Book contents
- Frontmatter
- Contents
- Preface
- Some notes on notation
- 1 Introduction
- 2 Errors
- 3 Cartesian coordinates
- 4 Vectors
- 5 The scalar product
- 6 The vector product and rotation
- 7 Matrices in physics
- 8 The transformation of matrices
- 9 The matrix eigenvalue equation
- 10 Exponential and logarithm functions
- 11 Sine and cosine functions
- 12 Graph plotting and curve sketching
- 13 Differentiation
- 14 Approximations
- 15 Power series and Taylor's expansion
- 16 Partial differentiation
- 17 Integration
- 18 The differential equation
- 19 Solving first-order differential equations
- 20 Second-order differential equations
- 21 Solving second-order differential equations
- 22 The complex exponential
- 23 The circuit equation
- 24 Harmonics and Fourier series
- 25 The diffusion equation
- 26 Waves
- 27 The rate of change of a vector
- 28 The scalar field and gradient operator
- 29 The vector field
- 30 Line integration
- 31 The potential field
- 32 Surface and volume integration
- 33 Flux and divergence
- 34 Circulation and the curl
- 35 Conclusion
- 36 Miscellaneous exercises
- Index
12 - Graph plotting and curve sketching
Published online by Cambridge University Press: 20 October 2009
- Frontmatter
- Contents
- Preface
- Some notes on notation
- 1 Introduction
- 2 Errors
- 3 Cartesian coordinates
- 4 Vectors
- 5 The scalar product
- 6 The vector product and rotation
- 7 Matrices in physics
- 8 The transformation of matrices
- 9 The matrix eigenvalue equation
- 10 Exponential and logarithm functions
- 11 Sine and cosine functions
- 12 Graph plotting and curve sketching
- 13 Differentiation
- 14 Approximations
- 15 Power series and Taylor's expansion
- 16 Partial differentiation
- 17 Integration
- 18 The differential equation
- 19 Solving first-order differential equations
- 20 Second-order differential equations
- 21 Solving second-order differential equations
- 22 The complex exponential
- 23 The circuit equation
- 24 Harmonics and Fourier series
- 25 The diffusion equation
- 26 Waves
- 27 The rate of change of a vector
- 28 The scalar field and gradient operator
- 29 The vector field
- 30 Line integration
- 31 The potential field
- 32 Surface and volume integration
- 33 Flux and divergence
- 34 Circulation and the curl
- 35 Conclusion
- 36 Miscellaneous exercises
- Index
Summary
An invaluable accessory to a computer or experimental system is a curveplotter. The stony columns of data in the digital print-out come to life as plateaux, peaks, dips, shoulders and so on. Indeed, the pictorial language of numerical trends is in every sense, graphic. What business is complete without its sales chart? Nevertheless the presentation of experimental data in the form of a graph is a surprisingly modern convention. It did not become popular until the late nineteenth century. Before that, the general form of the results of experiments was described only roughly, in words. For example, Michael Faraday, who is credited (among many other things) with first recognising the characteristic property of semiconductors in 1833 simply said, ‘The conducting power increases with the heat’. At that time, whole textbooks were written on ‘Natural Philosophy’ without graphs, even though Descartes had long since provided the conceptual framework for them. Today, such a statement would rarely be made without an accompanying graph of the data or sketch of the inferred functional form.
A graph can present experimental data or a theoretical prediction or the comparison of both in a clear and compact way. To maximise its effectiveness in your own work, you should give a little thought to the choice of origin, scales and functional forms which you use.
First, there is no necessity whatever that the meeting of the horizontal and vertical axes should coincide with the zero of either variable.
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- Information
- Introduction to Physical Mathematics , pp. 76 - 86Publisher: Cambridge University PressPrint publication year: 1985