Mathematics for Engineers I

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