Mathematical Foundations

Numbers, arithmetic, algebra and logarithms. The school-level toolkit every engineer relies on: number systems, arithmetic with units and significant figures, algebra and equation solving including quadratics, and exponents, radicals and logarithms with real engineering applications.

• Number Systems — Every calculation starts with numbers. Learn natural numbers, whole numbers, integers, rationals, irrationals, reals and complex numbers; primes, composites, even/odd; the number line, intervals and absolute value; inequalities and ordering; and how the number-system hierarchy fits together.
• Arithmetic, Units & Significant Figures — Accurate arithmetic is the backbone of engineering calculations. Learn order of operations, fractions, decimals, percentages and percentage change, ratios and proportions, powers and roots, approximation and rounding, significant figures, scientific and engineering notation, SI prefixes and unit conversion.
• Algebra & Equations — Algebra lets us write and solve relationships between quantities. Learn variables, constants and coefficients; expressions, equations and identities; linear and simultaneous equations; quadratic equations and the discriminant; factorisation and completing the square; polynomial, rational, radical, absolute-value, exponential and logarithmic equations; and inequalities.
• Exponents, Radicals & Logarithms — Exponential growth and decay appear everywhere in engineering. Learn laws of indices, negative and fractional powers, surds and rationalisation, exponential functions, logarithm definition and laws, common and natural logs, change of base, solving exponential/log equations, and applications — decibels, pH, half-life, RC circuits and semiconductor models.