Differential Equations MTH 242 Lecture 08 Dr Manshoor

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Differential Equations MTH 242 Lecture # 08 Dr. Manshoor Ahmed

Differential Equations MTH 242 Lecture # 08 Dr. Manshoor Ahmed

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Solution curves of a BVP that pass through two points

Solution curves of a BVP that pass through two points

Linear Differential Equations of Higher Order Example 1 Consider the function We can

Linear Differential Equations of Higher Order Example 1 Consider the function We can prove that this function is a solution of the boundary-value problem Since, Therefore,

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order

Linear Differential Equations of Higher Order Also, When Implies Since, for any choice

Linear Differential Equations of Higher Order Also, When Implies Since, for any choice of ‘c’ it follows that for the problem The solution is the one parameter family

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence Example 1 Let ‘a’ and ‘B’ are real numbers

Linear Dependence and Linear Independence Example 1 Let ‘a’ and ‘B’ are real numbers and then , and are linearly independent on any interval of the x-axis since So functions are linearly independent.

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Linear Dependence and Linear Independence

Summary • Higher order linear differential equation. • Homogeneous and non-homogeneous equations with constant

Summary • Higher order linear differential equation. • Homogeneous and non-homogeneous equations with constant coefficients. • Initial value problem (IVP) and it’s solution. • Existence and Uniqueness of Solutions. • Boundary value problem (BVP) and it’s solution. • Linear independence and dependence of functions. • Wronskian of a set of functions.

Differential Equations MTH 242 Lecture 29 Dr ManshoorDifferential Equations MTH 242 Lecture 29 Dr Manshoor
Differential Equations MTH 242 Lecture 13 Dr ManshoorDifferential Equations MTH 242 Lecture 13 Dr Manshoor
Differential Equations MTH 242 Lecture 09 Dr ManshoorDifferential Equations MTH 242 Lecture 09 Dr Manshoor
Differential Equations MTH 242 Lecture 04 Dr ManshoorDifferential Equations MTH 242 Lecture 04 Dr Manshoor
Differential Equations MTH 242 Lecture 15 Dr ManshoorDifferential Equations MTH 242 Lecture 15 Dr Manshoor
Differential Equations MTH 242 Lecture 12 Dr ManshoorDifferential Equations MTH 242 Lecture 12 Dr Manshoor
Differential Equations MTH 242 Lecture 11 Dr ManshoorDifferential Equations MTH 242 Lecture 11 Dr Manshoor
Differential Equations MTH 242 Lecture 02 Dr ManshoorDifferential Equations MTH 242 Lecture 02 Dr Manshoor
Differential Equations MTH 242 Lecture 10 Dr ManshoorDifferential Equations MTH 242 Lecture 10 Dr Manshoor
Differential Equations MTH 242 Lecture 18 Dr ManshoorDifferential Equations MTH 242 Lecture 18 Dr Manshoor
Differential Equations MTH 242 Lecture 03 Dr ManshoorDifferential Equations MTH 242 Lecture 03 Dr Manshoor
Differential Equations MTH 242 Lecture 14 Dr ManshoorDifferential Equations MTH 242 Lecture 14 Dr Manshoor
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