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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

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.

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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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