4 1. INTRODUCTION 5. Heat (or diffusion) equation ut − Δu = 0. 6. Schr¨odinger’s equation iut + Δu = 0. 7. Kolmogorov’s equation ut − n i,j=1 aijuxixj + n i=1 biuxi = 0. 8. Fokker–Planck equation ut − n i,j=1 (aiju)xixj − n i=1 (biu)xi = 0. 9. Wave equation utt − Δu = 0. 10. Klein–Gordon equation utt − Δu + m2u = 0. 11. Telegraph equation utt + 2dut − uxx = 0. 12. General wave equation utt − n i,j=1 aijuxixj + n i=1 biuxi = 0. 13. Airy’s equation ut + uxxx = 0. 14. Beam equation utt + uxxxx = 0.
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