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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

The coursework of the Introduction to numerical analysis course by Coursera has been structured to give the learners an insight into the various concepts of Numerical analysis and to help them develop their career in that direction. This course aims at enabling the candidates to have a detailed understanding of the process of numerical computing which requires assembling building blocks into computational pipelines and a basic understanding of its numerical methods, their strengths, limitations, failure modes and weaknesses.

Through this coursework, the participants will be trained to analyze and develop the primary characteristics of numerical algorithms. They will be able to represent them with diverse classic problems in numerical mathematics. The process of implementing constructions into working prototypes of numerical code will also be taught. This course is being instructed by Evgeni Burovski who is an assistant professor at the School of Applied Mathematics at HSE. The instructor ensures to deliver the programme in an interactive manner by including discussion forums, projects, e-learning videos and practice exercises as a part of conducting classes. This course is being offered by the National Research University Higher School of Economics on Coursera.

The Highlights

100% learning by Online mode
Flexible deadlines
Intermediate level course
Course completion takes up to 18 hours
Subtitles in English, French, Portuguese (Brazilian), Russian, Spanish

Programme Offerings

homework exercises
peer reviews
Graded Quizzes
e learning videos
reading resources

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 2152	yes	Coursera

The fees payable for the Introduction to numerical analysis course by Coursera is Rs.2,152/- for all candidates.

Fees payable for Introduction to numerical analysis course by Coursera

Total Certificate Fees Payable

Rs.2,152/-

Eligibility Criteria

Education

Candidates willing to apply for this programme must be well versed in the basics of college-level mathematics. They should know about calculus and linear algebra. They should be proficient with the basics of programming such as Python language

Certification Qualifying Details

The course completion certificate will be given by Coursera to those participants who have successfully, completed the name verification process, passed all the required assignments given during the course and paid the course certificate fee.

What you will learn

Mathematical skill

After the completion of the Introduction to numerical analysis course by Coursera the participants will have gained knowledge about the following:

The basic concepts of Machine Arithmetics
Understanding the process of Gaussian elimination
Learning about the Matrix norms
Learning Linear Multistep methods.
Understanding the Inverse quadratic interpolation
Expertise in Numerical derivatives

Application Details

Candidates keen on registering for the Introduction to numerical analysis course by Coursera can follow the process given below:

Step 1: In the initial stage, Visit the course page.

Step 2: As you enter the website, you will be able to see the tab ‘Enrol for Free’. Click it and proceed to create a login id.

Step 3: Thereafter, you will be given a dedicated dashboard and instantly your 7-day free trial will start off.

Step 4: Once the 7 days are over, the candidate can only learn ahead if he/she makes the payment.

Step 5: Once payment is made online, he/she can continue the learning process.

The Syllabus

About the University
Introduction.
Machine epsilon. Over and underflow.
Gaussian elimination.
LU decomposition: the matrix form of the Gaussian elimination
When does the Gaussian elimination work?
A crude estimate of the machine epsilon.
Systems of linear equations. Cramer's rule.
About the University
Rules on academic integrity in the course
A simple worked example.
Machine arithmetics. Representation of real numbers.
About the course
Slides
LU decomposition with pivoting. Permutation matrices

Solving non-linear equations
Fixed-point iteration.
Aside: convergence rates and related technicalities.
Localization of roots. Bisection.
Back to the fixed-point iteration.
Newton's iteration.
Inverse quadratic interpolation.
Roots of polynomials.
Slides
Roots of polynomials: the companion matrix
Multiple roots. Modified Newton's method
Fine-tuning the fixed-point iteration.

Introduction
The sensitivity of a linear system.
Vector norms.
Common matrix norms.
Cholesky decomposition.
QR decomposition.
Constructing the QR decomposition: Householder reflections.
Slides
Slides
Constructing the QR decomposition: Givens rotations
Banded matrices. Thomas algorithm.
Shermann-Morrison formula.
The sensitivity of a linear system. Condition number
Matrix norms.

Large- scale systems of linear equations
Simple iteration for a linear system. Jacobi iteration.
Successive over-relaxation.
Canonic form of two-step iterative methods for linear systems.
Copy of Simple iteration for a linear system. Jacobi iteration
Variational approaches: minimum residual method.
Slides
Convergence criteria for simple iteration.
Seidel's iteration.

Initial value problem for an ODE. Discretization
Approximation and convergence.
Truncation error or Euler-like schemes.
Asymptotic stability of ODEs. Stiffness.
Linear Multistep methods.
Slides
Zero-stability of linear multistep methods.
Runge-Kutta methods

Numerical derivatives
Numerical derivatives: finite differences.
Truncation and roundoff errors: interplay.
Richardson extrapolation.
Simple geometric quadratures: Trapezoids, Simpson's rule and all that.
A check of convergence.
Slides
Recap: Newton-Cotes vs Gaussian quadratures.
Gaussian quadratures.
Error bounds for quadratures. Romberg extrapolation.
Integrals with singularities.
Integration: numerical quadratures.
Convergence rates of simple quadratures.
Higher-order schemes.

Interpolation and approximation. Modeling of data
Linear least-squares problem.
Global polynomial interpolation.
Lagrange interpolating polynomial
Chebyshev nodes.
Slides
Interpolation of the Runge function.
Quantifying interpolation errors. Runge phenomenon
Ordinary least squares: the normal equations.
Ordinary least squares: QR decomposition of the design matrix

HSE University Frequently Asked Questions (FAQ's)

1: When is access given to the lectures and assignments?

Participants are given access to lectures and assignments depending upon the type of enrollment. In audit mode, access is given to most course materials however, to gain access to graded assignments and to get a Certificate; they have to purchase the Certificate experience.

2: What is audit access?

In audit access, participants can view the course videos and readings for free. Audit access does not provide a course certificate.

3: Can participants download the videos if they want to view it in offline mode?

The candidates will be able to download the video files if they want to view it in offline mode.

4: What are the computer requirements for using Coursera?

To use Coursera on a computer, participants will need a strong Internet connection, at least 1 GB of memory/RAM and an updated version of the browser they shall use.

5: Are assignment deadlines the same for everyone?

Many courses have personalized deadlines depending upon the date of enrollment in the course. There is no penalty for missing a deadline however some courses are on sessions, in which everyone has the same deadline.