MATH 131: Applied Calculus I

Credit Hours

3

Prerequisites

Math Placement Test or MATH 118

Description

An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration.

(Students may not receive credit for both MATH 131 and 161 without permission of the department chairperson. Math 131 is not a substitute for Math 161.)

See Course Page for additional resources.

Textbook

D. Hughes-Hallett, et al, Applied Calculus (packaged with WileyPLUS), 4th edition. Wiley (2009). ISBN: 978-0-47-057877-3.

Common Syllabus for MATH 131

Chapter 1.  Functions and Change [2 Weeks]
   1.1 – What is a function?
   1.2 – Linear functions.
   1.3 – Average rates of change and relative rates of change.
   1.4 – Applications of functions to economics.
   1.5 – Exponential functions.
   1.6 – The natural logarithm.
   1.7 – Exponential growth and decay.
   1.8 – New functions from old.
   1.9 – Proportionality and power functions.
   1.10 – Periodic functions.

Chapter 2.  Rate of Change:  The Derivative [2 Weeks]
   2.1 – Instantaneous rate of change.
   2.2 – The derivative function.
   2.3 – Interpretations of the derivative.
   2.4 – The second derivative.
   2.5 – Marginal cost and revenue.

Chapter 3.  Shortcuts to Differentiation [2 Weeks]
   3.1 – Derivative rules for powers and polynomials.
   3.2 – Exponential and logarithmic functions.
   3.3 – The chain rule.
   3.4 – The product and quotient rule.
   3.5 – Derivatives of periodic functions.

Chapter 4.  Using the Derivative [3 Weeks]
   4.1 – Local maxima and minima.
   4.2 – Inflection points.
   4.3 – Global maxima and minima.
   4.4 – Profit, cost, and revenue.
   4.5 – Average cost.
   4.6 – Elasticity of demand.
   4.7 – Logistic growth.
   4.8 – The surge function and drug concentration.

Chapter 5.  Accumulated Change:  The Definite Integral [2Weeks]
   5.1 – Distance and accumulated change.
   5.2 – The definite integral.
   5.3 – The definite integral as area.
   5.4 – Interpretations of the definite integral.
   5.5 – The fundamental theorem of calculus.