Purpose: The primary goal of this course is to complete the acquired knowledge seeing by the student in the course Math 102 about Numerical sequences. Also it enables students to be familiar with convergence of sequences and series, and to understand the relationship between improper integrals and infinite series.
Pedagogical Objectives: By the end of this course the student will be expected to
1. Recognize two adjacent sequences and know that they have the same limit.
2. Learn how to study the convergence of a sequence defined recursively by Un+1 = f(Un) according to the monotony of the function f.
3. Understand the concept of upper limit and lower limit of a real sequence.
4. Understand that the study of a numerical series is equivalent to the study of its partial sum sequence, and learn how to find the sum of a series.
5. Master the convergence tests of a nonnegative term series, and apply the appropriate tests.
6. Learn how to study an alternating series, and to distinguish between conditional convergence and absolute convergence.
7. Know how to apply Stirling formula and Euler constant.
8. Learn how to find the radius and the interval of convergence of a power series, and how to differentiate and integrate a power series.
9. Know the Maclaurin series for usual functions in order to find the series representation of analytic functions.
Numerical sequences : Recursive sequences, Adjacent sequences, Upper limits & Lower limits.
Numerical Series : Series operations, Convergence & Divergence, Tests of Convergence for series of non-negative terms, Absolute & Conditional convergence, Alternating series.
Power series: Radius & interval of convergence, Differentiation & Integration of power series, Representation of functions by power series, Taylor & Maclaurin series.
The acquired knowledge and the established calculations throughout this course must enable students to acquire necessary skills to solve problems and to continue developing and refining these skills.