`sin^2x + cos^2x = 1`
`y = frac (-b +- sqrt(b^2 - 4ac)) (2a)`
`(x + 2)^2 + (y - 3)^2 = 16`
`slope = m = frac (\text(change in y)) (\text(change in x)) = frac (Deltay) (Deltax)`

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HCC Math212

(according to LWW)

Ch 1.8 Functions & Models

What is Calculus?

  • Calculus is the study of change.
  • The study of how to quantify the change one variable experiences based on the change in another, related variable.
  • In mathematics, we express how two different variables are related using functions, for example ... `y=f(x)=3x^2 +1`
  • In mathematics, we quantify the relationship between the changes in two variables using fractions, for example ... `text(the change in y)/text(the change in x)`
  • The value of this fraction tells you how the change in `y` relates to the change in `x`. `x` is the independent variable here so it's value is changing and causing the value of `y` to change.

Where is Calculus Used?

Motion, electricity, heat, light, harmonics, acoustics, astronomy, dynamics, radioactive decay, birth and death rates, maximizing profits or revenue, minimizing cost, price elasticity of demand

Textbook Objectives for Section 1.8

  • Recognize and understand various business and economic terms
  • Create and evaluate mathematical models for real-life situations

LWW's Additional Objectives

  • Review necessary material on functions
  • Review necessary material on slope
  • Introduce necessary business terms: Cost, Revenue, Profit

Chapter 1 of this book is essentially all material that you are expected to know before taking this course. My experience with teaching this course is that it is time well spent for me to review some of this material during the first two classes. I will focus on Section 1.8 mostly but will also touch on Section 1.6. I'm assuming you already know the following:

This is all in Chapter 1 of the text so if you need to review this material, you can find the information you need there.

Function Review

`f(x)` tells you that `f` is a function, ` ... (More)

Introduction to HCC Math-212

This section of my website will be specific to a course I teach at Harford Community College, Math 212, Calculus with Applications. The textbook used for this course is: Essential Calculus, 2nd Ed, by Wright, Hurd, & New..

My intent is to post the material I present during the course so that my students can have access to it during the course as a reference and learning aid. I will also provide additional comments beyond just ... (More)

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