MAT 144

Calculus I

Functions, limits, continuity, differentiation of algebraic and trigonometric functions, applications of derivatives, definite integrals, approximate integration, and applications of the definite integral. Only 1 additional credit given to students who have received credit for M112.

Printed Copy of Syllabus

You can download a copy of the syllabus for this course by clicking on the semester link below.   The syllabus is in Microsoft Word format.

Here are some suggestions to help you be successful in acquiring these mathematical skills:

  • Do your homework.
  • Check your work
  • Learn from your mistakes.
  • Know how to get help if you need it.
  • Organize your class materials.
  • Don't be afraid to ask questions
  • Hand in assignments on time.

The demands that classes, homework, work and family place on your time is a very difficult load to carry.  One key to managing your time is developing a schedule, and sticking to it.    Remember that I am here to help you be successful!

 

Commentary

Calculus is fundamentally different from the mathematics that you have studied previously.   Calculus is less static and more dynamic.    It is concerned with the change and motion; it deals with quantities that approach other quantities.

The origins of calculus go back at least 2500 years to the ancient  Greeks, who found areas  using the "method of exhaustion."   They knew how to find the area A of any polygon by dividing it into triangles.  The more triangles they used the better the approximation.  

By indirect reasoning, Eudoxus (fifth century B.C.) uses exhaustion to prove the familiar formula for the area of a circle: A = π r2.   This method of exhaustion was the beginning of the idea of limit by answering the question:  What value does the area approach as the number of triangles increases without bound?  The area problem is the central problem in the branch of calculus called integral calculus.

Consider the problem of trying to find an equation of the tangent to a curve at any point on the curve.   This problem has given rise to the branch of calculus called differentia calculus, which was not invented until 2000 years after the integral calculus.

The two branches of calculus and their chief problems, the area problems and the tangent problem appear to be very different, but it turns out that there is a very  close connection between them.   They are inverse problems!

After  Sir Isaac Newton invented his version of calculus, he used it to explain the motion of the planets and Sun.    Today calculus is used in calculating the orbits of satellites and space craft, in predicting population sizes, in estimating how fast coffee prices rise, in forecasting weather, in measuring the cardiac output of the heart, in calculating life insurance premiums, and in a great variety of other areas.

 We will explore some of these in this course.