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.
Prerequisites:
AMS 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.
