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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



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

1.Purchase options

Students may purchase direct from the University bookstore or directly from the publisher, Cengage, via WebAssign
Note:  Students should purchase materials using your Stony Brook email to avoid access issues


Choose one of the following items:
a. Cengage Unlimited $119.99 (a digital subscription service (think Netflix or Apple Music)
b. WebAssign multi-term code $125 (full sequence WebAssign calculus, with e-book)
c. WebAssign single term $100 (one semester WebAssign calculus, with e-book))

Cengage Unlimited Subscription includes:

  • WebAssign and e-book access for calculus sequence with a free print rental. PLUS ANY Cengage materials you are using across ALL of your courses AND a library of 20,000 e-books.
  • Help yourself get a better grade in other courses with our study guides even if you are not using Cengage.
  • Access to Kaplan, the leading provider of test prep courses and materials.
  • Access to Quizlet, a hugely popular mobile and web-based study application that helps students make simple learning tools like flashcards and games.
  • Access to Career Center tools, students can build employability skills through career readiness tutorials and create a résumé / portfolio with Pathbrite.

2. How to access your course materials after purchase

3. Technical support


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 University bookstore or online.)


"Single Variable Calculus: Concepts & Contexts" by James Stewart, 4 th Edition + WebAssign MULTI-TERM access - ISBN: 9780357014363

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.



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.