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)
- 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.
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WebAssign Instant Access for Larson/Edwards' Calculus, Single-Term, 11th Edition
Cost: $100.00 from publisher
ePack: Multivariable Calculus, Loose-leaf Version, 11th + WebAssign Instant Access
for Larson/Edwards' Calculus, Single-Term
AUTHORS: Larson, Ron
Cost: $145.95 from publisher
AMS 261 IS ALSO OFFERED DURING SUMMER SCHOOL. CHECK THE SUMMER SCHOOL BULLETIN FOR
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.