Mathematics for Engineers I

- Algebraic simplifications, completing the square, the factor theorem, equations and inequalities, absolute values. - Polynomial, potency, logarithmic, exponential, trigonometric, and inverse trigonometric functions, their definitions, properties, and graphs. - Complex numbers in Cartesian and polar form, de Moivres theorem, vector representation of complex numbers. - The concept of function, domain of definition, range of function, composition of functions, inverse functions. - Limits of functions, continuity, asymptotes. - Definition and rules for derivatives, derivatives of elementary functions, implicit differentiation. - Function analysis: increasing and decreasing functions, extrema, concavity. - Applications of derivatives: tangents and normals, extreme value problems, linearisations, related rates, Taylor polynomials, and l'Hôpital's rule.