Study Guide

Objective

The student understands how, where and when to use the two basic concepts in mathematical analysis: derivation and integration.
The student can apply derivation and integration to various problems within their own field of study.
The student can use mathematical software to analyze measured data ​​or other collected data sets.

Content

- Limit calculations
- Definition of derivatives
- Tangent and linearisation
- Derivation rules
- Extreme value problems
- Second derivative and convexity
- Applications of derivatives in different fields
- Numerical derivation
- Primitive function (antiderivative)
- Definition of integrals
- Integration rules
- Area calculations, volume integrals
- Integral applications from own specialist area
- Numerical integration
- Mathematical software (Mathcad, Matlab, GeoGebra or equivalent) as a tool for solving problems

Location and time

Autumn 2023 - October, November - Vaasa/distance

Materials

All material is available in the Moodle course.
Exercises can be found in e-math.

Teaching methods

Teaching takes place in class or remotely via webex according to the schedule in PEPPI.


All material that belongs to the course is in Moodle - exercises are in e-math
Mathcad is used as an aid during the course.
The students are expected to have their own Mathcad installed on their computer.

Exam schedules

Presented at the start of the course, found in the Moodle course

Completion alternatives

Passed exams and completed assignments.
The exam takes place on site in Vaasa and is counted on paper.
The exam dates can be found in the Moodle course.

Student workload

Teaching in class: 12 lessons
Tent : 2 lessons
Own work : 67 hours

Content scheduling

Se lektionsplaneringen i Moodle

Evaluation scale

H-5

Assessment criteria, satisfactory (1)

Derivatives: Basic understanding of the concept of derivatives. Master simple derivation rules.
Integrals: Basic understanding of the integral concept. Master simple integration rules.
Modeling and numerical methods: Have some understanding of how to make a mathematical model and how it can be solved numerically.

Assessment criteria, good (3)

Derivatives: Is able to solve common types of extreme value problems using derivatives
Integrals: Is able to calculate areas and volumes using integrals. Is able to solve mechanical problems using integrals.
Modeling and numerical methods: Understands how to make a mathematical model and how it can be solved numerically.

Assessment criteria, excellent (5)

Derivatives: Can apply theory to more complicated applications and calculations.
Integrals: Can apply the theory to more complicated applications and calculations (rotational surfaces, arc lengths, etc.).
Modeling and numerical methods: Can construct and numerically solve more complicated models with calculation software.

Assessment methods and criteria

The course is assessed on the basis of the student's results in the exam (max. 40 points) and on the basis of calculated tasks (20 points).
At least 13 points in the exam and at least 20 points in total.

White word scale :

20 p = 1
28 p = 2
36 p = 3
44 p = 4
52 p = 5

Assessment criteria, fail (0)

The requirements for white word 1 could not be met

Assessment criteria, satisfactory (1-2)

Graphical understanding of the concept of derivatives.
Master simple derivation rules.
Can apply calculus of derivatives to simple problems

Basic understanding of the concept of integral.
Master simple integration rules and can calculate the value of a definite integral.
Can apply integral calculus to simple problems.


Has some understanding of how to make a mathematical model and how this can be solved numerically

Assessment criteria, good (3-4)

Can solve extreme value problems using derivatives

Can calculate areas of areas and volumes of solids of revolution using integrals. Can solve problems from physics using integrals.

Modeling and numerical methods
Has a good understanding of how to make mathematical models and can solve these calculation programs

Assessment criteria, excellent (5)

Can apply derivative calculus to more complicated applications and calculations.

Can apply integral calculations to more complicated applications and calculations. ( Surfaces of rotation, arc lengths )

Modeling and numerical methods
Can construct and numerically solve more complicated models with calculation programs

Qualifications

Functions and equations 1,
Geometry and vectors,
Functions and equations 2.