Course Syllabus
Lesson One: Introduction and Geometric Series
- vocabulary: monotonic, nonmonotonic, bounds, a bounded sequence, series, and geometric series
- geometric series problems and examples
- online activity with sequences
- a textbook assignment
Lesson two: Telescoping sequences and the Integral Test
- vocabulary: telescoping sequence, harmonic sequence, integral test, P-series
- what is a harmonic sequence
- integrals and the area under a curve
- what is a P-series
- downloadable worksheet
- a textbook assignment
Lesson three: Alternating series and the Ratio Test
- vocabulary: alternating series, error, ratio test
- find the bounds of an alternating sequence
- find the error of an approximation
- how to use the ratio test to determine convergence
- online activity
- textbook assignment
After Lesson three there will be a review of lessons 1-3 and Quiz #1
Lesson Four: Taylor Polynomials
- vocabulary: taylor polynomial
- find a taylor polynomial for sin(x) near 0
- find a third degree taylor polynomial for an exponential equation
- find a fourth degree taylor polynomial for sin(x) at certain x values
- downloadable worksheet
- textbook assignment
Lesson Five: McLaurin Sequence
- vocabulary: McLaurin sequence
- find an infinity McLauring sequence for e to the x, sin(x) and cos(x)
- find an infinite taylor for ln(x) at one
- use a calculator to find a McLaurin sequence for arctan(x)
- downloadable worksheet
- textbook assignment
Lesson Six: Power Series
- vocabulary: power series
- use a power series to determine convergence
- what sequences can you use a power series with
- center of convergence activity
- radius of convergence activity
- interval of convergence activity
- online activity
- textbook assignment
After Lesson six there will be a review of lessons 4-6 and Quiz #2