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

### 講師

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

1

## Machine arithmetics. Systems of linear algebraic equations.

11 個視頻 （總計 61 分鐘）, 4 個閱讀材料, 2 個測驗
11 個視頻
Introduction.56
A simple worked example.5分鐘
Machine arithmetics. Representation of real numbers.6分鐘
Machine epsilon. Over- and underflow.8分鐘
A crude estimate of the machine epsilon.2分鐘
Systems of linear equations. Cramer's rule.5分鐘
Gaussian elimination.10分鐘
LU decomposition: the matrix form of the Gaussian elimination.9分鐘
When does the Gaussian elimination work?2分鐘
LU decomposition with pivoting. Permutation matrices.8分鐘
4 個閱讀材料
Rules on the academic integrity in the course10分鐘
Slides10分鐘
2

## Numerical linear algebra.

12 個視頻 （總計 72 分鐘）, 2 個閱讀材料, 1 個測驗
12 個視頻
Sensitivity of a linear system.3分鐘
Vector norms.5分鐘
Matrix norms.3分鐘
Common matrix norms.4分鐘
Sensitivity of a linear system. Condition number.11分鐘
Cholesky decomposition.7分鐘
Banded matrices. Thomas algorithm.3分鐘
Shermann-Morrison formula.8分鐘
QR decomposition.6分鐘
Constructing the QR decomposition: Householder reflections.13分鐘
Constructing the QR decomposition: Givens rotations3分鐘
2 個閱讀材料
Slides10分鐘
Slides10分鐘
3

## Non-linear algebraic equations.

11 個視頻 （總計 71 分鐘）, 1 個閱讀材料, 1 個測驗
11 個視頻
Localization of roots. Bisection.4分鐘
Fixed-point iteration.4分鐘
Aside: convergence rates and related technicalities.7分鐘
Back to the fixed-point iteration.11分鐘
Fine-tuning the fixed-point iteration.5分鐘
Newton's iteration.16分鐘
Multiple roots. Modified Newton's method.3分鐘
Roots of polynomials.3分鐘
Roots of polynomials: the companion matrix.3分鐘
1 個閱讀材料
Slides10分鐘
4

## Iterative method for linear systems.

8 個視頻 （總計 55 分鐘）, 1 個閱讀材料, 1 個測驗
8 個視頻
Simple iteration for a linear system. Jacobi iteration.8分鐘
Convergence criteria for simple iteration.4分鐘
Seidel's iteration.9分鐘
Successive over-relaxation.3分鐘
Canonic form of two-step iterative methods for linear systems.10分鐘
Variational approaches: minimum residual method.5分鐘
Copy of Simple iteration for a linear system. Jacobi iteration.8分鐘
1 個閱讀材料
Slides10分鐘