This course explores real-valued sequences and series, including power and Taylor series. Topics include convergence and divergence tests and applications. These topics will be explored graphically, numerically, and symbolically. This course emphasizes abstraction, problem-solving, reasoning, communication, connections with other disciplines, and the appropriate use of technology.
Course Outcomes
Upon completion of the course the students should be able to:
- Recognize and define sequences in a variety of forms and describe their properties, including the concepts of convergence and divergence, boundedness, and monotonicity.
- Recognize and define series in terms of a sequence of partial sums and describe their properties, including convergence and divergence.
- Recognize series as harmonic, geometric, telescoping, alternating, or p-series, and demonstrate whether they are absolutely convergent, conditionally convergent, or divergent, and find their sum if applicable.
- Choose and apply the divergence, integral, comparison, limit comparison, alternating series, and ratio tests to determine the convergence or divergence of a series.
- Determine the radius and interval of convergence of power series, and use Taylor series to represent, differentiate, and integrate functions.
- Use techniques and properties of Taylor polynomials to approximate functions and analyze error.
Prerequisites
Equivalent placement test scores also accepted.
Prerequisite Courses
Additional Information
This course fulfills the following GE requirements: Science, Math, Computer Science/ASOT-B, Science, Math, Computer Science/AAOT, Science, Math, Computer Science/AAS, Science, Math, Computer Science/AGS, Science, Math, Computer Science/AS.