Study Guide

Objective

After completing the course, the student can use differential equations to model and solve technical problems.

Content

- Modeling problems using differential equations
- Solving separable differential equations and first-order linear equations
- Solving second-order differential equations with constant coefficients (oscillations)
- Discretization and numerical solution of differential equations using Euler's method

Evaluation scale

H-5

Assessment criteria, satisfactory (1)

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

Assessment criteria, good (3)

Can perform simple modeling and solve linear first-order differential equations.
Can solve second-order differential equations with constant coefficients.
Has mastered simple methods for numerically solving differential equations.

Assessment criteria, excellent (5)

Can perform more demanding modeling and 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.

Qualifications

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