Program
History and progress transfer
Session summary
Homework — optional, outside the timer
Theory of all steps of the program by blocks. Open a topic to read it.
How a session goes
A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.
Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.
About the course
The initial value problem and direction fields, first-order equations (separable, homogeneous, linear, Bernoulli, exact), reduction of order, linear equations with constant coefficients and the characteristic equation, undetermined coefficients, variation of parameters and systems in overview, applications: growth and decay, cooling, oscillations, Euler's method. Requires derivatives and integrals.
Course program: 28 lessons
Basic concepts
- What a differential equation is
- Initial value problem
- Direction field
- Checkpoint: basic concepts
First-order equations
- Separable equations
- Separating variables: more
- Homogeneous equations
- First-order linear equations
- Linear equations: more
- Bernoulli equation
- Exact equations
- Checkpoint: first-order equations
Second-order linear equations
- Reduction of order
- The characteristic equation
- Repeated roots
- Complex roots
- Characteristic equation: all cases
- Checkpoint: homogeneous linear equations
Non-homogeneous equations
- Undetermined coefficients
- Undetermined coefficients: more
- Variation of parameters (overview)
- Checkpoint: non-homogeneous equations
Systems and applications
- Systems of ODEs (overview)
- Growth and decay
- Newton's law of cooling
- Oscillations
- Euler's method
- Checkpoint: systems and applications