Study Guide

Objective

The student :
- understands the importance and use of differential equations in technical contexts
- is able to solve simple first-order differential equations
- is familiar with the method of solving linear second-order differential equations
- is able to use use mathematical software to numerically solve differential equations
- is able to use differential equations to model and solve technical problems.

Content

- Derivation rules and primitive functions
- Solving separable differential equations and first-order linear differential equations
- Modeling problems using differential equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method
- Solving differential equations using Excel, Mathcad

Evaluation scale

H-5

Assessment criteria, satisfactory (1)

Recognizes differential equations.
Can solve simple separable differential equations.
Can solve homogeneous second-order differential equations by using the characteristic equation.
Understands the importance and use of differential equations in technical contexts.
Can use software to numerically solve simple differential equations.

Assessment criteria, good (3)

Can perform simple modeling
Is able to solve separable differential equations and simple linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Is able to use simple methods for numerically solving differential equations.

Assessment criteria, excellent (5)

Can perform more demanding modeling .
Is able to solve first-order differential equations.
Understands the oscillator equation and can use it to model mechanical and electrical oscillations.
Can independently model and solve more demanding problems numerically using mathematical software.

Qualifications

Functions and Equations 1,
Geometry and Vectors,
Functions and Equations 2,
Derivatives and Integrals.