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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.
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Section 1: Week 1: Solutions of Equations in One Variable  

Lecture 1  30:40  
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. 

Lecture 2  30:08  
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.  
Section 2: Week 2: Interpolation and Polynomial Approximation  
Lecture 3  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).  
Lecture 4  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. 

Lecture 5  23:22  
In this lecture, you will be introduced to the concept of evenlyspaced data and. In addition, you will given several examples about evenlyspaced data.  
Lecture 6  32:51  
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. 

Lecture 7  18:08  
In this lecture, you will be introduced to newton's backward divided difference using binomial coefficient notation.  
Section 3: Week 3: Spline Interpolation  
Lecture 8  28:59  
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.  
Lecture 9  29:46  
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.  
Lecture 10  18:48  
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.  
Lecture 11  3 pages  
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! 

Lecture 12  4 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! 

Section 4: Week 4: Iterative Methods for Solving Linear Systems  
Lecture 13  17:16  
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. 

Lecture 14  17:01  
In this lecture, you will be introduced to gausssiedel method which is one of the iterative methods for solving linear systems.  
Lecture 15  10:43  
In this lecture, you will be introduced to whether matrix is diagonally dominant or not in order to use it for applying gausssiedel method. Moreover, several examples about that were given. 

Lecture 16  13:54  
In this lecture, you will be introduced to the successive over relaxation (SOR) method and how does this method depend on gausssiedel method?. In addition, the algorithm of SOR method was also given, At the end of this lecture, an example about SOR method was given. 

Lecture 17  14:10  
In this lecture, you will be introduced to the successive over relaxation (SOR) method and how does this method depend on gausssiedel method?. In addition, the algorithm of SOR method was also given, At the end of this lecture, an example about SOR method was given. 

Lecture 18  13:48  
In this lecture, you will be introduced to the successive over relaxation (SOR) method and how does this method depend on gausssiedel method?. In addition, the algorithm of SOR method was also given, At the end of this lecture, an example about SOR method was given. 

Section 5: Week 5: Numerical Integration and Differentiation  
Lecture 19  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. 

Lecture 20  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. 

Section 6: Week 6: Wrapping Up  
Lecture 21  01:32  
In this lecture, you will given a summary of all topics discussed in the Advanced numerical analysis course. 

Section 7: Week 7: Optional Final Exam  
Quiz 1 
Advanced Numerical Analysis Final Exam

20 questions 
Mohammed Kaabar is interested in several programming languages such as Scala, C++, C, JavaScript, Python, HTML 5 and MATLAB Programming.
He became IEEE Student Member, IEEE Computer Society Member, IEEE Electron Devices Society Member, IEEE Women in Engineering Society Member and IEEE Communications Society Member, in 2011 and 2012, respectively. In 2011 & 2012, he participated in several competitions, conferences, research papers and projects. In 2011, he attended also a threemonth course in numerical approximation techniques including error analysis, root finding, interpolation, function approximation, numerical differentiation, numerical integration and numerical solutions of initial value problems. Ultimately, he worked on several projects such as “PCA Implementation and Classification of Data in Recognition of Arabic Sign Language Alphabet using Polynomial Classifiers” and “Modeling a GaAs MESFET Device Structure using Silvaco Software:Athena and Atlas”. For more information about him, please visit his personal website: http://www.mohammedkaabar.net
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Amazing Course in Advanced Numerical Analysis
I would like to thank you Mohammed so much for offering an advanced course in numerical analysis. After taking your previous course "Introduction to Numerical Analysis", I really enjoyed in all discussed topics in your two courses because they are very interesting topics ranging from introductory level to advanced level. Thank you again for this great course.
Great Course
The Advanced Numerical Analysis course is a great course and very helpful in our life as well as it includes amazing topics in advanced numerical analysis such as newton's method, Muller's method, Divided difference, iterative methods and numerical integration & differentiation. In addition, the instructor is excellent because he taught the material of this course in an excellent way that makes everyone understands the course material easily without any difficulty.