Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic functions
- 2 Functions for science 1: the exponential function
- 3 Functions for science 2: trigonometric functions
- 4 Functions for science 3: inverse functions
- 5 Other functions of science
- 6 Differentiation 1: rates of change
- 7 Differentiation 2: stationary points
- 8 Differentiation 3: approximation of functions
- 9 Integration 1: introduction and standard forms
- 10 Integration 2: techniques of integration
- 11 Integration 3: further techniques
- 12 First-order ordinary differential equations
- 13 Second-order ordinary differential equations
- 14 Statistics 1: frequency distributions and associated measures
- 15 Statistics 2: probability and probability distributions
- 16 Statistics 3: sampling, sampling distributions and hypothesis testing
- 17 Partial differentiation 1: introduction
- 18 Partial differentiation 2: stationary points
- Answers to the exercises
- Index
1 - Basic functions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Basic functions
- 2 Functions for science 1: the exponential function
- 3 Functions for science 2: trigonometric functions
- 4 Functions for science 3: inverse functions
- 5 Other functions of science
- 6 Differentiation 1: rates of change
- 7 Differentiation 2: stationary points
- 8 Differentiation 3: approximation of functions
- 9 Integration 1: introduction and standard forms
- 10 Integration 2: techniques of integration
- 11 Integration 3: further techniques
- 12 First-order ordinary differential equations
- 13 Second-order ordinary differential equations
- 14 Statistics 1: frequency distributions and associated measures
- 15 Statistics 2: probability and probability distributions
- 16 Statistics 3: sampling, sampling distributions and hypothesis testing
- 17 Partial differentiation 1: introduction
- 18 Partial differentiation 2: stationary points
- Answers to the exercises
- Index
Summary
Scientific context
Many scientific laws are often expressed as relations between two or more physical quantities. In general these laws are obtained in one of two ways. Either the results of experiment are used directly to formulate empirical laws, or existing scientific knowledge is used, often together with mathematics, to arrive at new theories which can then be validated later by experiment. In formulating scientific laws we attempt to find a formula between the symbols representing the physical quantities of interest. Sometimes this is not possible and the relationship has to be expressed in the form of a table of values or a graph, for example.
If two quantities are related so that the value of one of them is uniquely determined when the other is known, then we say that there is a functional relationship between the variables. In these opening chapters we consider the basic mathematical functions which occur in science.
Example 1: loading a steel wire. Table 1.1 shows the results of an experiment to investigate how the length of a piece of mild steel wire changes when weights are attached to it. The unextended length of the wire is 2 m and its mean diameter is 1 mm.
It is clear that l increases with W but the nature of the relationship between the quantities W and l is more easily seen if we plot the points on a graph.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 1989