← Higher Math: Series and Multivariable Calculus

⇄ 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

Number series and convergence tests, absolute and conditional convergence, power series and Taylor series, Fourier series, functions of several variables — partial derivatives, the gradient, the tangent plane, extrema and Lagrange multipliers, double, triple and line integrals, Green's theorem. Requires limits, derivatives and integrals.

Course program: 33 lessons

Number series

  1. A series and its sum
  2. Comparison test
  3. Ratio test (d'Alembert)
  4. Root test (Cauchy)
  5. Integral test
  6. Convergence tests: pick the right one
  7. Checkpoint: number series

Alternating series

  1. Leibniz test
  2. Absolute and conditional convergence
  3. Type of convergence: more
  4. Checkpoint: alternating series

Power series

  1. Power series and radius of convergence
  2. Radius and interval: more
  3. Taylor series
  4. Taylor series: more
  5. Fourier series (overview)
  6. Checkpoint: power series

Functions of several variables

  1. Function of two variables
  2. Partial derivatives
  3. Partial derivatives: more
  4. Gradient and directional derivative
  5. Tangent plane
  6. Checkpoint: functions of several variables

Extrema

  1. Extrema of a function of two variables
  2. Extrema: more
  3. Constrained extremum: Lagrange multipliers
  4. Checkpoint: extrema

Multiple and line integrals

  1. Double integral
  2. Double integral: more
  3. Polar coordinates
  4. Triple integral (overview)
  5. Line integral and Green's theorem (overview)
  6. Checkpoint: multiple integrals