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Learn "Advanced Numerical Analysis" in Five Weeks Only
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219 students enrolled
Last updated 7/2013
English
Price: Free
Includes:
• 6.5 hours on-demand video
• 2 Supplemental Resources
• Access on mobile and TV
What Will I 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.
View Curriculum
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 is the target audience?
• 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.
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Curriculum For This Course
21 Lectures
06:49:37
+
Week 1: Solutions of Equations in One Variable
2 Lectures 01:00:48
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.
Newton’s Method for Systems
30:40

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.
Müller’s Method
30:08
+
Week 2: Interpolation and Polynomial Approximation
5 Lectures 02:17:03
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 I)
39:18

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.

Divided Difference (Part II)
23:24

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.
Evenly-Spaced Data
23:22

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 Forward Divided Difference
32:51

In this lecture, you will be introduced to newton's backward divided difference using binomial coefficient notation.
Newton’s Backward Divided Difference
18:08
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Week 3: Spline Interpolation
5 Lectures 01:17:33
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.
Linear Spline Interpolation
28:59

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.
29:46

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.
Cubic Spline Interpolation
18:48

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
3 pages

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!

Problem Set Solutions
4 pages
+
Week 4: Iterative Methods for Solving Linear Systems
6 Lectures 01:26:52
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.
Jacobi Method
17:16

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 I)
17:01

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.

Gauss-Siedel Method (Part II)
10:43

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 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
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Week 5: Numerical Integration and Differentiation
2 Lectures 38:49
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.
18:09

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.

20:40
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Week 6: Wrapping Up
1 Lecture 01:32

In this lecture, you will given a summary of all topics discussed in the Advanced numerical analysis course.

Course Conclusion
01:32
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Week 7: Optional Final Exam
0 Lectures 00:00

In this optional final exam, you will have several different multiple-choice questions.

During the final exam, feel free to use the course material to answer the questions. GOOD LUCK!.