A Beginner's Guide to Numerical Methods in MATLAB

Learn to select, apply and improve numerical methods.
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  • Lectures 36
  • Length 5 hours
  • Skill Level Beginner Level
  • Languages English
  • Includes Lifetime access
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About This Course

Published 4/2016 English

Course Description

This course is about Numerical Methods and covers some of the popular methods and approaches being used daily by mathematicians and everyone involved in computation.

This course will teach you about

  • How computers store numbers: what is floating point, what is precision and accuracy.
  • The kinds of errors you are likely to encounter when applying numerical methods, and how to minimize them.
  • One- and Two-Point iterative methods
  • Interpolation and Curve Fitting
  • Numerical Differentiation and Integration

This course consists of the following materials:

  • Video lectures, covering both the theory as well as demonstrating practical computer applications
  • MATLAB files that you can download and run
  • Quizzes related to the covered topics

What are the requirements?

  • Basic math knowledge
  • Fundamental knowledge of computing
  • Some familiarity with MATLAB is required to follow the examples

What am I going to get from this course?

  • Understand about the ways computer store numbers
  • Choose the right numerical methods to solve a problem
  • Measure (and avoid) the errors inherent in numeric calculations
  • See how algorithms are implemented in MATLAB

What is the target audience?

  • This course is designed for anyone interested in the numerical methods and their applications for solving real-world problems
  • Engineers, computer scientists, mathematicians and finance people will enjoy this course

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: Introduction
04:20

Some motivating examples of what the course can help you do.

Section 2: Machine Representation of Numbers
04:29

How do you store numbers using only 0s and 1s?

13:49

How computers actually store numbers. A discussion of mantissa, exponent and bias.

03:39

We talk about the notion of the machine epsilon and the fact that it's not really that useful when specifying calculation tolerances.

06:02

The two types of errors that reduce the accuracy of numerical methods.

2 questions

Use MATLAB to calculate round-off and truncation errors.

Section 3: Basic Concepts
07:50

What makes a function continuous?

03:41

The claim that a differentiable function that has equal states at two distinct point has a stationary point somewhere in between.

02:25

Another theorem you need to be aware of.

02:49

If a<b and f(a)f(b)<0 then the root of f(x) = 0 lies between a and b.

Section 4: One-Point Iterative Methods
08:59

What are one-point iterative methods and what are they used for?

07:20

The notion of convergence (and divergence, too).

06:02

A look at Aitken's Δ² process and Steffensen's method.

1 question

Use MATLAB to fast solve the root-finding problem.

03:29

What is the order of convergence and why do we care?

08:08

An extremely efficient and popular root finding method. Quadratic convergence, woo-hoo!

1 question

Use MATLAB to solve the root-finding problem.

12:13

Newton's method applied in many dimensions. Useful for solving systems of non-linear equations!

1 question

Use MATLAB to solve the root-finding problem.

13:56

What if you cannot get the Jacobian matrix in analytic form? Use finite differences! (Note: finite differences are actually discussed in a later section, so you can come back to this clip later.)

2 questions

Use MATLAB to solve a root-finding problem.

08:11

A way of speeding up polynomial evaluations.

1 question

Use MATLAB to evaluate polynomial.

Section 5: Two-Point Iterative Methods
06:06

A very simple method that leverages Bolzano's theorem.

2 questions

Use MATLAB to solve the root-finding problem.

05:10

Similar to the Bisection method, Regula Falsi can, in most cases, provide faster convergence than the Bisection method.

3 questions

Use MATLAB to solve the root-finding problem.

05:20

Yet another single-point iteration method.

2 questions

Use MATLAB to solve the root-finding problem.

Section 6: Interpolation and Curve Fitting
06:57

An introduction to the concept of interpolation, with a simple example.

06:52

A better way of defining the interpolating polynomial.

15:10

Did you think the Newton basis was cool? With divided difference, you don't even have to solve the triangular set of equations!

06:11

The derivations of divided differences took too much time, so the examples get their own separate lesson.

13:49

What kind of simplicifications can be made to divided differences if we assume the points are equally spaced?

13:26

An interpolation formula for Lagrange polynomial.

3 questions

Use MATLAB to determite the interpolated value of a point.

18:37

An improvement of Lagrangian interpolation.

2 questions

Use MATLAB to determite the interpolated value of a point.

Section 7: Differentiation
10:21

Finite difference approximations of derivatives - forward, backward and central differences.

04:38

Now a formula for the 2nd derivative approximation.

14:02

A look that the error terms in first and second derivatives that arise from using finite difference methods.

13:24

A method of combining approximations for improving accuracy.

Section 8: Integration (Quadrature)
02:22

Why would we want to integrate things numerically?

08:30

The simplest way of estimating the value of an integral.

06:44

Subdivide an integral into several strips, evaluate functions as midpoints, treat strips as rectangles. Profit!

09:16

A way of numerically calculating a specific type of integral.

06:11

Another numeric procedure for a very specific integral. Usable for calculating the Gamma function!

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Instructor Biography

Dmitri Nesteruk, Quantitative Finance Professional

Dmitri Nesteruk is a developer, speaker and podcaster. His interests lie in software development and integration practices in the areas of computation, quantitative finance and algorithmic trading. His technological interests include C#, F# and C++ programming as well high-performance computing using technologies such as CUDA. He has been a C# MVP since 2009.

Dmitri is a graduate of University of Southampton (B.Sc. Computer Science) where he currently holds a position as a Visiting Researcher. He is also an instructor on an online intro-level Quantitative Finance course, and has also made online video courses on CUDA, MATLAB, D, the Boost libraries and other topics.

Instructor Biography

Xenia Kuznetsova, Web developer

I am an engineer, mathematician and web developer. I make web applications using C# and .NET technology stack, and have 10 published scientific articles. I graduated from a university in 2011. At that time I engaged in research into matrix algebra and conducted work related to request processing optimization in a learning management system. Right now, I am interested in participating in research into financial engineering.

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