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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.

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

3 credits

 FALL 2024 Course Materials - Includes eBook and access (PLEASE ATTEND THE FIRST DAY OF CLASS FOR CLARIFICATION OF COURSE MATERIALS

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.