Integration Applications l Area Between Curves 6 1
Integration Applications l Area Between Curves (6. 1) l Average Value of a Function (6. 5) l Volumes of Solids (6. 2, 6. 3) l Created by Rotations l Created using Cross Sections l Arc Length of a Curve (8. 1) l Probability (8. 5) Differential Equations Semester Exam What is a differential equation? (9. 1) Solving Differential Equations Wednesday, Dec 14 Visual: (STV 229) Slope Fields (9. 2) Numerical: Euler’s Method (9. 2) 10 am – 12: 40 Analytical: pm. Separation of Variables (9. 3) l l l Applications of Differential Equations Infinite Sequences & Series (Ch 11) What is a sequence? A series? Review Session l Determining Series Convergence Divergence Test(STV 346) Monday, Dec 12, 5: 45 -6: 45 pm Integral Test and p-Series Test Methods of Integration l U-substitution (5. 5) l Integration by Parts (7. 1) l Trig Integrals (7. 2) l Trig Substitution (7. 3) l Partial-Fraction Decomposition (7. 4) l Putting it All Together: Strategies! (7. 5) l Improper Integrals (7. 8) l l l Ratio Test Nth-Root Test l Power Series l Intervals and Radii of Convergence l l Thursday, Dec 8, 2016 Comparison Tests Alternating Series Test New Functions from Old Taylor Series and Maclaurin Series MAT 146
Absolute Convergence and Conditional Convergence Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
l For what values of x does each series converge? l Determine the Radius of Convergence and the Interval of Convergence for each power series. Thursday, Dec 8, 2016 MAT 146
l For what values of x does this series converge? l Use the Ratio Test to determine values of x that result in a convergent series. Thursday, Dec 8, 2016 MAT 146
l For what values of x does this series converge? l Determine its Radius of Convergence and its Interval of Convergence. Thursday, Dec 8, 2016 MAT 146
l For what values of x does this series converge? l Determine its Radius of Convergence and its Interval of Convergence. Thursday, Dec 8, 2016 MAT 146
l For what values of x does this series converge? l Use the Ratio Test to determine values of x that result in a convergent series. Thursday, Dec 8, 2016 MAT 146
l For what values of x does this series converge? l Determine its Radius of Convergence and its Interval of Convergence. Thursday, Dec 8, 2016 MAT 146
l For what values of x does this series converge? l Determine its Radius of Convergence and its Interval of Convergence. Thursday, Dec 8, 2016 MAT 146
l If we let cn = 1 for all n, we get a familiar series: l This geometric series has common ratio x and we know the series converges for |x| < 1. l We also know the sum of this series: Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
Taylor Polynomials applet Thursday, Dec 8, 2016 MAT 146
Our goal is to generate polynomial functions that can be used to approximate other functions near particular values of x. The polynomial we seek is of the following form: Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
Thursday, Dec 8, 2016 MAT 146
Goal: Generate polynomial functions to approximate other functions near particular values of x. Create a third-degree polynomial approximator for Thursday, Dec 8, 2016 MAT 146
Create a 3 rd-degree polynomial approximator for Thursday, Dec 8, 2016 MAT 146
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