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HIGH ORDER DE Chapter 4, image - Coggle Diagram
HIGH ORDER
DE
Chapter 4
4.1.1
4.1.2
Differential Operators
4.1.3
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
Auxiliary Equation
Case I: Distinct Real Roots
Case II: Repeated Real Roots
Case III: Conjugate Complex Roots
Two Equations Worth Knowing
Higher-Order Equations
4.4 Undetermined Coefficients—Superposition Approach
Method of Undetermined Coefficient
Case I
Case II
-Assumes a particular solution based on the form of the right-hand side.
-Works well when the non-homogeneous term consists of exponentials, polynomials, sines, and cosines. :
4.5 Undetermined Coefficients—Annihilator Approach
Factoring Operators
Annihilator Operator
Undetermined Coefficient
4.6 Variation of Parameters
Linear First-Order DEs Revisited
Linear Second-Order DEs
4.7 Cauchy-Euler Equation
Method of Solution
Case II: Repeated Real Roots
Case II: Repeated Real Roots
Case III: Conjugate Complex Roots
4.9 Solving Systems of Linear DEs by Elimination
Systematic Elimination
Solution of a System
Method of Solution
4.10 Nonlinear Differential Equations
iNDEPENDIENTE
DEENDENT
Use of a Numerical Solver
MODELING WITH HIGHER-ORDER
Chapter 5
5.1 Linear Models:
Initial-Value Problems
5.1.1 Spring/Mass Systems:
Free Undamped Motion
Hooke’s Law
Newton’s Second Law
DE of Free Undamped Motion
Equation of Motion
Alternative Forms of x(t)
Graphical Interpretation
Systems with Variable Spring Constants
5.1.2 Spring/Mass Systems:
Free Damped Motion
DE of Free Damped Motio
Alternative Form of x(t)
5.1.3 Spring/Mass Systems:
Driven Motion
DE of Driven Motion with Damping
Transient and Steady-State Terms
DE of Driven Motion without Damping
Pure Resonance
5.1.4 Series Circuit Analogue
LRC-Series Circuits
