MAT 162: Calculus II, Section D01

Fall 2017

Day-by-day summary.
Solutions distributed in class.
Answer key (odd-numbered text problems).
The Fundamental Theorem of Calculus.
A summary of the exponential and logarithmic laws.
A review of some trig identities.
A worksheet on solids of revolution by disks.
Volume of a doughnut by disks/washers and by shells.
A worksheet on solids of revolution by disks and by shells.
Computing a volume two ways.
Work needed to lift an object high above the earth.
Worksheet on setting up pumping problems (Sec. 6.4)
The "chart method" for certain integrals.
Formula for integating powers of sec(x).
A trig sub worksheet.
A summary of partial fractions.
Method for integrating a rational function with linear/quadratic denominator.
Integrating the reciprocal of the root of a quadratic.
A worksheet of integration practice.
Best method for problems like p472 #39.
The area of a frustum.
Integrals for areas of surfaces of revolution.
Center of gravity and center of mass.
The Integral Test.
Integral-Test-based estimate of series sum.
The comparison tests (PVCT and LCT).
Absolute and conditional convergence.
Proof of the Root Test .
A summary of the tests for convergence of series.
A fundamental theorem about power series.
A property of polynomials.
An example of Taylor polynomials and remainders.
Two examples: graph of a function together with some of its Taylor polynomials.
Worksheet: The Maclaurin series for the cosine function.
An application of Taylor series.
The Generalized Binomial Theorem.