The Calculus Differential Equations Tutor Volume 2 - Higher Order Equations

Product Description Solving higher order differential equations is challenging for most students simply because the solution methods usually run several pages in length even for the easier problems. The student must identify the type of equation to solve and apply the appropriate solution method, which can lead to valuable lost time on an exam if the wrong solution method is chosen at the outset. Disk 1 Sect 1: Intro to Higher Order Differential Equations Sect 2: Identifying Linear Ordinary Differential Equations (ODEs) Sect 3: Solving Elementary Higher Order ODEs Sect 4: The Linear Differential Operator Sect 5: The Wronskian Test For Linearly Independent Solutions Sect 6: Wronskian Problems Disk 2 Sect 7: Homogeneous ODEs - Constant Coefficients & Real Roots Part 1 Sect 8: Part 2 of Above Sect 9: Part 3 of Above Sect 10: Homogeneous ODEs - Constant Coefficients & Complex Roots Part 1 Sect 11: Part 2 of Above Sect 12: Part 3 of Above Sect 13: Non-Homogeneous ODEs Undetermined Coefficients Part 1 Sect 14: Part 2 of Above Sect 15: Part 3 of Above Disk 3 Sect 16: Part 4 of Above Sect 17: Part 5 of Above Sect 18: Part 6 of Above Sect 19: Non-Homogeneous ODEs Variation of Parameters Part 1 Sect 20: Part 2 of Above Sect 21: Part 3 of Above Sect 22: Part 4 of Above We begin by showing the student real life applications of second order and higher ODEs to provide motivation for the material. Next, we show how to solve elemenary second order ODEs, and show the student that all solutions have a similar form. Next, we discuss linear independence of solutions and show the students how to use the wronskian test to determine of a set of functions describe the entire solution space of the ODE. We then get into the core solution techniques which revolve around constant coefficient differential equations. We examine the case where the roots of the characteristic polynomial are real and complex separately, to give the student a good grounding in what to do in either case. Next, we work several problems using the method of undetermined coefficients which allow us to solve higher order ODEs that are more complex. Every step is shown in the solution, and emphasis is placed on showing the student how to properly find the annihilator function for the right hand side of the equation in the solution. Finally, we use the method of Variation of Parameters to solve several equations and give the student practice in working these problems step by