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Chapter 2 Ordinary Differential Equations

Chapter 2 Ordinary Differential Equations Chapter 2 Ordinary Differential Equations Chapter 2 Ordinary Differential Equations Chapter 2 Ordinary Differential Equations Basic concepts, definitions, notations and classification Introduction modeling in engineering Differential equation - Definition Ordinary Differential equation (ODE) Partial Differential Equations (PDE) Differential operator D Order of DE Linear operator Linear and non-linear DE homogeneous ODE Non- homogeneous ODE Normal form of nt

2.2.4 Homogeneous Equations Homogeneous function Homogeneous equation Reduction to separable equation – substitution Homogeneous functions in Rn 2.2.5 Linear 1st order ODE General solution Solution of IVP 2.2.6 Special Equations Bernoulli Equation Ricatti equation Clairaut equation Lagrange equation Equations solvable for y

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CHAPTER 5 BERNOULLI AND ENERGY EQUATIONS

www.et.byu.edu

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Second Order Systems

www.et.byu.edu

Second Order Systems Second Order Equations 2 2 +2 +1 = s s K G s τ ζτ Standard Form τ2 d 2 y dt2 +2ζτ dy dt +y =Kf(t) Corresponding Differential Equation K = Gain τ= Natural Period of Oscillation ζ= Damping Factor (zeta) Note: this has to be 1.0!!!

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1 HOMOGENEOUS TRANSFORMATIONS - Ira A. Fulton …

www.et.byu.edu

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www.et.byu.edu

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Chapter 5 Special Functions

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www.sjsu.edu

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