MA265 CALCULUS III (3 Cr.)

COURSE DESCRIPTION

Prerequisite: MA 163 and MA 211

General Introduction and Goals

MA 265 is the last in the sequence of three calculus courses. These courses serve many majors: mathematics education, science, mathematics, computer science, and social science. MA 265 shares the goals of the other calculus courses. It provides students with the opportunity to develop logical reasoning, complex problem-solving skills, and an understanding of the applications of multiple dimensional calculus.

Course Content

1. Vector and Three-dimensional Analytic Geometry
   • Space coordinates and vectors in space
   • Lines and planes in space
   • Dot product, cross product and applications
   • Cylindrical and spherical coordinates
2. Vector-Values Functions and Space Curves
   • Definitions and geometry of vector-valued functions
   • Differentiation and integration of vector-valued functions
   • Tangent and normal vectors of space curves
   • Applications: Arc length; velocity, acceleration and projectile motion
3. Multivariable Functions
   • Definitions and geometry of multivariable function
   • Limits and continuity
   • Partial derivatives and differential
   • Chain rules and implicit differentiation
   • Directional derivatives and gradients
   • Tangent planes and normal lines
   • Optimizing multivariable functions and applications
   • Taylor series of multivariable functions
4. Multiple Integrals
   • Iterated integrals
   • Double integrals and area in the plane
   • Double integrals in polar coordinates
   • Applications: Center of mass and moment of inertia; surface area
   • Triple integrals and applications
   • Triple integrals in cylindrical and spherical coordinates
   • Jacobian and change of variables
5. Selected Topics from Vector Analysis
   • Vector fields
   • Line integrals
   • Conservative vector fields and independence of path
   • Green's Theorem
   • Parametric surfaces
   • Surface integrals
   • Divergence Theorem
   • Stokes's Theorem

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