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5.6 Eigenvalue estimates

5.6 Eigenvalue estimates

5.6 Minimization principle

5.6 Minimization principle

5.6 Rayleigh quotient

5.6 Rayleigh quotient derivation

5.5 Proof of

5.5 Proof of orthogonal eigenfunctions

5.5 Self-adjointness of

5.5 Self-adjointness of the Sturm-Liouville operator

5.5 Lagrange's identity

5.5 Lagrange's identity and Green's formula

3.3 Fourier Sine

3.3 Fourier Sine and Cosine series

5.3 Sturm-Liouville Theorems

5.3 Sturm-Liouville Theorems

Introduction to Sturm-Liouville

Introduction to Sturm-Liouville problems

4.4 Normal modes

4.4 Normal modes of vibration

4.4 Vibrating string

4.4 Vibrating string equation with fixed ends

4.2 The Vibrating

4.2 The Vibrating String equation

3.6 Complex Fourier

3.6 Complex Fourier series

3.2 Fourier's Theorem

3.2 Fourier's Theorem example

3.2 Fourier's Theorem

3.2 Fourier's Theorem

3.2 Smooth and

3.2 Smooth and piecewise smooth functions

2.5 Uniqueness of

2.5 Uniqueness of Laplace equation solutions

2.5 Well-posedness

2.5 Well-posedness

2.5 Maximum Principle

2.5 Maximum Principle

2.5 Mean Value

2.5 Mean Value Theorem

2.5 Steady state

2.5 Steady state temperatures on the disk

2.5 Steady state

2.5 Steady state temperatures of a rectangle

2.5 Introduction to

2.5 Introduction to the Laplace equation

2.4 Heat Equation

2.4 Heat Equation for a circular rod