Introduction to Numerical Analysis

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

311 students enrolled

What Will I Learn?

- 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.

Requirements

- Basics of Linear Algebra
- The desire to learn

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.

Who is the target audience?

- 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 For This Course

27 Lectures

07:20:32
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Week 1: Mathematical Preliminaries and Error Analysis
6 Lectures
01:13:27

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.

Course Introduction

05:47

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.

Mathematical Preliminaries

25:45

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.

examples and their solutions using number systems.

Floating-Point Arithmetic

22:10

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.

Error Analysis

19:45

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!

Problem Set 1

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!

Problem Set 1 Solutions

1 page

**In this quiz, you will have 10 different multiple-choice questions which are based on the material of week 1.Each question is worth 2% which means that 10 questions are worth 20%, you are allowed to attempt thisquiz till five times , and the only maximum one will be taken into account in final grade of this quiz.**

Mathematical Preliminaries and Error Analysis

10 questions

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Week 2: Solutions of Equations in One Variable
5 Lectures
01:56:37

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.

Introduction to Maple 11

17:20

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.

Solutions of Equations in One Variable (Part I)

55:35

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.

Solutions of Equations in One Variable (Part II)

43:42

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!

Problem Set 2

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!

Problem Set 2 Solutions

2 pages

Each question is worth 2% which means that 10 questions are worth 20%, you are allowed to attempt this

quiz till five times , and the only maximum one will be taken into account in final grade of this quiz.

**During the quiz, feel free to use the course material to answer the questions. GOOD LUCK!.**

Solutions of Equations in One Variable

10 questions

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Week 3: Interpolation and Polynomial Approximation
5 Lectures
01:07:46

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.

Linear Interpolation

11:02

In this lecture, you will be given an example about the first linear interpolation method which is called "solving a System of Equations".

Solving a System of Equations

17:34

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.

Lagrange Polynomials

39:10

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!

Problem Set 3

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!

Problem Set 3 Solutions

1 page

**In this quiz, you will have 10 different multiple-choice questions which are based on the material of week 3.Each question is worth 2% which means that 10 questions are worth 20%, you are allowed to attempt thisquiz till five times , and the only maximum one will be taken into account in final grade of this quiz.**

**During the quiz, feel free to use the course material to answer the questions. GOOD LUCK!.**

Interpolation and Polynomial Approximation

10 questions

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Week 4: Spline Interpolation
5 Lectures
01:17:34

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.

Linear Spline Interpolation

29:00

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.

Quadratic Spline Interpolation

29:46

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.

Cubic Spline Interpolation

18:48

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!

Problem Set 4

3 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!

Problem Set 4 Solutions

4 pages

**In this quiz, you will have 10 different multiple-choice questions which are based on the material of week 4.Each question is worth 2% which means that 10 questions are worth 20%, you are allowed to attempt thisquiz till five times , and the only maximum one will be taken into account in final grade of this quiz.**

**During the quiz, feel free to use the course material to answer the questions. GOOD LUCK!.**

Spline Interpolation

10 questions

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–

Week 5: Direct Methods for Solving Linear Equations
6 Lectures
01:24:08

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.

Gaussian Elimination Method

28:54

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.

Cramer's Rule

32:42

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.

Pivoting Strategies

20:48

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!

Problem Set 5

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!

Problem Set 5 Solutions

3 pages

Each question is worth 2% which means that 10 questions are worth 20%, you are allowed to attempt this

quiz till five times , and the only maximum one will be taken into account in final grade of this quiz.

**During the quiz, feel free to use the course material to answer the questions. GOOD LUCK!.**

Direct Methods for Solving Linear Equations + General Course Questions

10 questions

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.

Course Conclusion

01:44

About the Instructor