### Prerequisites

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

- Determine the convergence of series and sequences
- Use series to represent and model functions
- Apply calculus to functions in Cartesian, polar, cylindrical, and spherical coordinates
- Find extrinsic properties (E.G. curvature, arc length) of vector-valued functions

**Quantitative Reasoning:**Students will be able to reason mathematically.

- Sequences
- Infinite Series
- Comparison and Integral Tests
- Ratio and Root Tests
- Alternating Series and Absolute Convergence
- Power Series
- Taylor and MacLaurin Series
- Calculations with Taylor Series
- Conic Sections and Quadratic Equations
- Parameterizations of Curves
- Calculus with Parameterized Curves
- Polar Coordinates
- Polar Graphs
- Polar Equations for Conic Sections
- Integration in Polar Coordinates
- Vectors in the Plane
- Cartesian (Rectangular) Coordinates and Vectors in Space
- Dot Products
- Cross Products
- Lines and Planes in Space
- Surfaces in Space
- Cylindrical and Spherical Coordinates
- Vector-Valued Functions and Space Curves
- Modeling Projectile Motion
- Arc Length and the Unit Tangent Vector
- Curvature
- Introduction to Differential Equations (Optional)

In order to give the instructor the greatest flexibility in assigning a grade for the course, grades will be based on various instruments at the instructor’s discretion. However, to maintain instructional integrity there must be four class exams or three class exams and a project. A final exam will be given if there are less than four exams or a project may be substituted for the final exam if there are four in-class exams. At least 60% of the grade will be based on quantifiable work (exams, homework, quizzes, etc.). The remaining portion of the grade may be based on quantifiable work, attendance, projects, journal work, etc., at the instructor's discretion.

The following is a compilation of acceptable grading instruments: In class exams and a final, attendance, homework or quizzes, research paper, modeling projects on the calculator or computer. Other projects or assignments may be assigned as deemed appropriate at the instructor's discretion.