### AMS 151, Applied Calculus I

*Catalog Description*: Review of functions and their applications; analytic methods of differentiation;
interpretations and applications of differentiation; introduction to integration.
Intended for CEAS majors. Not for credit in addition to MAT 125 or 126 or 131 or 141.

*Prerequisites*: B or higher in MAT 123 or level 5 on Math Placement Test.

3 credits

**Spring 2018 (For AMS 151 and AMS 161):**

*****NOTE: DO NOT ORDER COURSE MATERIALS THROUGH AMAZON. ALL MATERIALS SHOULD BE PURCHASED
THROUGH THE PUBLISHER, CENGAGE, using the link
http://www.cengagebrain.com/course/2481196 (Microsite expires June 1, 2018)
*

Instructions:

- Students will either get registered immediately based on matching email address or they will have access to the code to type/copy into their WebAssign registration page.
- students can learn how to register for their Cengage course in just THREE clicks of their mouse! http://www.cengage.com/start-strong
- https://www.cengage.com/training

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Option 1:
**

WebAssign Instant Access for Calculus, Multi-Term Courses, 1st Edition

AUTHORS: WebAssign copyright 2013

ISBN-10: 1-285-85825-5

ISBN-13: 978-1-285-85825-8

Cost: $125.00 from publisher

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Or,
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Option 2:
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ePack: Custom Single Variable Calculus Concepts, 4th + WebAssign Instant Access for
Stewart's Calculus: Concepts and Contexts, Multi-Term

Authors: Stewart - copyright 2009

ISBN10: 1-305-71363-X

ISBN-13: 978-1-305-71365-5

Cost: $169.00 from publisher

**Topics**

1. Library of Functions: properties and uses of common functions, including linear,
exponential, polynomial, logarithmic, and trigonometric functions; qualitative understanding
of situations where these different functions arise - 9 hours

2. Introduction to Derivatives: limits; definition and interpretations of the derivative;
local linearity - 6 hours

3. Techniques of Differentiation: derivatives of common functions from chapter I;
product quotient and chain rules, implicit function differentiation - 8 hours

4. Applications of Differentiation: maxima and minima, studying families of curves,
applications to science, engineering and economics, Newton's method - 9 hours

5. Introduction to Integrals: definition and interpretations of integrals; fundamental
theorem of calculus - 4 hours

6. Review and Tests - 6 hours

**Learning Outcomes for AMS 151, Applied Calculus I**

1.) Demonstrate how use the behavior of common mathematical functions model important
real-world situations.

* linear functions;

* exponential functions;

* logarithmic functions;

* trigonometric functions.

2.) Demonstrate a conceptual and technical understanding of the derivative, including:

* different mathematical and applied settings where the derivative represents
a rate of change;

* the technical definition of the derivative and using this definition to calculate
the derivative of simple functions.

3.) Demonstrate proficiency with the rules for differentiation of.

* power function and polynomials;

* exponential and logarithmic functions;

* trigonometric functions and inverse tangent;

* products and quotients of functions;

* compositions of functions using the chain rule.

4.) Demonstrate facility in applying differentiation to problems in:

* physics and engineering;

* economics and business;

* biomedical sciences.

5.) Build mathematical models for optimization problems and solve them.

* maximization problems, with and without side constraints

* minimization problems, with and without side constraints.

6.) Demonstrate a conceptual understanding of integration, including

* integration as the inverse operation to differentiation;

* integration as the area under the graph of a function;

* the definite and infinite integral.