A Beginner's Guide to Numerical Methods in MATLAB
4.1 (76 ratings)
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A Beginner's Guide to Numerical Methods in MATLAB

Learn to select, apply and improve numerical methods.
4.1 (76 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
592 students enrolled
Last updated 4/2016
English [Auto-generated]
Current price: $34.99 Original price: $49.99 Discount: 30% off
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This course includes
  • 5 hours on-demand video
  • 16 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll 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
Course content
Expand all 36 lectures 04:50:28
+ Introduction
1 lecture 04:20

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

Preview 04:20
+ Machine Representation of Numbers
4 lectures 27:59

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

Base 2 Representation

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

Floating-Point Representation

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

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

Round-Off and Truncation Errors

Use MATLAB to calculate round-off and truncation errors.

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

What makes a function continuous?

Function Continuity

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

Rolle's Theorem

Another theorem you need to be aware of.

First Mean Value Theorem

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

Bolzano's Theorem
+ One-Point Iterative Methods
8 lectures 01:08:18

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


The notion of convergence (and divergence, too).

Preview 07:20

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

Acceleration of Convergence

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

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

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

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

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

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

Use MATLAB to evaluate polynomial.

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

A very simple method that leverages Bolzano's theorem.

Bisection Method

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

Use MATLAB to solve the root-finding problem.

Regula falsi method
3 questions

Yet another single-point iteration method.

Secant Method

Use MATLAB to solve the root-finding problem.

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

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

Polynomial Interpolation

A better way of defining the interpolating polynomial.

Newton Basis

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

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

Divided Differences: Examples

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

Forward Differences

An interpolation formula for Lagrange polynomial.

Lagrangian Interpolation

Use MATLAB to determite the interpolated value of a point.

Lagrangian interpolation
3 questions

An improvement of Lagrangian interpolation.

Neville's Algorithm

Use MATLAB to determite the interpolated value of a point.

Neville's algorithm
2 questions
+ Differentiation
4 lectures 42:25

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

First Derivative Approximations

Now a formula for the 2nd derivative approximation.

Second Derivative Approximations

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

Error Terms by Taylor Series Expansion

A method of combining approximations for improving accuracy.

Richardson Interpolation
+ Integration (Quadrature)
5 lectures 33:03

Why would we want to integrate things numerically?


The simplest way of estimating the value of an integral.

Trapezium Rule

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

Midpoint Rule

A way of numerically calculating a specific type of integral.


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

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

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 this course is for:
  • 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