Advanced Numerical Analysis

Learn "Advanced Numerical Analysis" in Five Weeks Only
0.0 (0 ratings) Instead of using a simple lifetime average, Udemy calculates a
course's star rating by considering a number of different factors
such as the number of ratings, the age of ratings, and the
likelihood of fraudulent ratings.
212 students enrolled
Instructed by Mohammed K A Kaabar
Free
Start Learning Now
  • Lectures 21
  • Contents Video: 6.5 hours
    Other: 7 mins
  • Skill Level Expert Level
  • Languages English
  • Includes Lifetime access
    30 day money back guarantee!
    Available on iOS and Android
Wishlisted Wishlist

How taking a course works

Discover

Find online courses made by experts from around the world.

Learn

Take your courses with you and learn anywhere, anytime.

Master

Learn and practice real-world skills and achieve your goals.

About This Course

Published 7/2013 English

Course 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.

What are the requirements?

  • Introduction to Numerical Analysis
  • Linear Algebra
  • The desire to learn

What am I going to get from this course?

  • 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.

What 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.

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

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

23:22
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.
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.
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
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.
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.
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.
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!

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
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.
17:01
In this lecture, you will be introduced to gauss-siedel method which is one of the iterative methods for solving linear systems
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. 


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. 
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. 

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. 

Section 5: Week 5: Numerical Integration and Differentiation
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. 
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
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
20 questions

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!.

Students Who Viewed This Course Also Viewed

  • Loading
  • Loading
  • Loading

Instructor Biography

Mohammed K A Kaabar, Online Instructor of Numerical Analysis at Udemy

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.

Ready to start learning?
Start Learning Now