6_1_Differential_Eq_Slope_Fields

6_1_Differential_Eq_Slope_Fields - 6.1 Differential...

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Unformatted text preview: 6.1 Differential Equations & Slope Fields HW: p. 407 # 15, 13, 15, 1927, 3747, 53, 55 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: intro (1 of 19) 6.1 Differential Equations & Slope Fields Ch 3.9 Definition of Differentials: Let y = f(x) be differentiable on an open interval containing x. The differential of x, dx, is a nonzero real number. The differential of y, dy, is: dy = f ' (x) dx Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: definition of differentials (2 of 19) 6.1 Differential Equations & Slope Fields Ch 4.1: Solve the differential equation: f ' (x) = 4x, f(0) = 6 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: Solve differential eq (3 of 19) 6.1 Differential Equations & Slope Fields What about ....? Solve the diff eq: (2+x) y ' xy = 0 More complex than we have done so far. This is where we are headed. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: solve diff eq (4 of 19) 6.1 Differential Equations & Slope Fields What about ....? Solve the diff eq: (2+x) y ' xy = 0 Note that problems of this complexity are covered later in the chapter. This is offered here because students wanted to see that there is no new procedure involved. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: solve diff eq (5 of 19) 6.1 Differential Equations & Slope Fields Start with verify problems: Verify a solution is correct for the diff eq. p. 409 # 2 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: verify solutions (6 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: intro (7 of 19) 6.1 Differential Equations & Slope Fields What about: dy/dx = x + y If we cannot solve a diff eq analytically, consider the slope field associated with the equation. This gives us a graphical representation of the slopes of the general solution. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: intro (8 of 19) 6.1 Differential Equations & Slope Fields Links for Slope Fields dy/dx represents the slope of y Equation Plotter: Slope Fields Start with: dy/dx = x Slope Field Worksheet prepared by Nancy Stephenson and available at apcentral.collegeboard.com Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: diff eq & slope fields (9 of 19) Title: slope field (10 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: intro (11 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (12 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: slope field recognition (13 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (14 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (15 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (16 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (17 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (18 of 19) 6.1 Differential Equations & Slope Fields Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Title: example (19 of 19) ...
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This note was uploaded on 09/09/2011 for the course MATH 1431 taught by Professor Any during the Fall '08 term at University of Houston.

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