# Numerical Methods

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Intermediate

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33 Lessons

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`lang: en_US`

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

#### Accuracy and Precision

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

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#### Absolute & Relative error

Learn Absolute Error and Relative Error from Error Analysis.

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#### RoundOff error

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

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#### Truncation error

Get brief understanding on Truncation error from Error Analysis.

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#### Total numerical error

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

Bracketing methods for non-linear equations

4 Lessons

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#### Roots

Discussion on roots and taxonomy of root-finding methods.

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#### What is Bracketing?

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

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#### Bisection method

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

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#### False position method

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

Open methods for solving non-linear equations

4 Lessons

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#### Open Method Convergence

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

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#### Newton Raphson method

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

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#### Secant method

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

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#### Brent’s method

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

Optimization in MATLAB

5 Lessons

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#### Optimization

Get introduced with the concept of Optimization in MATLAB.

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#### One Dimensional Optimization

Learn the concept of One-Dimensional Optimization.

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#### Golden Section Search

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

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#### Parabolic Interpolation

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

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#### Multidimensional Optimization

Discussion of Multidimensional Optimization along with MATLAB Code.

Gauss Elimination in MATLAB

5 Lessons

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#### Gauss Elimination Graphical Method

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

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#### Gauss Elimination with Cramer’s rule

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

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#### Naive Gauss Elimination

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

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#### Gauss Elimination using Pivoting

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

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#### Tridiagonal Systems using Gauss elimination

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

LU Factorization using MATLAB

4 Lessons

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#### Gauss Elimination as LU Factorization

Discussion on Gauss elimination as LU factorization with MATLAB implementation.

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#### LU Factorization with Pivoting

Discussion on LU Factorization with Pivoting along with MATLAB Code.

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#### Cholesky Factorization

Discussion on Cholesky factorization along with its MATLAB implementation.

Iterative methods

4 Lessons

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#### Introduction to Iterative Methods

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

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#### Gauss-Seidel Iterative Method

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

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#### Successive Substitution for non-linear system

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

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#### Newton-Raphson method for non-linear system

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

Eigenvalues and Eigenvectors

1 Lesson

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#### Eigenvalues in MATLAB

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

Certification Quiz

1 Lesson

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#### Quiz

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