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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

 

FALL 2018:

The AMS Department recommends the Cengage Unlimited option ( cengage.com/unlimited ) for students who may enroll in future courses where departments use Cengage Publishing textbooks/eBooks  (Note:  AMS will use the same course materials for AMS 151 (Calculus I) and AMS 161 (Calculus II)) :

1. Sign Up: Sign up for Cengage Unlimited and pay $119.99 for 4 months, $179.99 for 12 months, or $239.99 for 24 months for all course materials, no matter how many you use.
2. Access: Access digital learning platforms, ebooks, online homework and study tools. Browse over 22,000 ebooks and digital resources across 70 disciplines.
3. Receive: Want print? If you are using one of Cengage's digital learning platforms, you would pay $7.99 for shipping.
4. Keep: When the subscription ends, students can keep up to six textbooks in a “digital locker” and access time any them for up to a year at no cost.

  1. Video:  What is Cengage Unlimited?   https://youtu.be/Q9zc3RDO_u4
  2. Discover how you can navigate Cengage Unlimited - https://youtu.be/EahVuabghQQ

 

Course Materials:

WebAssign and textbook/e-Book entitled "Single Variable Calculus:  Concepts & Contexts" by James Stewart, 4th edition of hard copy of book.
Cengage Unlimited ISBN:  9780357700006, one-term access (4 months) IAC
(You may purchase WebAssign from Cengage Unlimited either through the Bookstore or online.)

NOTE:  Your access to WebAssign is live for the entire duration of Calculus I and II, even if your Cengage Unlimited subscription ends.  However, any print rental is due back by the end date of your Cengage Unlimited subscription.  Alternatively, looseleaf print products may be purchased at a discounted price through Cengage Unlimited.

 

 

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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