A Beginner's Guide to Numerical Methods in MATLAB
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A Beginner's Guide to Numerical Methods in MATLAB

Learn to select, apply and improve numerical methods.
4.3 (11 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.
118 students enrolled
Last updated 4/2016
English
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Includes:
  • 5 hours on-demand video
  • 16 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What Will I Learn?
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
View Curriculum
Requirements
  • Basic math knowledge
  • Fundamental knowledge of computing
  • Some familiarity with MATLAB is required to follow the examples
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
Who 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
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Curriculum For This Course
Expand All 36 Lectures Collapse All 36 Lectures 04:50:28
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Introduction
1 Lecture 04:20

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

Preview 04:20
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Machine Representation of Numbers
4 Lectures 27:59

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

Base 2 Representation
04:29

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

Floating-Point Representation
13:49

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

Machine Epsilon
03:39

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

Round-Off and Truncation Errors
06:02

Use MATLAB to calculate round-off and truncation errors.

Quiz: Round-Off and Truncation Errors
2 questions
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Basic Concepts
4 Lectures 16:45

What makes a function continuous?

Function Continuity
07:50

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

Rolle's Theorem
03:41

Another theorem you need to be aware of.

First Mean Value Theorem
02:25

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

Bolzano's Theorem
02:49
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One-Point Iterative Methods
8 Lectures 01:08:18

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

Introduction
08:59

The notion of convergence (and divergence, too).

Preview 07:20

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

Acceleration of Convergence
06:02

Use MATLAB to fast solve the root-finding problem.

Acceleration of сonvergence
1 question

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

Order of Convergence
03:29

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

Newton's Method (a.k.a. Newton-Raphson)
08:08

Use MATLAB to solve the root-finding problem.

Newton's Method
1 question

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

Multidimensional Extensions of Newton's Method
12:13

Use MATLAB to solve the root-finding problem.

Multidimensional extensions of Newton's method
1 question

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.)

Approximate Newton's Method
13:56

Use MATLAB to solve a root-finding problem.

Approximate Newton's Method
2 questions

A way of speeding up polynomial evaluations.

Horner's Algorithm for Polynomial Equations
08:11

Use MATLAB to evaluate polynomial.

Horner's Algorithm
1 question
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Two-Point Iterative Methods
3 Lectures 16:36

A very simple method that leverages Bolzano's theorem.

Bisection Method
06:06

Use MATLAB to solve the root-finding problem.

Bisection method
2 questions

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

Regula Falsi Method
05:10

Use MATLAB to solve the root-finding problem.

Regula falsi method
3 questions

Yet another single-point iteration method.

Secant Method
05:20

Use MATLAB to solve the root-finding problem.

Secant method
2 questions
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Interpolation and Curve Fitting
7 Lectures 01:21:02

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

Polynomial Interpolation
06:57

A better way of defining the interpolating polynomial.

Newton Basis
06:52

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

Divided Differences
15:10

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

Divided Differences: Examples
06:11

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

Forward Differences
13:49

An interpolation formula for Lagrange polynomial.

Lagrangian Interpolation
13:26

Use MATLAB to determite the interpolated value of a point.

Lagrangian interpolation
3 questions

An improvement of Lagrangian interpolation.

Neville's Algorithm
18:37

Use MATLAB to determite the interpolated value of a point.

Neville's algorithm
2 questions
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Differentiation
4 Lectures 42:25

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

First Derivative Approximations
10:21

Now a formula for the 2nd derivative approximation.

Second Derivative Approximations
04:38

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

Error Terms by Taylor Series Expansion
14:02

A method of combining approximations for improving accuracy.

Richardson Interpolation
13:24
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Integration (Quadrature)
5 Lectures 33:03

Why would we want to integrate things numerically?

Introduction
02:22

The simplest way of estimating the value of an integral.

Trapezium Rule
08:30

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

Midpoint Rule
06:44

A way of numerically calculating a specific type of integral.

Gauss-Hermite
09:16

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

Gauss-Laguerre
06:11
About the Instructor
Dmitri Nesteruk
4.5 Average rating
228 Reviews
2,319 Students
11 Courses
Quant Finance • Algotrading • Software/Hardware Engineering

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.

Xenia Kuznetsova
4.3 Average rating
11 Reviews
118 Students
1 Course
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.