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The aim of this course is to analyze the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, and approximation of functions. In addition to that, integration, differential equations and direct and iterative methods in linear algebra. Students eager to earn some knowledge about this subject have the best opportunity to learn something from 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 needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

**Certification**

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Course Credit: MIT

### Course Curriculum

Root Finding: Solutions of Equations in One Variable | |||

Aitken Extrapolations | 00:05:00 | ||

Wallis Equation | 00:05:00 | ||

2-D Newton | 00:05:00 | ||

Bairstow’s Method | 00:05:00 | ||

Quadrature: Numerical Integration | |||

Quadrature | 00:05:00 | ||

Newton-Cotes | 00:05:00 | ||

Polynomial Interpolation | 00:05:00 | ||

Bernoulli Polynomials | 00:05:00 | ||

Bernoulli Numbers | 00:05:00 | ||

Some Numerical Fun with Euler Maclaurin | 00:05:00 | ||

Circumference of the Ellipse | 00:00:00 | ||

Extrapolation | 00:05:00 | ||

Growth of Weeds | 00:05:00 | ||

Gauss/Laguerre Quadrature | 00:05:00 | ||

ODEs: Initial-Value Problems for Ordinary Differential Equations | |||

Errors vs Evaluations | 00:05:00 | ||

ODE via Taylor Series | 00:05:00 | ||

Rates of Convergence | 00:05:00 | ||

One e = 0.6 Kepler Orbit | 00:05:00 | ||

Toward J0 (r) | 00:05:00 | ||

Ax=b: Direct Methods for Solving Linear Algebra | |||

Wilkinson’s example | 00:05:00 | ||

Condition Number | 00:05:00 | ||

Ax = b Iterations | 00:05:00 | ||

Rates of SOR Convergence | 00:05:00 | ||

Ax=λx: Iterative Techniques in Matrix Algebra; Approximating Eigenvalues | |||

Householder Reflections | 00:05:00 | ||

Jacobi’s Method of Successive 2D Rotations | 00:05:00 | ||

Precursor to Problem 36 | 00:05:00 | ||

Eigenvalues | 00:05:00 | ||

The Geometry of QR | 00:05:00 | ||

Eigenvalues of Chain Matrix | 00:05:00 | ||

Assessment | |||

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

Certification | 00:00:00 |

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