#### AMS 261, Applied Calculus III

*Catalog Description*: Vector algebra and analytic geometry in 2- and 3-dimensions: multivariable differential
calculus and tangent planes; multivariable integral calculus; optimization and Lagrange
multipliers; vector calculus including Green's and Stoke's theorems. May not be taken
for credit in addition to MAT 203 or 205.

*Prerequisites*:
AMS 161 or MAT 127 or 132 or 142.

4 credits: 3 hours of lecture and 1 hour of recitation

*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.
*

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 "Multi Variable Calculus" by Ron Larson and
Bruce Edwards, 11th edition of looseleaf print of book (ISBN: 978-1-337-27537-8)

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 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.

************************************************************

AMS 261 IS ALSO OFFERED DURING SUMMER SCHOOL. CHECK THE SUMMER SCHOOL BULLETIN FOR
TIMES.

**Topics**

1. Vector algebra and analytic geometry in two and three dimensions - 6 hours

2. Multivariate Differential Calculus- partial derivatives and gradients, tangent
planes - 6 hours

3. Multivariate Integral Calculus: double and triple integrals, change of variables
and Jacobians, polar coordinates, applications to probability - 10 hours

4. Optimization: maxima and minima, Lagrange multipliers - 6 hours

5 . Vector Calculus: vector-valued functions, curves in space, linear integrals, surface
integrals, Green's Theorem, Stoke's Theorem - 10 hours

6. Review and Tests - 4 hours

**Learning Outcomes for AMS **
**261, Applied Calculus III**

1.) Demonstrate a firm understanding of the vector algebra and the geometry of two-and
three-dimensional space. Specifically students should be able to:

* explain and apply both the geometric and algebraic properties of vectors
in two and three dimensions.

* compute dot and cross products, and explain their geometric meaning.

* sketch and interpret vector-valued functions in two and three dimensions.

* differentiate and integrate vector-valued functions.

* explain and apply polar, cylindrical and spherical coordinate systems.

2.) Demonstrate an understanding of scalar functions in several dimensions, and the
application of differential and integral calculus to multi-variable functions. Specifically
students should be able to:

* describe and sketch curves and surfaces in three-dimensional space.

* compute the partial derivatives of multi-variable functions.

* compute and explain directional derivatives and gradients.

* determine the extreme values of multiple variable functions.

* use Lagrange multipliers to solve constrained optimizations problems.

* solve double- and triple-integrals using iterated integration.

* set up double- and triple-integrations problems in both Cartesian and curvilinear
coordinate systems.

* explain and apply the use of Jacobians in solving double- and triple-integrals
by coordinate substitution.

3.) Demonstrate a understanding of the fundamental concepts of vector algebra and
vector calculus; specifically students should be able to:

* describe and sketch vector fields in two and three dimensions.

* compute and interpret line and surface integrals through scalar or vector
fields.

* explain and apply Green’s Theorem.

* explain and apply the Divergence Theorem.

* explain and apply Stokes’ Theorem.

4.) Strengthen ability in communicating and translating of mathematical concepts,
models to real world settings:

* present solutions to problems in a clear, well-laid out fashion;

* explain key concepts from the class in written English;

*convert problems described in written English into an appropriate mathematical
form;

* convert the mathematical solutions into a written answer.

* use the maple computer program as an aid in solving and visualizing mathematical
problems.