Course Objective

MATH 200 is the first course in a three-term sequence providing an introduction to calculus. Two geometric problems are central to calculus:

  1. Finding the slope of a tangent line to a curve (the differential calculus) and
  2. Finding the area under a curve (the integral calculus).
In the present course (MATH 200) we will consider both of these problems, for curves arising from algebraic (polynomial-like), transcendental (trigonometric, exponential, and logarithmic) functions. After a brief review of functions, we will introduce the concept of limit (basic to calculus). We will then define the derivative and study various applications. Next, we will define the definite integral and study its relation to the indefinite integral, through the Fundamental Theorem of Calculus. We will also study elementary applications of the definite integral. The calculus sequence then continues with MATH 201(calculus techniques to trigonometric functions, additional techniques of integration, infinite sequence and series, conic sections, and polar coordinates), followed by MATH 307 for those who wish to study functions of more than one independent variable.
"To solve a problem is to make a discovery; a great problem means a great discovery, but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery."--George Polya

"Do not imagine that mathematics is hard and repulsive to commonsense." -- Sir William Thomson, Lord Kelvin

"Mathematics is the art of giving the same name to different things" -- Henri Poincare

"Don't worry about your difficulties in mathematics. I can assure you that mine are still greater." -- Albert Einstein

"A MATHEMATICIAN, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. ...
The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." -- G.H. Hardy

"Life is good for only two things, discovering mathematics and teaching mathematics." -- Simeon Poisson