MATH& 163 Calculus III

5 credits

The third quarter of the calculus sequence serves as an introduction to series, vectors, multivariable functions, partial differentiation, and multiple integration. Curves in planes and space are described in polar, parametric, and vector-valued form. Real world applications are emphasized.

Prerequisites: MATH& 152

Quarters Offered: Winter, Spring

Global Outcomes:
This course teaches to the global outcome of Critical Thinking.

Student Outcomes/Competencies:
Upon successful completion of this course students will be able to:

Use appropriate convergence tests to discuss the behavior of infinite series
Compute the Maclaurin and Taylor series expansions of basic and transcendental functions, and use them to solve relevant applications
Define vector-valued functions, and identify their key characteristics and graphs
Evaluate and interpret algebraic and calculus operations on vector functions and functions of two or more variables graphically, numerically, and analytically
Describe curves in planes and space using polar, parametric, and vector-valued forms, and identify situations where these alternate coordinate systems can simplify calculations
Calculate a path of motion, and describe its curvature, arc length, velocity, and acceleration
Differentiate and integrate parametric equations, polar equations, and vector-valued functions
Use double integrals in multiple coordinate systems, and apply principles to finding centers of mass and moments of inertia, volumes of solids, and other applications
Calculate partial derivatives for functions of several variables, using the chain rule as necessary, and use them to solve relevant applications
Use mathematical critical thinking skills, problem solving, pattern recognition, and substitution, following structural rules and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

Total Hours: 50 Lecture Hours: 50