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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. 

PrerequisitesAMS 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

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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.

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