AMS 261 | Applied Mathematics & Statistics (2024)

AMS 261, Applied Calculus III

SUMMER and FALL 2023 Course Materials - Includes text and access

WebAssign for Larson's "Multivariable Calculus 12e" single-term Instant Access, Cengage Publishing - ISBN: 9780357749289

WINTER and SPRING 2024 Course Materials - Includes text and access

WebAssign for Larson' Calculus, Instant Access9780357749289

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 AMS261, 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.