MATE-1204 Differential Calculus (Honors)

This course is recommended for students with a better mathematical background from high school, students most interested in this discipline and, in particular, students of mathematics. In the University’s different programs of study, it is equivalent to the course MATE-1203 and its content is the same but in more depth, as it is offered to students who are more prepared and more competitive. Functions: Function algebra, trigonometric functions, exponential functions, inverse functions, logarithms, trigonometric inverses, problem solving principles. Limits and derivatives: Velocity and tangents, limit of a function, calculating limits, continuity, limits at infinity, rates of change, derivatives, derived function, derivation rules, derivatives of trigonometric functions, chain rule, implicit derivation, derivatives of logarithms, derivatives of a higher order, hyperbolic functions. Applications of derivatives: Related rates, maximums and minimums, Mean Value Theorem, derivatives and graphs, L’Hopital Rule, curve plotting, optimization. Integrals: antiderivatives, areas and distance, defined integral, Fundamental Theorem of Calculus, integration by substitution, areas between curves, volumes of rotation solids using the slice and cylindrical shell methods.