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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

 

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

Or,                                             

Option 2:

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.

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