Below are the course objectives for each lesson:
Lesson 1 Objectives: By the end of lesson 1 the student will be able to:
- Define the terms monotonic, nonmonotonic, bounds, a bounded sequence, series, and geometric series
- Determine if a series divergers
- Determine if a series has a limit
- Identify the greatest lower bound and least upper bound for a series that converges
- Identify a geometric series
Lesson 2 Objectives: By the end of lesson 2 the student will be able to:
- Define the terms telescoping sequence, harmonic sequence, integral test, P-series
- Use an integral to find area under a curve
- Apply the integral test to harmonic sequences
- Apply the integral test to P-series
Lesson 3 Objectives: By the end of lesson 3 the student will be able to:
- Define the terms alternating series, error, ratio test
- Find the maximum error of a sequence
- Identify and alternating sequence
- Apply the ratio test to series
After lesson 3 is a review and quiz. The only objective is for the student to pass the quiz with an 80% accuracy.
Lesson 4 Objectives: By the end of lesson 4 the student will be able to:
- Define the term Taylor polynomial,
- Approximate values for sin(x) and ln(x) using a Taylor polynomial
- Find the max error of a Taylor approximation
- Develop Taylor polynomial approximations for a variety of functions
Lesson 5 Objectives: By the end of lesson 5 the student will be able to:
- Define the term McLaurin sequence
- Find an infinite McLaurin sequence for several functions
- Find an infinite taylor approximation for ln(x) at x = 1
- Use a calculator to find a McLaurin sequence for arctan(x)
- Lesson 6 Objectives: By the end of lesson 6 the student will be able to:
- Define the term power series
- Use a power series to find the center, radius and interval of convergence
- Check the endpoints of an interval of convergence discretely
- Develop a power series