There are many problems which simply do not have analytical solutions, or those whose exact solution is beyond our current state of knowledge. There are also many problems which are too long (or tedious) to solve by hand. When such problems arise we can exploit numerical analysis to reduce the problem to one involving a ? nite number of unknowns and use a computer to solve the resulting equations. The text starts with a description of how we could perform some very basic calculations (that is, simply using the computer as a calculator).

It then moves on to solving problems which cannot, in practice, be solved by hand. Sometimes the solution of these problems can become as intricate and involved as the original problems and requires almost as much ? nesse and care to obtain a solution. There are several options available to us, both in terms of language and also overall approach. In this book we elect to express our ideas in terms of the syntax of the computer package MATLAB. Once you have mastered the syntax of MATLAB it will be easier for you to learn other languages, if you should decide you need to. The Structure of This Text

This text is designed to be used as a source of reference for MATLAB commands (mainly through the glossary in Appendix B) and the examples given in the chapters. This is an approach we have found works well with our students. The text gives an introduction to numerical methods and the manipulation of the quantities used therein (for instance matrices). At each stage, short codes are given to allow the reader to try their own examples. Examples of code which can be typed at the MATLAB prompt will appear within the general text in this font (this font is also used for the names of MATLAB codes), while longer examples will be written gt;> commands to be entered Results

It then moves on to solving problems which cannot, in practice, be solved by hand. Sometimes the solution of these problems can become as intricate and involved as the original problems and requires almost as much ? nesse and care to obtain a solution. There are several options available to us, both in terms of language and also overall approach. In this book we elect to express our ideas in terms of the syntax of the computer package MATLAB. Once you have mastered the syntax of MATLAB it will be easier for you to learn other languages, if you should decide you need to. The Structure of This Text

This text is designed to be used as a source of reference for MATLAB commands (mainly through the glossary in Appendix B) and the examples given in the chapters. This is an approach we have found works well with our students. The text gives an introduction to numerical methods and the manipulation of the quantities used therein (for instance matrices). At each stage, short codes are given to allow the reader to try their own examples. Examples of code which can be typed at the MATLAB prompt will appear within the general text in this font (this font is also used for the names of MATLAB codes), while longer examples will be written gt;> commands to be entered Results