#### 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

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

1. Sign Up: Sign up for Cengage Unlimited and pay $119.99 for 4 months, $179.99 for
12 months, or $239.99 for 24 months for all course materials, no matter how many you use.

2. Access: Access digital learning platforms, ebooks, online homework and study tools.
Browse over 22,000 ebooks and digital resources across 70 disciplines.

3. Receive: Want print? If you are using one of Cengage's digital learning platforms,
you would pay $7.99 for shipping.

4. Keep: When the subscription ends, students can keep up to six textbooks in a “digital locker”
and access time any them for up to a year at no cost.

- Video:
**What is Cengage Unlimited?****https://youtu.be/Q9zc3RDO_u4** -
**Discover how you can navigate Cengage Unlimited -****https://youtu.be/EahVuabghQQ**

**
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 Bookstore or
online.)

**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.

**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.