By the end of this course, students must be able to:
Understand and analyze sequences and series – Identify whether a sequence or series converges or diverges.
Apply convergence tests – Correctly use the Ratio Test, Root Test, and other tests to determine series convergence.
Represent functions as power series – Express given functions as power series and determine their radius and interval of convergence.
Construct and use Taylor and Maclaurin series – Formulate Taylor and Maclaurin series for functions and use them for approximation and analysis.
Interpret mathematical results – Understand the connection between series representations and the behavior of functions.
Develop analytical problem-solving skills – Apply theoretical concepts to solve practical mathematical problems involving series and function expansion.