#### 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.Purchase options**

Students may purchase direct from the University bookstore or directly from the publisher,
Cengage, via WebAssign

**Note:** Students should purchase materials using your
**Stony Brook email**
to avoid access issues

Choose one of the following items:

a.
Cengage Unlimited $119.99 (a digital subscription service (think Netflix or Apple Music)

b. WebAssign multi-term code $125 (full sequence WebAssign calculus, with e-book)

c. WebAssign single term $100 (one semester WebAssign calculus, with e-book))

Cengage Unlimited Subscription includes:

- WebAssign and e-book access for calculus sequence with a free print rental. PLUS ANY Cengage materials you are using across ALL of your courses AND a library of 20,000 e-books.
- Help yourself get a better grade in other courses with our study guides even if you are not using Cengage.
- Access to
**Kaplan**, the leading provider of test prep courses and materials. - Access to
**Quizlet,**a hugely popular mobile and web-based study application that helps students make simple learning tools like flashcards and games. - Access to
**Career Center tools**, students can build employability skills through career readiness tutorials and create a résumé / portfolio with Pathbrite.

**2. How to access your course materials after purchase**

- Sign in to Blackboard and click on your course.
- Go to Tools, then click Access WebAssign.
- When at WebAssign, click Verify Payment.
- Additional help: https://play.vidyard.com/dAtEqvNNpKTogGj75zGtau

**3. Technical support**

**
**

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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.