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, 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.