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In this course, you will be Introduced to several methods of numerical approximation such as error analysis, root finding, interpolation, polynomial approximation and the direct methods for solving linear equations.
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 numerical analysis methods.
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Section 1: Week 1: Mathematical Preliminaries and Error Analysis  

1  05:47  
In this lecture, you will be introduced to the description of the "Introduction to Numerical Analysis" Course including course prerequisite, textbook, supplemental material, course objectives, course schedule, course grading, quizzes, course certificates and contact information.  
2  25:45  
In this lecture, you will be given an introduction to the definition of numerical analysis, types of solution in mathematics, numerical analysis computer software and overview about number systems.  
3  22:10  
In this lecture, you will be given an introduction to the floatingpoint arithmetic (FPA) definition including several examples and their solutions using number systems. 

4  19:45  
In this lecture, you will be introduced to several errors in mathematics such as converting error, overflow error, underflow error and roundoff error with the examples of the ways of performing termination for these errors.  
5  1 page  
This problem set 1 is a review for the material of week 1 and quiz 1. I highly recommend you to solve this problem set 1 before attempting to solve QUIZ 1. GOOD LUCK! 

6  1 page  
After you are done with solving the problem set 1, please review your answers with the given solutions in order to learn from your mistakes. Then, please solve QUIZ 1. GOOD LUCK! 

7 
Mathematical Preliminaries and Error Analysis

10 questions  
Section 2: Week 2: Solutions of Equations in One Variable  
8  17:20  
In this lecture, you will be introduced to some basics of maple 11 such as how to write a mathematical equation or function using maple 11 in order to find the derivative of it, plot it and solve it to find the roots/zeros.  
9  55:35  
In this lecture, you will be introduced to several methods used in solving equations in one variable such as bisection method, secant method and false position method. Several examples, proofs, theorems and comparison of each method in terms of advantages and disadvantages will be given in each method. 

10  43:42  
In this lecture, you will be also introduced to two other methods used in solving equations in one variable such as newton method and fixedpoint iteration method. Several examples, proofs, theorems and comparison of each method in terms of advantages and disadvantages will be given in each method.  
11  2 pages  
This problem set 2 is a review for the material of week 2 and quiz 2. I highly recommend you to solve this problem set 5 before attempting to solve QUIZ 2. GOOD LUCK! 

12  2 pages  
After you are done with solving the problem set 2, please review your answers with the given solutions in order to learn from your mistakes. Then, please solve QUIZ 2. GOOD LUCK! 

13 
Solutions of Equations in One Variable

10 questions  
Section 3: Week 3: Interpolation and Polynomial Approximation  
14  11:02  
In this lecture, you will be introduced to the definition of linear interpolation and its applications. Then, several steps for using linear interpolation and linear interpolation methods will be given in this lecture.  
15  17:34  
In this lecture, you will be given an example about the first linear interpolation method which is called "solving a System of Equations".  
16  39:10  
In this lecture, you will be introduced to the second method used in linear interpolation which is called "Lagrange Polynomials", and how to use it to approximate any value not available in the table of data. In addition, you will be introduced to the Lagrange Polynomials Error Formula with examples.  
17  1 page  
This problem set 3 is a review for the material of week 3 and quiz 3. I highly recommend you to solve this problem set 3 before attempting to solve QUIZ 3. GOOD LUCK! 

18  1 page  
After you are done with solving the problem set 3, please review your answers with the given solutions in order to learn from your mistakes. Then, please solve QUIZ 3. GOOD LUCK! 

19 
Interpolation and Polynomial Approximation

10 questions  
Section 4: Week 4: Spline Interpolation  
20  29:00  
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.  
21  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.  
22  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.  
23  3 pages  
This problem set 4 is a review for the material of week 4 and quiz 4. I highly recommend you to solve this problem set 4 before attempting to solve QUIZ 4. GOOD LUCK! 

24  4 pages  
After you are done with solving the problem set 4, please review your answers with the given solutions in order to learn from your mistakes. Then, please solve QUIZ 4. GOOD LUCK! 

25 
Spline Interpolation

10 questions  
Section 5: Week 5: Direct Methods for Solving Linear Equations  
26  28:54  
In this lecture, you will be introduced to gaussian elimination method with a review to linear algebra and how to use this direct method to solve a system nXm of linear equations.  
27  32:42  
In this lecture, you will be first given a review about the determinant in linear algebra and how to find it. Then, you will be introduced to cramer's rule and how to use it to solve a system nXm of linear equations.  
28  20:48  
In this lecture, you will be introduced to pivoting strategies such as gaussian elimination with partial pivoting and how to use this direct method to solve a system nXm of linear equations.  
29  3 pages  
This problem set 5 is a review for the material of week 5 and quiz 5. I highly recommend you to solve this problem set 5 before attempting to solve QUIZ 5. GOOD LUCK! 

30  3 pages  
After you are done with solving the problem set 5, please review your answers with the given solutions in order to learn from your mistakes. Then, please solve QUIZ 5. GOOD LUCK! 

31 
Direct Methods for Solving Linear Equations + General Course Questions

10 questions  
32  01:44  
In this lecture, you will given a summary of all topics discussed in the introduction to numerical analysis course, and the other topics that will be discussed in the next version of the course. 
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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