Advanced Numerical Analysis

Learn "Advanced Numerical Analysis" in Five Weeks Only

Created byMohammed K A Kaabar

Last updated 7/2013

English

What you'll learn

Use the divided difference to interpolate and approximate functions by polynomials.
Use the iterative methods with algorithms to implement several numerical methods.
Apply the midpoint rule for finding numerical integration.
Apply the trapezoidal rule for finding numerical integration.
Use the divided difference formula to proof the approximation part and error part in the basic quadrature rules.
The ability to use computer software such as Maple to apply several numerical methods and approximations.

Course content

7 sections • 21 lectures • 6h 42m total length

Newton’s Method for Systems30:40
In this lecture, you will be introduced to newton's method for system using inverse jacobian with partial derivatives and vectors. At the end of this lecture, you will given an example of how to use newton's method for system in order to solve system of linear equations.
Müller’s Method30:08
In this lecture, you will be introduced to muller's method and how to use it to approximate a function in the neighborhood of the root by quadratic poloynomial. At the end of this lecture, you will given an example of how to use muller's method for solving system of linear equations.

Divided Difference (Part I)39:18
In this lecture, you will be introduced to interpolation: divided difference method and how to use it to construct polynomial of order (n) . At the end of this lecture, you will given an example of how to use divided difference method in order to construct polynomial of order (n).
Divided Difference (Part II)23:24
In this lecture, you will be introduced to interpolation: divided difference method and how to use it to find the distance between two points using both delta notation and del notation . At the end of this lecture, you will given an example of how to find the squared and cubic distance between two points using both delta notation and del notation.
Evenly-Spaced Data23:22
In this lecture, you will be introduced to the concept of evenly-spaced data and. In addition, you will given several examples about evenly-spaced data.
Newton’s Forward Divided Difference32:51
In this lecture, you will be introduced to newton's forward divided difference using binomial coefficient notation. In addition, you will given an example of how to use newton's forward divided difference to approximate a polynomial at a point not in the table of data.
Newton’s Backward Divided Difference18:08
In this lecture, you will be introduced to newton's backward divided difference using binomial coefficient notation.

Linear Spline Interpolation28:59
In this lecture, you will be introduced to spline interpolation in general and linear splines in particular. Then, you will given an example about linear spline interpolation, and how to use Maple 11 to solve it.
Quadratic Spline Interpolation29:46
In this lecture, you will be introduced to quadratic splines. Then, you will given an example about quadratic spline interpolation, and how to use Maple 11 to solve it.
Cubic Spline Interpolation18:48
In this lecture, you will be introduced to cubic splines. Then, you will given an example about cubic spline interpolation, and how to use Maple 11 to solve it.
Problem Set3:00
This problem set is a review for the material of week 3.
I highly recommend you to solve this problem set before looking at problem set solutions.
GOOD LUCK!
Problem Set Solutions4:00
After you are done with solving the problem set, please review your answers with the given solutions in order to learn from your mistakes.
GOOD LUCK!

Jacobi Method17:16
In this lecture, you will be introduced to jacobi method which is one of the iterative methods for solving linear systems. In addition, you will given an example of how to use jacobi method to solve a system of linear equations.
Gauss-Siedel Method (Part I)17:01
In this lecture, you will be introduced to gauss-siedel method which is one of the iterative methods for solving linear systems.
Gauss-Siedel Method (Part II)10:43

In this lecture, you will be introduced to whether matrix is diagonally dominant or not in order to use it for applying gauss-siedel method. Moreover, several examples about that were given.
Successive Over Relaxation (SOR) Method (Part I)13:54

In this lecture, you will be introduced to the successive over relaxation (SOR) method and how does this method depend on gauss-siedel method?. In addition, the algorithm of SOR method was also given, At the end of this lecture, an example about SOR method was given.
Successive Over Relaxation (SOR) Method (Part II)14:10
In this lecture, you will be introduced to the successive over relaxation (SOR) method and how does this method depend on gauss-siedel method?. In addition, the algorithm of SOR method was also given, At the end of this lecture, an example about SOR method was given.
Successive Over Relaxation (SOR) Method (Part III)13:48
In this lecture, you will be introduced to the successive over relaxation (SOR) method and how does this method depend on gauss-siedel method?. In addition, the algorithm of SOR method was also given, At the end of this lecture, an example about SOR method was given.

Basic Quadrature Rules (Midpoint Rule)18:09

In this lecture, you will be introduced to the midpoint rule which is one of the basic quadrature rules. Moreover, you will be introduced the proofs of both approximation part and error of midpoint rule.
Basic Quadrature Rules (Trapezoidal Rule)20:40

In this lecture, you will be introduced to the trapezoidal rule which is one of the basic quadrature rules. Moreover, you will be introduced the proofs of both approximation part and error of trapezoidal rule.

Requirements

Introduction to Numerical Analysis
Linear Algebra
The desire to learn

Description

In this course, you will be Introduced to several numerical approximation methods such as interpolation: divided difference, polynomial approximations, iterative methods for solving linear systems, numerical differentiation and numerical integration.

During five weeks of the course, you will be learning these methods and compare them as well.

The course is divided into five weeks where each week you will find a set of video lectures posted with a PDF version of lecture notes as well.

You are welcome to take this course if you want to learn and study the advanced numerical analysis methods.

Who this course is for:

Anyone who wants to learn advanced methods in numerical analysis.
Students who had a background in the bascis of numerical analysis.
Students who had a background in the linear algebra.

Advanced Numerical Analysis

What you'll learn

Course content

Week 1: Solutions of Equations in One Variable2 lectures • 1hr 1min

Week 2: Interpolation and Polynomial Approximation5 lectures • 2hr 17min

Week 3: Spline Interpolation5 lectures • 1hr 25min

Week 4: Iterative Methods for Solving Linear Systems6 lectures • 1hr 27min

Week 5: Numerical Integration and Differentiation2 lectures • 39min

Week 6: Wrapping Up1 lecture • 2min

Week 7: Optional Final Exam0

Requirements

Description

Who this course is for: