Calculus II (MAT 146) Dr. Day Wednesday November 8, 2017

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Presentation transcript:

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 Wednesday, November 8, 2017 MAT 146

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}. Wednesday, November 8, 2017 MAT 146

Fact or Fiction? Wednesday, November 8, 2017 MAT 146

Our first Series Convergence Test Our first Series Convergence Test . . . The nth-Term Test also called The Divergence Test Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Converge or Diverge? Wednesday, November 8, 2017 MAT 146

Converge or Diverge? (9) Wednesday, November 8, 2017 MAT 146

Converge or Diverge? (12) Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Absolute Convergence and Conditional Convergence Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146

Wednesday, November 8, 2017 MAT 146