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Mathematics
Course Resources
MATH 1920 - Calculus II
Resource List by Course Content
The resources listed on this page are meant only as general instruction materials. Students are expected to contact their instructors regarding the specific requirements for their classes.
*All video resources below link to Khan Academy unless otherwise noted
Newton Leibniz and Usain Bolt: Why we study differential calculus
Chapter 5 – INTEGRALS
5.1 Area and Distance (treat as review with 5.9)
5.2 The Definite Integral (treat as review)
5.3 Evaluating the Definite Integral (CO 2)
5.4 The Fundamental Theorem of Calculus (CO 2)
5.5 The Substitution Rule (CO 1)
- Indefinite Integration (part III)
- Indefinite Integration (part IV)
- Another u-substitution example: Finding the antiderivative using u-substitution.
- Definite integral with substitution
5.6 Integration by Parts (CO 1)
- Indefinite Integration (part V)
- Integration by Parts (part 6 of Indefinite Integration)
- Indefinite Integration (part 7) : Another example using integration by parts.
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)
5.8 Integration Using Tables and Computer Algebra Systems (CO 1 & CO 9)
5.9 Approximate Integration (CO 3)
5.10 Improper Integrals (CO 6)
Chapter 6 – APPLICATIONS OF INTEGRATIO
6.1 More about Area (CO 5)
6.2 Volumes (CO 5)
- Solid of Revolution (part 1)
- Solid of Revolution (part 2)
- Solid of Revolution (part 3)
- Solid of Revolution (part 4)
6.3 Volumes by Cylindrical Shells (CO 5)
- Solid of Revolution (part 5)
- Solid of Revolution (part 6)
- Solid of Revolution (part 7)
- Solid of Revolution (part 8)
6.4 Arc Length (CO 5)
H.2 Area and Lengths in Polar Coordinates (CO 4)
6.5 Average Value of a Function (optional as time permits)
6.6 Applications to Physics and Engineering (CO 5)
6.7 Applications to Economics and Biology (optional as time permits)
6.8 Probability (optional as time permits)
Chapter 8 – INFINITE SEQUENCES AND SERIES
8.1 Sequences (CO 7)
8.2 Series (CO 7)
8.3 Integral and Comparison Tests; Estimating Sums (CO 7)
8.4 Other Convergence Tests (CO 7)
8.5 Power Series (CO 7)
8.6 Functions as Power Series (CO 8)
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
- Polynomial approximation of functions (part 1)
- Polynomial approximation of functions (part 2)
- Approximating functions with polynomials (part 3)
- Polynomial approximation of functions (part 4)
- Polynomial approximations of functions (part 5)
- Polynomial approximation of functions (part 6)
- Polynomial approximation of functions (part 7)
- Taylor Polynomials: Approximating a function with a Taylor Polynomial
- 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
