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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
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)
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.
In audit access, participants can view the course videos and readings for free. Audit access does not provide a course certificate.
The candidates will be able to download the video files if they want to view it in offline mode.
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.
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.