Lesson 57 – Linear Differential Equations

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Presentation transcript:

Lesson 57 – Linear Differential Equations IBHL - Calculus - Santowski Calculus - Santowski 11/10/2018

Lesson Objectives Review the previous types of First Order Diff Eqns that we already know how to solve Introduce linear Diff Eqns and then solving using an “integration factor” Calculus - Santowski 11/10/2018

(A) Linear Diff Eqns Consider the following Diff Eqns. Two are linear Diff Eqns and two are not Calculus - Santowski 11/10/2018

(A) Linear ODEs A differential equation is linear, if dependent variable and its derivatives are of degree one, coefficients of a term does not depend upon dependent variable. A linear first order equation is an equation that can be expressed in the form Where P and Q are functions of x

(B) Example to Discuss Solve the linear Diff Eqn Here is our graphical solution (slope field diagram) Calculus - Santowski 11/10/2018

(B) Example to Discuss Solve the linear Diff Eqn Multiply through by e3x ?? ?? So we get Calculus - Santowski 11/10/2018

(B) Example to Discuss Solve the linear Diff Eqn Multiply through by e3x …. So we get Calculus - Santowski 11/10/2018

(B) Example to Discuss Calculus - Santowski 11/10/2018

(B) Example to Discuss Solve the linear Diff Eqn Multiply through by e3x So HOW did we get e3x as the “integrating factor”? We use (To see WHY, read through Paul Dawkins notes …. Link also at end of ppt) Calculus - Santowski 11/10/2018

(C) Examples for Practice Solve the following linear Diff Eqns ….. Calculus - Santowski 11/10/2018

(D) Further Examples for Practice Solve the following linear Diff Eqns ….. Calculus - Santowski 11/10/2018

(D) Further Examples for Practice Solve the following linear Diff Eqns ….. Calculus - Santowski 11/10/2018

Further Practice .. http://www.cse.salford.ac.uk/physics/gsmcdonald/H- Tutorials/ordinary-differential-equations-integrating- factor.pdf Calculus - Santowski 11/10/2018

(G) Resources Detailed Notes & explanations/derivations from Paul Dawkins http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx From patrickJMT: https://www.youtube.com/watch?v=Et4Y41ZNyao https://www.youtube.com/watch?v=RnYzatmp-_s From Mathispower4u https://www.youtube.com/watch?v=HAb9JbBD2ig https://www.youtube.com/watch?v=zN0TmKEXFh8 Calculus - Santowski 11/10/2018