# Chris Fox's Engineering Section

## Mathematics and Statistics

Mathematics was originally concerned with the properties of numbers and space, but is now generally concerned with deductions made from assumptions about abstract entities.

Everything, whether natural or man-made, consists of individual components; examples are atoms in a crystal, leaves on a tree and parts of a spaceship. Mathematics aims to find the relationships between components.

Mathematics can be divided into three main parts. One part, which includes algebra, is concerned with assembling and combining sets of objects. Another, which includes geometry, deals with the measurement of space and time. The third, which includes calculus, derives from the need to understand ideas of continuity and limit.

Statistics is the science of collecting and classifying numerical data. It may be either descriptive, where the data is summarised, or inferential, where conclusions are drawn about a larger quantity of which the data is a sample. In the latter case, the probability of error can be calculated.

Mathematics is fundamental to much of science and engineering. Algebra and dimensional analysis can be used to relate variables to each other. Calculus is useful due to the need for optimisation, as it allows the maximum and minimum values of variables to be determined. And geometry helps with dimensioning.

Statistics can be used to regulate the production and quality of products. It is also useful in research and development.

[Functions] [Straight Lines and Curves] [Trigonometry] [Sequences and Series] [Partial Fractions] [Calculus: Differentiation] [Exponential Functions and Logarithms] [Matrices] [Vectors] [Lines and Planes] [Calculus: The Second Derivative] [Taylor and Maclaurin Series] [Calculus: Integration] [Gradient Vector] [Imaginary Numbers] [Calculus: Ordinary Differential Equations] [Orthogonal Curvilinear Co-ordinates] [Scalar and Vector Fields] [Line Integrals] [Surface Integrals] [Volume Integrals] [Vector Analysis] [Conservative Fields] [The Curl of a Vector Field] [The Divergence of a Vector Field] [Solution of Non-Linear Equations] [Regression Analysis] [Simultaneous Equations] [Eigenproblems] [Interpolation] [Solution of Ordinary Differential Equations] [Dimensional Analysis and Similarity] [Probability] [Distributions] [Measures of Central Tendency] [Measures of Dispersion] [Statistical Process Control] [Tolerance Limits]