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Time: 20 hours
Level: Intermediate
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 Introduction Resource- Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful...
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- Overview Resource
- A fundamental concept in mathematics is that of a function.
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- 1 Real functions Resource
- In Section 1 we formally define real functions and describe how they may arise when we try to solve equations. We remind you of some basic real functions and their graphs, and describe how some of the...
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- 2 Graph sketching Resource
- In Section 2 we describe how the graphs of polynomial and rational functions may be sketched by analysing their behaviour – for example, by using techniques of calculus. We assume that you are familiar...
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- 3 New graphs from old Resource
- In Section 3 we consider how to sketch the graphs of more complicated functions, sometimes involving trigonometric functions. We look at graphs which are sums, quotients and composites of different functions,...
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- 4 Hyperbolic functions Resource
- In Section 4 we introduce the hyperbolic functions sinh, cosh and tanh, which are constructed from exponential functions. These hyperbolic functions share some of the properties of the trigonometric functions...
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- 5 Curves from parameters Resource
- In Section 5 we show how functions may be used to sketch curves in the plane, even when these curves are not necessarily the graphs of functions.
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| | 6 Solutions to the exercises
- 6 Solutions to the exercises Resource
- Section 6 contains solutions to the exercises that appear throughout sections 1-5.
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| | References and Acknowledgements | |
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