Introduction to Numerical Analysis

Learn the "Introduction to Numerical Analysis" in Five Weeks Only.
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  • Mohammed K A Kaabar Certified Online Instructor of Numerical Analysis at Udemy

    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 three-month 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.mohammed-kaabar.net

    Mohammed Kaabar Website

    Mohammed Kaabar Website

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  • Lifetime access to 27 lectures and 5 quizzes
  • 7+ hours of high quality content
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Introduction to Numerical Analysis

Learn the "Introduction to Numerical Analysis" in Five Weeks Only.
0 reviews

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COURSE DESCRIPTION

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.

    • Basics of Linear Algebra
    • The desire to learn
    • Over 27 lectures and 7.5 hours of content!
    • Understand the error analysis and its applications in computational methods.
    • Solve a system of linear equations using several methods such as Bisection Method, Fixed-Point Iteration Method and Newton’s Method.
    • Use the interpolation and polynomial approximation to develop numerical methods and algorithms.
    • Use the direct methods for solving linear equations.
    • The ability to use computer software such as Maple to apply several numerical methods and approximations.
    • This course is intended for anyone who had a little bit of linear algebra background and the desire to learn
    • If you do not have linear algebra background, Don't worry because I will give a review for linear algebra

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CURRICULUM

  • SECTION 1:
    Week 1: Mathematical Preliminaries and Error Analysis
  • 1
    Course Introduction
    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
    Mathematical Preliminaries
    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
    Floating-Point Arithmetic
    22:10
    In this lecture, you will be given an introduction to the floating-point arithmetic (FPA) definition including several
    examples and their solutions using number systems.
  • 4
    Error Analysis
    19:45
    In this lecture, you will be introduced to several errors in mathematics such as converting error, overflow error, underflow error and round-off error with the examples of the ways of performing termination for these errors.
  • 5
    Problem Set 1
    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
    Problem Set 1 Solutions
    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
    Introduction to Maple 11
    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
    Solutions of Equations in One Variable (Part I)
    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
    Solutions of Equations in One Variable (Part II)
    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 fixed-point iteration method. Several examples, proofs, theorems and comparison of each method in terms of advantages and disadvantages will be given in each method.
  • 11
    Problem Set 2
    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
    Problem Set 2 Solutions
    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
    Linear Interpolation
    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
    Solving a System of Equations
    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
    Lagrange Polynomials
    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
    Problem Set 3
    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
    Problem Set 3 Solutions
    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
    Linear Spline Interpolation
    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
    Quadratic Spline Interpolation
    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
    Cubic Spline Interpolation
    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
    Problem Set 4
    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
    Problem Set 4 Solutions
    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
    Gaussian Elimination Method
    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
    Cramer's Rule
    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
    Pivoting Strategies
    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
    Problem Set 5
    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
    Problem Set 5 Solutions
    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
    Course Conclusion
    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.

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