MATH242 Calculus III
Department of Science, Technology, Engineering & Mathematics: Mathematics
- I. Course Number and Title
- MATH242 Calculus III
- II. Number of Credits
- 4 credits
- III. Number of Instructional Minutes
- 3000
- IV. Prerequisites
- MATH141 (C or better)
- Corequisites
- None
- V. Other Pertinent Information
- At least 4 hours of testing are given.
- VI. Catalog Course Description
- This course is a continuation of Math 141. Topics for this course include: vectors and solid analytic geometry, surfaces, partial and directional derivatives, Lagrange multipliers, multiple integrals, cylindrical and spherical coordinates, line and surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem.
- VII. Required Course Content and Direction
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Course Learning Goals
Students will:
- use vector-valued functions to parameterize curves and describe motion in space, find unit tangent and normal vectors, find tangential and normal components of acceleration, and find arc length and curvature;
- find partial derivatives of functions of several variables, find directional derivatives and gradients, find tangent planes, and use Lagrange multipliers to find extrema;
- evaluate multiple integrals in rectangular, polar, cylindrical and spherical coordinates, and use multiple integrals to find areas, volumes, centers of mass, and surface areas; and
- evaluate line and surface integrals, find work done in a vector field, use Green's Theorem, Stokes' Theorem, and the Divergence Theorem to evaluate integrals.
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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
- Surfaces
- Vector Valued Functions and Limits
- Derivatives and Integrals of Vector-Valued Functions
- Velocity and Acceleration
- Tangent Vectors and Normal Vectors
- Arc Length and Curvature
- Functions of Several Variables
- Limits and Continuity
- Partial Derivatives
- Chain Rules
- Directional Derivatives and Gradients
- Differentials
- Tangent Planes
- Extrema of Functions of Several Variables
- Applications of Extrema of Functions of Two Variables
- Lagrange Multipliers
- Iterated Integrals and Area
- Double Integrals and Volume
- Double Integrals in Polar Coordinates
- Surface Area
- Triple Integrals and Volume
- Triple Integrals in Cylindrical and Spherical Coordinates
- Center of Mass
- Vector Fields
- Line Integrals
- Conservative Vector Fields
- Green’s Theorem
- Divergence and Curl
- Surface Integrals
- Stokes’ Theorem
- Divergence Theorem
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Assessment Methods for Course Learning Goals
The student applies 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 consists of open-ended questions reflecting theoretical and applied situations.
A minimum of 70% of a student's grade must be determined from proctored assessments and work. These proctored assessments include tests, quizzes, and other proctored in-class assignments.
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Reference, Resource, or Learning Materials to be used by Student:
Departmentally-selected textbook and a TI-30X IIS scientific calculator (not the MultiView series). Details provided by the instructor of each course section. See course syllabus.
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Review/Approval Date - 1/99; Revised 4/06; Revised 09/2013; New Core 8/2015; Updated 11/2019