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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

 

SUMMER 2018 Textbook:

"Single Variable Calculus" by James Stewart; Cengage Publishing; 4th edition, 2010; ISBN:  978-0-495-55972-6

 

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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)                                         

Instructions:

  • 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.                     
  • students can learn how to register for their Cengage course in just THREE clicks of their mouse!  http://www.cengage.com/start-strong                     
  • https://www.cengage.com/training                     

 

Option 1:                                                                                                                                                                     

WebAssign Instant Access for Calculus, Multi-Term Courses, 1st Edition
AUTHORS: WebAssign copyright 2013
ISBN-10: 1-285-85825-5
ISBN-13: 978-1-285-85825-8
Cost: $125.00 from publisher

Or,                                                                                                                                                                       

Option 2:                                                                                              

ePack:  Custom Single Variable Calculus Concepts, 4th + WebAssign Instant Access for Stewart's Calculus:  Concepts and Contexts, Multi-Term
Authors:  Stewart - copyright 2009
ISBN10:  1-305-71363-X
ISBN-13:  978-1-305-71365-5
Cost:  $169.00 from publisher

 

Topics
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.

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