Introduction to Calculus

This course is intended for students who have not taken OAC Calculus or equivalent and is intended to prepare them for courses which have "OAC Calculus or equivalent" as a prerequisite.

Calculus is the part of mathematics which deals with the concept of change. This makes it at once both difficult and useful. In this introductory course we will deal with functions of one variable and their derivatives and integrals. We will show how the derivative is useful in defining (and finding the equations of) tangents to curves, in problems concerning velocity, and in optimization (finding the value of the variable for which a function is largest or smallest). We will also study the connection between derivatives and integrals and describe the application of integrals to finding areas between curves. Fundamental to all of these notions is that of limiting processes. These processes will be discussed in a number of settings including the summation of infinite series. Numerical approximations to various limiting processes will be used frequently.

Topics to be discussed include: limits, derivatives, tangents, rate of change, maxima and minima, curve sketching, trigonometric functions, logarithmic and exponential functions, antiderivatives, fundamental theorem of calculus, areas and infinite series.

The text will be announced later.

Note: Each student should have a pocket calculator of the "scientific" type (i.e. including logarithms and trigonometric functions).

The final grade will be based on assignments or quizzes, a midterm examination and a final examination (50%).