and/or in the first final exam.

Arviointiasteikko

0-5

Opiskelumuodot ja opetusmenetelmät

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 dead-lines.

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

Oppimateriaalit

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.

Opiskelijan ajankäyttö ja kuormitus

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

Sisällön jaksotus

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.

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