 EqWorld The World of Mathematical Equations Mathematical Books > Handbook of Mathematics for Engineers and Scientists > Contents > T8. Linear Equations and Problems of Mathematical Physics  To book contents

### T8. Linear Equations and Problems of Mathematical Physics

• T8.1. Parabolic Equations
• T8.1.1. Heat Equation wt = awxx
• T8.1.2. Nonhomogeneous Heat Equation wt = awxx + Φ(x, t)
• T8.1.3. Equation of the Form wt = awxx + bwx + cw + Φ(x, t)
• T8.1.4. Heat Equation with Axial Symmetry wt = a(wrr + r−1wr)
• T8.1.5. Equation of the Form wt = a(wrr + r−1wr) + Φ(r, t)
• T8.1.6. Heat Equation with Central Symmetry wt = a(wrr + 2r−1wr)
• T8.1.7. Equation of the Form wt = a(wrr + 2r−1wr) + Φ(r, t)
• T8.1.8. Equation of the Form wt = awxx + (1 − 2β)x−1wx
• T8.1.9. Equations of the Diffusion (Thermal) Boundary Layer
• T8.1.10. Schrodinger Equation iwt = −kwxx + U(x)w
• T8.2. Hyperbolic Equations
• T8.2.1. Wave Equation wtt = a2wxx
• T8.2.2. Equation of the Form wtt = a2wxx + Φ(x, t)
• T8.2.3. Klein--Gordon Equation wtt = a2wxxbw
• T8.2.4. Equation of the Form wtt = a2wxxbw + Φ(x, t)
• T8.2.5. Equation of the Form wtt = a2(wrr + r−1wr) + Φ(r, t)
• T8.2.6. Equation of the Form wtt = a2(wrr + 2r−1wr) + Φ(r, t)
• T8.2.7. Equations of the Form wtt + kwt = a2wxx + bw
• T8.3. Elliptic Equations
• T8.3.1. Laplace Equation Δw = 0
• T8.3.2. Poisson Equation Δw + Φ(x) = 0
• T8.3.3. Helmholtz Equation Δw + λw = −Φ(x)
• T8.4. Fourth-Order Linear Equations
• T8.4.1. Equation of the Form wtt + a2wxxxx = 0
• T8.4.2. Equation of the Form wtt + a2wxxxx = Φ(x, t)
• T8.4.3. Biharmonic Equation ΔΔw = 0
• T8.4.4. Nonhomogeneous Biharmonic Equation ΔΔw = Φ(x, y)
• References for Chapter T8

To book contents

The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.