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.
Prerequisites: B or higher in MAT 123 or level 5 on Math Placement Test.
3 credits
WebAssign for Stewart/Kokoska's "Calculus: Concepts & Contexts", 5e Single-Term Instant Access 9780357748978
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 indefinite integral.