← Higher Math: Limits, Derivatives, Integrals

⇄ Sync
Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

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

Sequences and limits, remarkable limits and equivalences, continuity, the derivative and its rules, the differential, L'Hôpital and Taylor, studying a function and asymptotes, the indefinite integral (substitution, by parts, rational fractions), the definite integral, areas, volumes of solids of revolution and improper integrals.

Course program: 31 lessons

Limits

  1. A sequence and its limit
  2. Limit of a function
  3. The first remarkable limit
  4. The second remarkable limit and the number e
  5. Equivalent infinitesimals
  6. Limits: more
  7. Continuity and points of discontinuity
  8. Checkpoint: limits and continuity

Derivative

  1. Derivative by definition
  2. Table of derivatives and rules
  3. Derivative of a composite function
  4. Implicit and parametric functions
  5. The differential and approximate calculations
  6. Derivatives: more
  7. Checkpoint: the derivative

Applications of the derivative

  1. L'Hôpital's rule
  2. Taylor's formula
  3. Studying a function
  4. Asymptotes of a graph
  5. Checkpoint: applications of the derivative

Indefinite integral

  1. Antiderivative and the table of integrals
  2. Substitution
  3. Integration by parts
  4. Integrating rational fractions
  5. Integrals: more
  6. Checkpoint: the indefinite integral

Definite integral

  1. The definite integral and the Newton–Leibniz formula
  2. Area of a region and volume of a solid of revolution
  3. Improper integrals
  4. Definite integral: more
  5. Checkpoint: the definite integral