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. 

Prerequisites: AMS 161 or MAT 127 or 132 or MPE level 9.

SBC: STEM+

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

FALL 2024 Course Materials - Includes eBook and access:

WebAssign for Larson/Edwards' "Calculus", 12e Single-Term Instant Access 9780357749289 

 

AMS 261 IS ALSO OFFERED DURING WINTER AND SUMMER SESSIONS. CHECK THE UNDERGRADUATE BULLETIN FOR DATES.

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. Optimization: maxima and minima, Lagrange multipliers - 6 hours
4.  Multivariate Integral Calculus:  double and triple integrals, change of variables and Jacobians, polar coordinates, applications to probability - 10 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 an 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.