'Homogeneous equation' presentation slideshows

Chapter 8: Recurrence Relations

Chapter 8: Recurrence Relations. Discrete Mathematical Structures: Theory and Applications. Learning Objectives. Learn about recurrence relations Learn the relationship between sequences and recurrence relations Explore how to solve recurrence relations by iteration

2.4k views • 44 slides

Time Domain Representations of Linear Time-Invariant Systems

Time Domain Representations of Linear Time-Invariant Systems. Chapter 2. Introduction. Several methods can be used to describe the relationship between the input and output signals of LTI system.

887 views • 43 slides

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS. Differential Equations. An equation which involves unknown function and its derivatives ordinary differential equation (ode) : not involve partial derivatives partial differential equation (pde) : involves partial derivatives

1.11k views • 39 slides

Generalized Inverses of Rectangular and Singular Square Matrices

Generalized Inverses of Rectangular and Singular Square Matrices. Philip C. Nelson. William Paterson University Department of Mathematics Advisor: Dr. Phadia Spring 2008. Outline. Background and Motivation Definition of Generalized Inverse

510 views • 32 slides

Ch 7.9: Nonhomogeneous Linear Systems

Ch 7.9: Nonhomogeneous Linear Systems. The general theory of a nonhomogeneous system of equations parallels that of a single n th order linear equation. This system can be written as x ' = P ( t ) x + g ( t ), where. General Solution.

806 views • 31 slides

Ch 7.7: Fundamental Matrices

487 views • 27 slides

Ch 7.7: Fundamental Matrices

561 views • 27 slides

Engineering Mathematics ?

Engineering Mathematics ?. ??? ?? Oct. 13, 2004. 1.5 Integrating Factors. The equation is not exact on any rectangle. Because and and ? =?The equation is not exact on any rectangle.

616 views • 24 slides

Ch 3.2: Fundamental Solutions of Linear Homogeneous Equations

Ch 3.2: Fundamental Solutions of Linear Homogeneous Equations. Let p , q be continuous functions on an interval I = ( ? , ? ), which could be infinite. For any function y that is twice differentiable on I , define the differential operator L by

1.62k views • 22 slides

METHOD OF UNDETERMINED COEFFICIENTS

2.09k views • 22 slides

Ch 7.8: Repeated Eigenvalues

Ch 7.8: Repeated Eigenvalues. We consider again a homogeneous system of n first order linear equations with constant real coefficients x ' = Ax .

370 views • 19 slides

Lecture 9

Lecture 9. Second Order Linear Differential Equations: Method of Variation of Parameters Systems of First Order Linear Differential Equations Fourier Series. The Linear Case. A linear second order differential equations is written as associate the so called associated homogeneous equation

590 views • 16 slides

Section 4.3

268 views • 15 slides

Cavitation Models

Cavitation Models. Roman Samulyak, Yarema Prykarpatskyy. Center for Data Intensive Computing Brookhaven National Laboratory U.S. Department of Energy rosamu@bnl.gov, yarpry@bnl.gov. Talk outline. Modeling of the equation of state for two-phase fluid systems

396 views • 15 slides

A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system

REVIEW. A matrix equation has the same solution set as the vector equation which has the same solution set as the linear system whose augmented matrix is. Therefore: A x = b has a solution if and only if b is a linear combination of columns of A. REVIEW. Theorem 4:

181 views • 12 slides

Ch 7.4: Basic Theory of Systems of First Order Linear Equations

Ch 7.4: Basic Theory of Systems of First Order Linear Equations. The general theory of a system of n first order linear equations parallels that of a single n th order linear equation. This system can be written as x ' = P ( t ) x + g ( t ), where. Vector Solutions of an ODE System.

360 views • 10 slides

Tutorial 9

Tutorial 9. Second Order Linear Differential Equations, part II. Homogeneous Linear Equations with Constant Coefficients. Consider a nonhomogeneous equation with constant coefficients:

233 views • 8 slides

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients. The method of undetermined coefficients can be used to find a particular solution Y of an n th order linear, constant coefficient, nonhomogeneous ODE provided g is of an appropriate form.

431 views • 5 slides

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients

Ch 4.3: Nonhomogeneous Equations: Method of Undetermined Coefficients. The method of undetermined coefficients can be used to find a particular solution Y of an n th order linear, constant coefficient, nonhomogeneous ODE provided g is of an appropriate form.

350 views • 5 slides

Forced Harmonic Oscillator

k. F 0 cos ?t. m. b. Forced Harmonic Oscillator. Solution:. General solution of associated homogeneous equation (Transient Term) (Decays to zero as t ? ? ). Particular solution of inhomogeneous equation (Steady State Term). In special case of underdamped oscillation ( ? 2 < ? 0 ).

480 views • 2 slides