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

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 criteria, satisfactory (1-2)

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 (3-4)

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.

Qualifications

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