Faculty of Science

Objectives

To provide the basic techniques of differential calculus. Students are gradually introduced to the mathematical culture of proofs.

Contents

Brief review of properties of real numbers; Real-valued functions of a real variable; Polynomial, exponential, logarithmic and trigonometric (circular) functions; hyperbolic functions, inverses; Polar coordinates; Limits, continuity and basic theorems of continuous functions; Derivative: differentiability and differentiation, product rule, chain rule; Higher derivatives; Applications of the derivative: monotone functions, extrema, mean-value theorems; l'Hospital's Rule.

Prerequisite: