This course will expand on the applications and techniques of differentiation learned in the first and second quarters. It will introduce the student to the calculus of sequences and series and the use of the MacLauren and Taylor series to approximate functions. It will introduce the student to the calculus of curvilinear functions and the concept of the vector and vector functions.
Prerequisite or Corequisite
MATH& 152 or instructor permission
Quarters Offered
Fall,
Winter,
Spring
Course Outcomes
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
Institutional Outcomes
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
Course Content Outline
- 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)