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.
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)
- 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.
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WebAssign Instant Access for Calculus, Multi-Term Courses, 1st Edition
AUTHORS: WebAssign copyright 2013
Cost: $125.00 from publisher
ePack: Custom Single Variable Calculus Concepts, 4th + WebAssign Instant Access for
Stewart's Calculus: Concepts and Contexts, Multi-Term
Authors: Stewart - copyright 2009
Cost: $169.00 from publisher
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
* 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.