READOS / Engineering
Practical Mathematics for Engineering and Manufacturing
Fractions, ratios, formulas, units, geometry, trigonometry, graphs, logarithms, vectors, matrices, probability and spreadsheets.
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- 01Fractions, decimals and percentages in technical work: tolerances, yields, markups and GST without slipsA practical refresher on fractions, decimals and percentages for engineering, manufacturing and business work, from inch fractions and rounding to yield chains, markup versus margin and GST.
- 02Ratio, proportion and scaling: drawing scales, gear ratios, mixtures and the square-cube lawHow ratios and direct and inverse proportion work in technical tasks, from drawing scales and pulley ratios to mixing, dilution and recipe scaling, and why areas and volumes scale differently.
- 03Rearranging formulas with confidence: transposition, order of operations and checking the answerHow to rearrange engineering and business formulas safely, from inverse operations to squares, roots, fractions and variables that appear twice, with checks that catch errors early.
- 04Powers, roots and scientific notation: index laws, SI prefixes and why some quantities grow so fastA practical guide to powers, roots and scientific and engineering notation, converting squared and cubed units, and why energy, stiffness and fan power rise with the square or cube of a change.
- 05Inch and metric conversion on legacy drawings: tolerances, threads, pipe sizes and other trapsHow to convert imperial drawings and data to metric without errors: exact factors, converting tolerance limits, why threads and pipe sizes must not be converted, and other common traps.
- 06Areas, volumes and masses for the workshop: estimating material, weight, coatings and liftsHow to calculate areas, volumes and masses of plates, bars, tubes, tanks and welds, use densities and mass-per-metre figures, and apply them to quoting, coating, handling and lifting.
- 07Right-angle trigonometry for setting out and machining: squares, slopes, tapers, offsets and sine barsHow Pythagoras and sine, cosine and tangent solve everyday setting-out, fabrication and machining problems, from squaring a slab and grading a ramp to tapers, pipe offsets and sine bars.
- 08Circles, arcs, chords and bolt circles: hole patterns, rolled shells, bends and radius checksHow circumference, arc length, chords and sagitta solve practical problems, from bolt-circle hole coordinates and rolled cylinders to sheet metal bend allowances and finding a radius from a chord.
- 09Straight-line relationships and estimating models: slopes, intercepts, calibration and trend linesHow the equation of a straight line underpins cost estimates, break-even, sensor calibration, interpolation and trend lines, how to fit a line to data and where straight-line thinking fails.
- 10Growth, decay and logarithms in engineering and business: compounding, cooling, depreciation and learning curvesHow exponential growth and decay describe compounding, demand growth, cooling, discharge, depreciation and learning curves, how logarithms solve for time, and why straight-line intuition fails.
- 11Vectors and resolving forces: components, equilibrium, moments, sling angles and slopesHow to break forces into components, find resultants, apply equilibrium and moments, and use them for lifting slings, ramps, brackets and guy wires, with the checks that keep loads safe.
- 12Rates of change and areas under curves: the practical ideas of calculus without heavy mathematicsHow slopes and areas on charts give speeds, flow rates, energy, distance and accumulated cost, how to calculate them from data, and how optimisation finds the best batch or order size.
- 13Simultaneous equations and matrices in practice: blending, product mix, structures and circuitsHow pairs and systems of equations solve blending, product-mix, structural and circuit problems, how matrices and spreadsheets handle larger systems, and how to spot unreliable solutions.
- 14Probability for quality and reliability: sampling risk, rare events, redundancy and false alarmsHow basic probability explains acceptance sampling, defect counts, the normal distribution, series and parallel reliability and why inspections with good accuracy still reject many good parts.
- 15Spreadsheet methods for engineering calculations: structure, goal seek, iteration, lookups and checksHow to build engineering and estimating spreadsheets that are easy to check: separating inputs and results, units, lookups, goal seek, iteration, sensitivity tables and built-in checks.
These topic-based reading collections are organised alphabetically; chapters may be read in any order.
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