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A Beginner's Guide to Numerical Methods in MATLAB

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Learn to select, apply and improve numerical methods.

129 students enrolled

Current price: $10
Original price: $50
Discount:
80% off

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- 5 hours on-demand video
- 16 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

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

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

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.

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