Mathematics 271
MATH 271: Calculus and Analytic Geometry III
Prerequisites: Math 172
Credit hours: (4)
This course extends the concepts of the limit, differentiation, and integration to vector-valued functions and to functions of several variables. This includes partial differentiation, iterated integrals, volume and surface area of three-dimensional regions, and optimization of functions or several variables. Students may not receive credit for both MATH 271 and MATH 252.
Detailed Description of Course
The following topics will be covered:
1) Vector calculations including the magnitude, dot and cross products
2) Calculus of vector-valued functions, including tangent vectors, arc length, and curvature
3) Functions of several variables and equations of three-dimensinoal objects, including planes and spheres
4) Partial derivatives, differentiability of functions of several variables, the gradient, and directional derivatives
5) Lagrange multipliers and optimization of functions of several variables
6) Iterated integrals, including volume and surface area
7) Calculus of coordinate transformations, including cylindrical and spherical coordinates
8) Vector fields, line integrals, Green's Theorem, the Divergence Theorem and Stokes' Theorem
Detailed Description of Conduct of Course
Instructors will use a combination of lectures, group work and computer laboratory sessions. Some may require students to present homework problems to the rest of the class on a regular basis. Software packages and graphing utilities will be used on solving problems and as illustrative aids.
Student Goals and Objectives of the Course
Students are expected to learn the basic principles of Calculus and Analytic Geometry and to demonstrate the use of these principles in problem solving. In addition to paper and pencil problem solving, students will use appropriate graphing calculator and computer algebra system technology.
Students will be able to:
1) Interpret relationships among numeric, symbolic and graphical information as applied to the real world;
2) Solve problems using numeric, symbolic and graphical information
Assessment Measures
Graded tasks may include tests, quizzes, homework exercises, papers, class participation and attendance. Students will be required to demonstrate literacy in the use of mathematical software packages and/or graphing calculators as effective tools in problem solving.
Other Course Information
This course is primarily intended for freshman and sophomore students, especially those majoring in mathematics, computer science, the natural sciences, psychology, or economics. Students may not receive credit for both MATH 271 and MATH 252.
Review and Approval
November 2, 2017