Math 160 Welcome to Dr Shannons class http

Math 160 Welcome to Dr. Shannon’s class http: //faculty. salisbury. edu/~kmshann on/math 160/welcome. htm

Introduction

Introduction Continued

Excerpt from a tour of the calculus by David Berlinski As its campfires glow against the dark, every culture tells stories to itself about how the gods lit up the morning sky and set the wheel of being into motion. The great scientific culture of the west - our culture - is no exception. The Calculus is the story this world first told itself as it became the modern world. The sense of intellectual discomfort by which the calculus was provoked into consciousness in the seventeenth century lies deep within memory. It arises from an unsettling contrast, a division of experience. Words and numbers are, like the human beings that employ them, isolated and discrete; but the slow and measured movement of the stars across the night sky, the rising and setting of the sun, the great ball bursting and unaccountably subsiding, the thoughts and emotions that arise at the far end of consciousness, linger for moments or for months, and then, like barges moving on some sullen river, silently disappear – these are, all of them, continuous and smoothly flowing processes. Their parts are inseparable. How can language account for what is not discrete and number for what is not divisible? Space and time are the great imponderables of human experience, the continuum within which every life is lived and every river flows. In its largest, most architectural aspect, the calculus is a great, even spectacular theory of space and time, a demonstration that in the real numbers there is an instrument adequate to their representation. If science begins in awe as the eye extends itself throughout the cold of space, past the girdle of Orion and past the galaxies pinwheeling on their axes, then in the calculus mankind has created an instrument commensurate with its capacity to wonder.

Four Problems We will leave this to the year long calculus sequence We will tackle this one last….

3. The Tangent or Velocity Problem R e v e n u e Quantity We will begin with this problem

4. Optimization Problems The biggest, smallest, cheapest, most profitable, fastest, etc…… Profit Price It turns out that solving the tangent problem will help us solve this problem so we will attack this second. Cost per Item Quantity Produced

Some of the tools developed to facilitate solution of these problems, you have already seen. In particular, let’s talk about functions and “analytic geometry” or the Cartesian Plane. (x, y) { y Independent Variable Often (but not always) called x Function Dependent Variable Often (but not always) called y } x y = f(x)

3. The Tangent or Velocity Problem R e v e n u e Quantity We will begin with this problem… Let us talk about the solution!