Modelling and control by Anthony Rossiter

# Videos on logarithms and exponentials

These videos give an introduction to exponential and logarithm functions and their key attributes. It is assumed that students have been introduced to these functions before, albeit briefly, and thus the focus is more on identifying and understanding the key properties that will be used in engineering problem solving.

The videos do spend a little time demonstrating that some key results are true, but students could skip those parts and concentrate on the key results if they want too. Use the left hand toolbar to access the other chapters and themes.

 It is implicit that for many engineering topics, students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials, logarithms and Laplace. This section contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

## Logarithms and exponentials 1 - introduction to exponentials

A rapid review of indices or powers as a lead into the definition of an exponential function as a special case of a power function.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Logarithms and exponentials 2 - properties of exponentials

Derives and explains the key properties of exponential functions such as key values, asymptotic behaviour, sketches, monotonicity and so on.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Logarithms and exponentials 3 - definition of logarithms

Introduces logarithms as the inverse function of an exponential and uses this definition to derive and demonstrate core properties (or rules) of logs which students will need for common problem solving.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Logarithms and exponentials 4 - algebra with logarithms

A number of worked examples demonstrating the use of the rules and the importance of estimation skills when using logarithms.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Logarithms and exponentials 5 - range and domain

As exponential and logarithm are inverse functions, their range and domains must be linked. This brief video gives a illustration of this.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Logarithms and exponentials 6 - miscellaneous

Highlights a few engineering problem solving skills linked to logarithms. How do we identify exponential behaviour in a noisy signal and what is logarithmic graph paper.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.