This is an advanced course which discusses about the iterative methods to solve matrix system of equations. This course will teach you how the order of millions or even billions of states and how all the bits of information can be tracked to solve the system.

Disease modeling can be solved by using this method to recognize the health state for every human on earth with more advanced scientific computing skills after finishing this course.

**Assessment**

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer need to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

**Certification**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

- Add the certificate to your CV or resume and brighten up your career
- Show it to prove your success

Course Credit: University of Washington

### Course Curriculum

Lecture1 : Vectors & Matrices | 00:42:00 | ||

Lecture2 : Logic, Loops, and Iterations | 00:39:00 | ||

Lecture3 : Plotting & Importing/Exporting Data | 00:45:00 | ||

Lecture4 : Supplement: About your computer | 00:08:00 | ||

Lecture5 : Supplement: A bit more about your computer | 00:08:00 | ||

Lecture6 : Supplement: Benchmarking | 00:10:00 | ||

Lecture7 : Supplement: Computational Complexity | 00:12:00 | ||

Lecture8 : Supplement: Element-wise multiplication | 00:07:00 | ||

Lecture9 : Supplement: Dot-times | 00:10:00 | ||

Lecture10 : Supplement: Function Handles | 00:07:00 | ||

Lecture11 : Linear Systems of Equations | 00:42:00 | ||

Lecture12 : Supplement: Matrix Modeling | 00:09:00 | ||

Lecture13 : Supplement: Condition Numbers | 00:07:00 | ||

Lecture14 : Supplement: More on condition numbers | 00:13:00 | ||

Lecture15 : Gaussian Elimination for Ax=b | 00:40:00 | ||

Lecture16 : LU Matrix Decomposition for Ax=b | 00:51:00 | ||

Lecture17 : Supplement: LU decomposition | 00:09:00 | ||

Lecture18 : Iteration Methods for Ax-b | 00:47:00 | ||

Lecture19 : Eigenvalues and Eigenvectors | 00:44:00 | ||

Lecture20 : Eigen-decompositions and Iterations | 00:49:00 | ||

Lecture21 : The Singular Value Decomposition (SVD) | 00:45:00 | ||

Lecture22 : Principal Componenet Analysis (PCA) | 00:51:00 | ||

Lecture23 : PCA for Face Recognition | 00:48:00 | ||

Lecture24 : Least-Squares Fitting Methods | 00:45:00 | ||

Lecture25 : Polynomial Fits and Splines | 00:44:00 | ||

Lecture26 : Data Fitting with Matlab | 00:39:00 | ||

Lecture27 : Unconstrained Optimization (Derivative-Free Methods) | 00:46:00 | ||

Lecture28 : Unconstrained Optimization (Derivative Methods) | 00:49:00 | ||

Lecture29 : Linear Programming and Genetic Algorithms | 00:57:00 | ||

Lecture30 : Numerical Differentiation Methods | 00:47:00 | ||

Lecture31 : Supplement: Mean Value Theorem | 00:06:00 | ||

Lecture32 : Higher-order Accuracy Schemes for Differentiation and Integration | 00:45:00 | ||

Lecture33 : Higher-order Integration Schemes | 00:50:00 | ||

Lecture34 : Ordinary Differential Equations and Time-stepping | 00:47:00 | ||

Lecture35 : Error and Stability of Time-stepping Schemes | 00:45:00 | ||

Lecture36 : General Time-stepping and Runge-Kutta Schemes | 00:45:00 | ||

Lecture37 : Supplement: Using ODE45 & Runge-Kutta methods | 00:09:00 | ||

Lecture38 : Application of Runge-Kutta to Lorenz Equation | 00:30:00 | ||

Lecture39 : Supplement: Vector fields and phase-planes | 00:06:00 | ||

Lecture40 : Vectorized Time-step Integrators | 00:41:00 | ||

Lecture41 : Supplement: Indexing equations | 00:10:00 | ||

Lecture42 : Supplement: Big systems of ODEs | 00:05:00 | ||

Lecture43 : Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum | 00:50:00 | ||

Lecture44 : Theory of the Fourier Transform | 00:49:00 | ||

Lecture45 : Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) | 00:48:00 | ||

Lecture46 : Supplement: Discrete Fourier Transform | 00:08:00 | ||

Lecture47: FFT and Image Compression | 00:43:00 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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