Mathematics Learning Lab - Math 1920

Chapter 5 – INTEGRALS

5.7 Additional Techniques of Integration (CO 1)

• Integrals: Trig Substitution 1
• Integrals: Trig Substitution 2
• Integrals: Trig Substitution 3 (long problem)

G Integration of Rational Functions by Partial Fractions (CO 1)

• Partial Fraction Expansion 1
  (review)
• Partial Fraction Expansion 2
• Partial Fraction Expansion 3

 

Chapter 8 – INFINITE SEQUENCES AND SERIES

8.7 Taylor and Maclaurin Series (CO 8)

• Maclauren and Taylor Series Intuition
• Cosine Taylor Series at 0 (Maclaurin)
• Sine Taylor Series at 0 (Maclaurin)
• Taylor Series at 0 (Maclaurin) for e to the x
• Visualizing Taylor Series for e^x

8.8 Applications with Taylor Polynomials (optional as time permits)

• Visualizing Taylor Series Approximations
• Generalized Taylor Series Approximation
• Error or Remainder of a Taylor Polynomial Approximation
• Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation

 

Whole Course Questions

• Euler's Formula and Euler's Identity
• AP Calculus BC Exams: 2008 1 a: Part 1a of the 2008 BC free response
• AP Calculus BC Exams: 2008 1 b&c: Parts b and c of problem 1 (free response)
• AP Calculus BC Exams: 2008 1 c&d : parts c&d of problem 1
• AP Calculus BC Exams: 2008 1 d : Part 1d of the 2008 AP Calculus BC exam
• Calculus BC 2008 2 a
• Calculus BC 2008 2 b &c
• Calculus BC 2008 2d
• 2011 Calculus BC Free Response #1a : Velocity and acceleration vectors for particle
• 2011 Calculus BC Free Response #1 (b & c) : Position and slope of particle's path at a given time
• 2011 Calculus BC Free Response #1d : Arc length for a curve
• 2011 Calculus BC Free Response #3a : Arc length of a function
• 2011 Calculus BC Free Response #3 (b & c) : Volume of a solid of rotation and Chain Rule for rates of change
• 2011 Calculus BC Free Response #6a : Taylor Series approximation of sin(x)
• 2011 Calculus BC Free Response #6b : Taylor Series for cos x at x=0
• 2011 Calculus BC Free Response #6c : Calculating the 6th derivative at 0 from the Taylor Series approximation
• 2011 Calculus BC Free Response #6d : Lagrange error bound for Taylor Polynomial approximation