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Intermediate Level

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

Approx. 18 hours to complete
English
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Intermediate Level

Basic command of college-level mathematics (linear algebra and calculus). Basic level of programming proficiency: python programming language.

Approx. 18 hours to complete
English

Week
1

## Week 1

4 hours to complete

## Machine arithmetics. Systems of linear algebraic equations.

4 hours to complete
11 videos (Total 61 min), 4 readings, 2 quizzes
11 videos
Introduction.56s
A simple worked example.5m
Machine arithmetics. Representation of real numbers.6m
Machine epsilon. Over- and underflow.8m
A crude estimate of the machine epsilon.2m
Systems of linear equations. Cramer's rule.5m
Gaussian elimination.10m
LU decomposition: the matrix form of the Gaussian elimination.9m
When does the Gaussian elimination work?2m
LU decomposition with pivoting. Permutation matrices.8m
Rules on the academic integrity in the course10m
Slides10m
Week
2

## Week 2

3 hours to complete

## Numerical linear algebra.

3 hours to complete
12 videos (Total 72 min), 2 readings, 1 quiz
12 videos
Sensitivity of a linear system.3m
Vector norms.5m
Matrix norms.3m
Common matrix norms.4m
Sensitivity of a linear system. Condition number.11m
Cholesky decomposition.7m
Banded matrices. Thomas algorithm.3m
Shermann-Morrison formula.8m
QR decomposition.6m
Constructing the QR decomposition: Householder reflections.13m
Constructing the QR decomposition: Givens rotations3m
Slides10m
Slides10m
Week
3

## Week 3

3 hours to complete

## Non-linear algebraic equations.

3 hours to complete
11 videos (Total 71 min), 1 reading, 1 quiz
11 videos
Localization of roots. Bisection.4m
Fixed-point iteration.4m
Aside: convergence rates and related technicalities.7m
Back to the fixed-point iteration.11m
Fine-tuning the fixed-point iteration.5m
Newton's iteration.16m
Multiple roots. Modified Newton's method.3m
Roots of polynomials.3m
Roots of polynomials: the companion matrix.3m
Slides10m
Week
4

## Week 4

2 hours to complete

## Iterative method for linear systems.

2 hours to complete
8 videos (Total 55 min), 1 reading, 1 quiz
8 videos
Simple iteration for a linear system. Jacobi iteration.8m
Convergence criteria for simple iteration.4m
Seidel's iteration.9m
Successive over-relaxation.3m
Canonic form of two-step iterative methods for linear systems.10m
Variational approaches: minimum residual method.5m
Copy of Simple iteration for a linear system. Jacobi iteration.8m