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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  20 questions  
In this optional final exam, you will have several different multiplechoice questions. During the final exam, feel free to use the course material to answer the questions. GOOD LUCK!. 
Mohammed Kaabar received Master of Science in Mathematics and Bachelor of Science in Theoretical Mathematics from Washington State University (WSU), Pullman, WAm USA. He is a former lab instructor and math tutor at the Math Learning Center (MLC) at Washington State University, Pullman. He is the author of (A Friendly Introduction to Differential Equations) and (A First Course in Linear Algebra) Books, and his research interests are numerical analysis, differential equations, linear algebra, and real analysis. He is an invited Technical Program Committee (TPC) member in many conferences such as ICECCS 14, ENCINS 15, eQeSS 15, SSCC 15, ICSoEB 15, CCA 14, WSMEAP 14, EECSI 14, JIEEEC 13 and WCEEENG 12. He is an editor for the American Mathematical Society (AMS) Blog, and he is also a certified peer reviewer and member of the math editorial board at Multimedia Educational Resource for Learning and Online Teaching (MERLOT) which is a program of the California State University System partnering with education institutions, professional societies, and industry.