MA 001 Preparatory Mathematics I.
Homework sheets and exam papers from Autumn 2004 of MA 001
are available here.
Students are encouraged to look these up and work out as many problems as they can.
Function, Inverse function, Elementary functions and their graphs, Limit, Continuity, Derivative and its geometrical significance. Differentiability. Derivatives of sum, difference, product and quotient of functions. Derivatives of polynomial, rational, trigonometric, logarithmic, exponential, hyperbolic, inverse trigonometric and inverse hyperbolic functions. Differentiation of composite and implicit functions.
Tangents and Normals, Increasing and decreasing functions. Maxima and Minima.
Integrations as the inverse process of differentiation, Integration by parts
and by substitution. Definite integrals and its application to the
determination of areas.