#### 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

*Text/Course Materials for
Spring 2018 -
WebAssign
REQUIRED for this course
:
*

**
****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/2367925 (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 Larson/Edwards' Calculus, Single-Term, 11th Edition

AUTHORS: Larson/Edwards

ISBN-10: 1-337-87964-9

ISBN-13: 978-1-337-87964-4

Cost: $100.00 from publisher

*
OR,
*

** Option 2:**

ePack: Multivariable Calculus, Loose-leaf Version, 11th + WebAssign Instant Access
for Larson/Edwards' Calculus, Single-Term

AUTHORS: Larson, Ron

ISBN-10: 1-337-80721-4

ISBN-13: 978-1-337-80721-0

Cost: $145.95 from publisher

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

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.