Linear Equations and Problems of Mathematical Physics (original) (raw)

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Mathematical Books >Handbook of Mathematics for Engineers and Scientists > Contents > T8. Linear Equations and Problems of Mathematical Physics

T8. Linear Equations and Problems of Mathematical Physics

T8.1. Parabolic Equations
- T8.1.1. Heat Equation w t = aw xx
- T8.1.2. Nonhomogeneous Heat Equation w t = aw xx + Φ(x, t)
- T8.1.3. Equation of the Form w t = aw xx + bw x + cw + Φ(x, t)
- T8.1.4. Heat Equation with Axial Symmetry w t = a(w rr + r_−1_w r)
- T8.1.5. Equation of the Form w t = a(w rr + r_−1_w r) + Φ(r, t)
- T8.1.6. Heat Equation with Central Symmetry w t = a(w rr + 2_r_−1_w_ r)
- T8.1.7. Equation of the Form w t = a(w rr + 2_r_−1_w_ r) + Φ(r, t)
- T8.1.8. Equation of the Form w t = aw xx + (1 − 2β)x_−1_wx
- T8.1.9. Equations of the Diffusion (Thermal) Boundary Layer
- T8.1.10. Schrodinger Equation i w t = −kw xx + U(x)w
T8.2. Hyperbolic Equations
- T8.2.1. Wave Equation w tt = a_2_w xx
- T8.2.2. Equation of the Form w tt = a_2_w xx + Φ(x, t)
- T8.2.3. Klein--Gordon Equation w tt = a_2_w xx − bw
- T8.2.4. Equation of the Form w tt = a_2_w xx − bw + Φ(x, t)
- T8.2.5. Equation of the Form w tt = _a_2(w rr + r_−1_w r) + Φ(r, t)
- T8.2.6. Equation of the Form w tt = a_2(w rr + 2_r_−1_w r) + Φ(r, t)
- T8.2.7. Equations of the Form w tt + k w t = a_2_w xx + bw
T8.3. Elliptic Equations
- T8.3.1. Laplace Equation Δ_w_ = 0
- T8.3.2. Poisson Equation Δ_w_ + Φ(x) = 0
- T8.3.3. Helmholtz Equation Δ_w_ + λ_w_ = −Φ(x)
T8.4. Fourth-Order Linear Equations
- T8.4.1. Equation of the Form w tt + a_2_w xxxx = 0
- T8.4.2. Equation of the Form w tt + a_2_w xxxx = Φ(x, t)
- T8.4.3. Biharmonic Equation ΔΔ_w_ = 0
- T8.4.4. Nonhomogeneous Biharmonic Equation ΔΔ_w_ = Φ(x, y)
References for Chapter T8

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