8. Applications To Linear Differential Equations

8.1.         Introduction

8.2.         Review Of Results Concerning Linear Differential Equations Of First And Second Orders

8.3.         Exercises

8.4.         Linear Differential Equations Of Order N

8.5.         The Existence-Uniqueness Theorem

8.6.         The Dimension Of The Solution Space Of A Homogeneous Linear Differential Equation

8.7.         The Algebra Of Constant-Coefficient Operators

8.8.         Determination Of A Basis Of Solutions For Linear Equations With Constant Coefficients By Factorization Of Operators

8.9.         Exercises

8.10.      The Relation Between The Homogeneous And Nonhomogeneous Equations

8.11.      Determination Of A Particular Solution Of The Nonhomogeneous Equation. The Method Of Variation Of Parameters

8.12.      Nonsingularity Of The Wronskian Matrix Of N Independent Solutions Of A Homogeneous Linear Equation

8.13.      Special Methods For Determining A Particular Solution Of The Nonhomogeneous Equation.  Reduction To A System Of First-Order Linear Equations

8.14.      The Annihilator Method For Determining A Particular Solution Of The Nonhomogeneous Equation

8.15.      Exercises