Download PDF An Introduction to Programming and Numerical Methods in MATLAB by S.R. Otto

Sinopsis

MATLAB is an incredibly powerful tool, but in order to use it safely you need to be able to understand how it works and to be very precise when you enter commands. Changing the way you enter a command, even subtly can completely change its meaning.
 

The main aim of this text is to teach you to converse with MATLAB and understand its responses. It is possible to interact with MATLAB using a “phrase book” approach, which is fine if the answer is what you expect. However it is far better to learn the language so that you can understand the response. As well as learning the language it is essential that you learn the grammar or syntax; this is perhaps even more important with computer languages than conventional languages! MATLAB uses an interpreter to try to understand what you type and this can come back with suggestions as to where you might have gone wrong: sometimes what you have written makes sense to MATLAB but does not mean what you expect! So you need to be careful. It is crucial that you formulate ideas clearly in your head (or on paper) before trying to translate them into MATLAB (or any other language).

 

We begin by discussing mathematical operations performed on scalars1. It is crucial that the material in this chapter is understood before proceeding, as it forms the basis of all that is to follow2.

We shall start by introducing MATLAB commands which can be typed at the MATLAB prompt; these will ultimately form part of our vocabulary of MATLAB commands. MATLAB already has an extensive vocabulary: however we will learn that we can expand this set. As the name MATLAB (MATrix LABoratory) suggests, most of the commands work with matrices and these will be discussed in due course. We shall start with scalar operations, for which MATLAB acts like a very powerful calculator.

Content

1. Simple Calculations with MATLAB
2. Writing Scripts and Functions
3. Loops and Conditional Statements
4. Root Finding
5. Interpolation and Extrapolation
6. Matrices 
7. Numerical Integration
8. Solving Differential Equations
9. Simulations and Random Numbers
10. A Mathematical Introduction to Matrices

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