1. Calculus II (MAT 146) Dr. Day Wednesday November 8, 2017
Integration Applications
Area Between Curves (6.1)
Average Value of a Function (6.5)
Volumes of Solids (6.2, 6.3)
Created by Rotations
Created using Cross Sections
Arc Length of a Curve (8.1)
Probability (8.5)
Methods of Integration
U-substitution (5.5)
Integration by Parts (7.1)
Trig Integrals (7.2)
Trig Substitution (7.3)
Partial-Fraction Decomposition (7.4)
Putting it All Together: Strategies! (7.5)
Improper Integrals (7.8)
Differential Equations
What is a differential equation? (9.1)
Solving Differential Equations
Visual: Slope Fields (9.2)
Numerical: Euler’s Method (9.2)
Analytical: Separation of Variables (9.3)
Applications of Differential Equations
Infinite Sequences & Series (Ch 11)
What is a sequence? A series?
Determining Series Convergence
Divergence Test
Integral Test
Comparison Tests
Alternating Series Test
Ratio Test
Nth-Root Test
Power Series
Intervals and Radii of Convergence
New Functions from Old
Taylor Series and Maclaurin Series
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2. What is an Infinite Series?
We start with a sequence {an}, n going from 1 to ∞, and define {si} as shown.
The {si} are called partial sums. These partial sums themselves form a sequence.
An infinite series is the summation of an infinite number of terms of the sequence {an}.
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3. Fact or Fiction?
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4. Our first Series Convergence Test
Our first Series Convergence Test The nth-Term Test also called The Divergence Test
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18. Converge or Diverge?
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19. Converge or Diverge? (9)
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20. Converge or Diverge? (12)
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22. Absolute Convergence and Conditional Convergence
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