Chapter 1 FirstOrder Differential Equations Sec 1 1

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Chapter 1: First-Order Differential Equations

Chapter 1: First-Order Differential Equations

Sec 1. 1: Differential Equations and Mathematical Models Definition: Differential Equation An equation containing

Sec 1. 1: Differential Equations and Mathematical Models Definition: Differential Equation An equation containing the derivatives of one or more dependent variables with respect to one or more independent variables, is said to be a differential equation (DE) 1 2

Sec 1. 1: Differential Equations and Mathematical Models 2 3 6 4 7 5

Sec 1. 1: Differential Equations and Mathematical Models 2 3 6 4 7 5

Sec 1. 1: Definitions and Terminology Classification 9 8 Classification By Type Order

Sec 1. 1: Definitions and Terminology Classification 9 8 Classification By Type Order

Classification By Type (ODE, PDE) Classification By Type If an equation containing only ordinary

Classification By Type (ODE, PDE) Classification By Type If an equation containing only ordinary derivatives it is said to be Ordinary Differential Equation (ODE) 1 An equation involving partial derivatives it is said to be Partial Differential Equation (PDE) 8

Classification By Order The order of a differential equation (ODE or PDE) is the

Classification By Order The order of a differential equation (ODE or PDE) is the order of the highest derivative in the equation. 3 1 4 2 5 . n-th order DE

Classification By Type ODE or PDE Order highest derivative

Classification By Type ODE or PDE Order highest derivative

System of DE System of two Ordinary Differential Equations 2 ed order, linear, ODE

System of DE System of two Ordinary Differential Equations 2 ed order, linear, ODE

Navier-Stokes Equations q. ODE or PDE qorder? ? On e. M illio n. D

Navier-Stokes Equations q. ODE or PDE qorder? ? On e. M illio n. D olla r

Sec 1. 1: Differential Equations and Mathematical Models Definition: Solution of an ODE A

Sec 1. 1: Differential Equations and Mathematical Models Definition: Solution of an ODE A continuous function is said to be a solution of a DE if it satisfies the DE on an interval I

Sec 1. 1: Definitions and Terminology Families of Solutions at h W ? ?

Sec 1. 1: Definitions and Terminology Families of Solutions at h W ? ? ? f i d

Sec 1. 1: Definitions and Terminology Families of Solutions One-parameter family of solutions Two-parameter

Sec 1. 1: Definitions and Terminology Families of Solutions One-parameter family of solutions Two-parameter family of solutions n-parameter family of solutions Particular Solution: A solution of DE that is free of arbitrary parameters

Sec 1. 1: Definitions and Terminology Trivial Solution y=0 is said to be trivial

Sec 1. 1: Definitions and Terminology Trivial Solution y=0 is said to be trivial solution Singular Solution sometimes a DE has a solution that is not a member of a family of solutions. This solution is called singular solution one-parameter family of solutions Verify? ? Not a member of the family no value for c

Sec 1. 1: Definitions and Terminology Piecewise-Defined Solution Verify? ? Explicit and Impicit Solutions

Sec 1. 1: Definitions and Terminology Piecewise-Defined Solution Verify? ? Explicit and Impicit Solutions Explicit Solution Implicit Solution Verify? ?

Sec 1. 1: Homework Problems

Sec 1. 1: Homework Problems

Sec 1. 1: Homework Problems

Sec 1. 1: Homework Problems

Solving Differential Equations Solving Differential Equations A differentialSolving Differential Equations Solving Differential Equations A differential
Differential Equations ordinary differential equations Definition A differentialDifferential Equations ordinary differential equations Definition A differential
FirstOrder Logic Review 1 Firstorder logic Firstorder logicFirstOrder Logic Review 1 Firstorder logic Firstorder logic
FirstOrder Logic Review 1 Firstorder logic Firstorder logicFirstOrder Logic Review 1 Firstorder logic Firstorder logic
FirstOrder Logic Review 1 Firstorder logic Firstorder logicFirstOrder Logic Review 1 Firstorder logic Firstorder logic
FirstOrder Logic Review 1 Firstorder logic Firstorder logicFirstOrder Logic Review 1 Firstorder logic Firstorder logic
Chapter 1 FirstOrder Differential Equations 1 Sec 1Chapter 1 FirstOrder Differential Equations 1 Sec 1
Chapter 1 FirstOrder Differential Equations 1 Sec 1Chapter 1 FirstOrder Differential Equations 1 Sec 1
Chapter 1 FirstOrder Differential Equations 1 Sec 1Chapter 1 FirstOrder Differential Equations 1 Sec 1
Differential Equations Ordinary differential equation ODE Partial differentialDifferential Equations Ordinary differential equation ODE Partial differential
Chapter 38 DIFFERENTIAL EQUATIONS 952021 differential equations byChapter 38 DIFFERENTIAL EQUATIONS 952021 differential equations by
Chapter 2 Firstorder Differential Equations Chapter 1 IntroductionChapter 2 Firstorder Differential Equations Chapter 1 Introduction
Chapter 2 Firstorder Differential Equations Chapter 1 IntroductionChapter 2 Firstorder Differential Equations Chapter 1 Introduction
17 SECONDORDER DIFFERENTIAL EQUATIONS SECONDORDER DIFFERENTIAL EQUATIONS Secondorder17 SECONDORDER DIFFERENTIAL EQUATIONS SECONDORDER DIFFERENTIAL EQUATIONS Secondorder
18 SECONDORDER DIFFERENTIAL EQUATIONS SECONDORDER DIFFERENTIAL EQUATIONS 1818 SECONDORDER DIFFERENTIAL EQUATIONS SECONDORDER DIFFERENTIAL EQUATIONS 18