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AMS 161, Applied Calculus II

Catalog Description: Analytic and numerical methods of integration; interpretations and applications of integration; differential equations models and elementary solution techniques; phase planes; Taylor series and Fourier series. Intended for CEAS majors. Not for credit in addition to MAT 127 or 132 or 142 or 171.

PrerequisitesAMS 151 or MAT 131 or MAT 126.

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, 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 SINGLE-TERM access; ISBN: 9781337898522

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. Concepts on Integration and Methods of Integration: substitution, integration by parts, volume problems, approximating integrals with Riemann sums, improper integrals  - 10 hours
2. Applications of the Integral: volume and other geometric applications, parametric curves, arc lengths; probability; economic interpretations - 6 hours
3. Elements of Differential Equations: slope fields, Euler's method, applications and modeling - 7 hours
4. Systems of first-order differential equations and second-order differential equations, including solutions involving complex numbers - 8 hours.
5. A pproximations and series: Taylor series, Fourier polynomials - 5 hours
6. Review and Tests - 6 hours

Learning Outcomes for AMS 161, Applied Calculus II

1.) Demonstrate a conceptual understanding of the Fundamental Theorem of Calculus and its technical application to evaluate definite and indefinite integrals.  
        * Solve problems graphically and analytically that illustrate how integration and differentiation are inverse operations;
        * Use the Fundamental Theorem of Calculus to evaluate definite integrals whose limits are functions of x.

2.) Demonstrate skill in integrating basic mathematical functions, such as:
        * polynomials, 
        * exponential functions
        * sine and cosine functions.

3.) Develop facility with important integration tools such as:
        * reverse chain rule;
        * substitution methods; 
        * integration by parts;
        * tables of integrals.

4.) Solve problems involving geometric applications of integration: 
        * area problems;
        * volume problems;
        * arclength problems

5.) Develop basic skills with using numerical methods to evaluate integrals
       * right-hand, left-hand, and trapezoidal rules;
       * Simpson’s rule.

6.) Solve problems involving applications of integration to in physics and economics.
       * center of mass problems;
       * force problems;
       * work problems;
       * present value of multi-year investments.

7.) Solve problems with sequences and series, including:
       * find limits of sequences;
       * test series for convergence;
       * sum series.

8.) Demonstrate facility with constructing and using Taylor and Fourier series.
       * Taylor series for simple functions
       * Taylor series for composite functions and products of functions;
       * Taylor series to integration problems;
       * simple Fourier series.  

9.) Model problems with simple types of differential equations and solve these problems:
       * model problems with solve first-order linear differential equations and solve them;
       * use separation of variables to solve rate problems such as Newton’s law of cooling and logistic equations;
       * solve second-order linear differential equations.