MATH242 Calculus III
Department of Science, Technology, Engineering & Mathematics: Mathematics
Course Number and TitleMATH242 Calculus III
Number of Credits4 credits
Minimum Number of Instructional Minutes Per Semester3000 minutes
PrerequisitesMATH141 (C or better)
Other Pertinent InformationAt least 4 hours of testing will be given.
Catalog Course DescriptionTopics for this course include vectors and solid analytic geometry, surfaces, partial differentiation, directional derivatives, Lagrange multipliers, multiple integrals, cylindrical coordinates, spherical coordinates, Jacobians.
Required Course Content and Direction
Learning Goals:Course Specific:
The student will be able to:
- apply vector techniques to solid analytic geometry problems, find curvature, find tangential and normal components of acceleration.
- find moments, centroid and moments of inertia of three dimensional figures.
- find partial derivatives for functions, of several variables, find directional derivatives, find extrema of functions, and use Lagrange multipliers to find extrema.
- evaluate iterated integrals.
- convert between rectangular, cylindrical, and spherical coordinates. Use change of variables and Jacobians.
- use multiple integration to solve area, volume, surface, and moment problems.
Planned Sequence of Topics and/or Learning Activities:
- Vectors in the Plane
- Vectors in three Dimensions
- The Dot Product
- The Cross Product
- Lines and Planes in Space
- Vector Valued Functions and Limits
- Derivatives and Integrals
- Velocity and Acceleration
- Tangent and Vectors and Normal Vectors
- Arc Length and Curvature
- Functions of Several Variables
- Limits and Continuity
- Partial Derivatives
- Chain Rules
- Directional Derivatives
- Tangent Planes and Normal
- Extrema of Functions of Several Variables
- Applications of Extrema of Function of Two Variables
- Lagrange Multipliers
- Iterated Integrals and Area
- Double Integrals and Volume
- Double Integrals in Polar Coordinates
- Surface Area
- Triple Integrals
- Moments and Center of Mass
- Cylindrical Spherical Coordinates
- Cylindrical and Spherical Coordinates in Space
- Change of Variables: Jacobians
Assessment Methods for Core Learning Goals:All Core Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.
Reference, Resource, or Learning Materials to be used by Students:Departmental selected textbook. Details provided by the instructor of each course section. See Course Format.
Teaching Methods EmployedPrimary teaching methods are lecture, recitation, problem solving, and class discussion as appropriate.
Review/Approval Date - 1/99; Revised 4/06