Numerical Methods

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Intermediate

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Numerical methods are techniques by which mathematical problems are formulated so that they can be solved with arithmetic and logical operations. Because digital computers excel at performing such operations, numerical methods are sometimes referred to as computer mathematics. In the pre-computer era, the time and drudgery of implementing such calculations seriously limited their practical use. However, with the advent of fast, inexpensive digital computers, the role of numerical methods in engineering and scientific problem solving has exploded. Because they figure so prominently in much of our work, We believe that Numerical Methods should be a part of every engineer’s and scientist’s basic education. Just as we all must have solid foundations in the other areas of mathematics and science, we should also have a fundamental understanding of Numerical Methods. In particular, we should have a solid appreciation of both their capabilities and their limitations.

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Numerical Methods

Error Analysis

5 Lessons

The concept of different types of errors associated with both calculations and measurements are introduced in this lesson.

Video lesson

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Learn Absolute Error and Relative Error from Error Analysis.

Text lesson

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The roundoff error is important for engineering and scientific problem solving which will be taught in this section

Text lesson

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Get brief understanding on Truncation error from Error Analysis.

Text lesson

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This lesson discusses the total numerical error and how the errors can be minimized.

Text lesson

Bracketing methods for non-linear equations

4 Lessons

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Discussion on roots and taxonomy of root-finding methods.

Text lesson

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The most simplistic numerical techniques are based on bracketing the problem and in this lesson we will understand What is Bracketing?

Text lesson

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Understand the Bisection method with solving a problem as well as with MATLAB Code.

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Understand False Position method with solving the same problem along with MATLAB Code.

Video lesson

Open methods for solving non-linear equations

4 Lessons

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Quickly understand the difference between bracketing methods and opem method with convergence.

Text lesson

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Understand Newton Raphson method with solving a problem along with MATLAB Code.

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Understand the Secant & Modified Secant method with solving the same problem via MATLAB Code.

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Brent's method is a “hybrid” method that combines aspects of the bisection and secant methods.

Video lesson

Optimization in MATLAB

5 Lessons

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Get introduced with the concept of Optimization in MATLAB.

Text lesson

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Learn the concept of One-Dimensional Optimization.

Text lesson

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Discussion on Golden Section search, an Optimization technique to find extremes of a function along with MATLAB Code.

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Discussion of Parabolic Interpolation of One-Dimensional Optimization along with MATLAB Code.

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Discussion of Multidimensional Optimization along with MATLAB Code.

Text lesson

Gauss Elimination in MATLAB

5 Lessons

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Gauss Elimination is an algorithm for solving linear algebraic equations. This lesson discusses about the steps of Gauss elimination & graphical method.

Text lesson

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Discussion on Cramer’s rule, a solution to small numbers of the equation along with the concept of determinants.

Text lesson

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Discussion on the procedure of elimination in Naive Gauss elimination method along with MATLAB Code.

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Discussion on Gauss Elimination using Pivoting along with its implementation in MATLAB.

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Discussion on solving Tridiagonal systems using Gauss Elimination along with MATLAB Code.

Video lesson

LU Factorization using MATLAB

4 Lessons

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This lesson will help you in getting a brief introduction about LU Factorization.

Text lesson

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Discussion on Gauss elimination as LU factorization with MATLAB implementation.

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Discussion on LU Factorization with Pivoting along with MATLAB Code.

Text lesson

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Discussion on Cholesky factorization along with its MATLAB implementation.

Video lesson

Iterative methods

4 Lessons

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Discussion on Iterative methods or approximate methods to provide an alternative to the Gauss elimination methods.

Text lesson

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Discusion on commonly used iterative method for solving linear algebraic equations, the Gauss-Seidel method along with MATLAB Code.

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Discussion on the Successive Substitution method for solving non-linear algebraic equations.

Text lesson

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Discussion on the Newton-Raphson method for solving non-linear algebraic equations along with MATLAB Code.

Text lesson

Eigenvalues and Eigenvectors

1 Lesson

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Discussion on Eigenvalues and Eigenvectors in MATLAB along with the implementation.

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Certification Quiz

1 Lesson

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