← Higher Math: Numerical Methods

⇄ 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

Errors and floating point, roots of equations (bisection, Newton, fixed-point iteration), interpolation and least squares, numerical derivatives and integrals (trapezoids, Simpson), linear systems (Gaussian elimination with pivoting, Jacobi, Gauss–Seidel), differential equations (Euler, Runge–Kutta). Problems: one or two iterations by hand on convenient numbers.

Course program: 31 lessons

Computational errors

  1. Absolute and relative error
  2. Rounding and significant figures
  3. Floating-point numbers
  4. Errors: more
  5. Checkpoint: errors

Nonlinear equations

  1. Bisection method
  2. Newton's method (tangents)
  3. Newton's method: more
  4. Fixed-point iteration and convergence
  5. Checkpoint: nonlinear equations

Interpolation and approximation

  1. Linear interpolation
  2. The Lagrange interpolation polynomial
  3. Newton polynomial and divided differences
  4. Least squares
  5. Interpolation: more
  6. Checkpoint: interpolation and approximation

Numerical derivatives and integrals

  1. Numerical differentiation
  2. Rectangles and trapezoids
  3. Simpson's rule
  4. Integrals: more
  5. Checkpoint: derivatives and integrals

Systems of linear equations

  1. Gaussian elimination with pivoting
  2. Jacobi method
  3. Gauss–Seidel method
  4. Conditioning (overview)
  5. Checkpoint: systems of equations

Differential equations

  1. Euler's method
  2. Improved Euler method
  3. Runge–Kutta 4 (overview)
  4. Differential equations: more
  5. Checkpoint: differential equations