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1. Nonlinear Waves in Fluids

2. Shock Waves

3. Theories for Linear Waves

4. The Equations of Inviscid Compressible Flow

5. Models for Linear Wave Propagation

6. Energetic rate-independent systems

7. Beyond rate-independence

8. Applications in continuum mechanics and physics of solids

9. Rate-independent systems in Banach spaces

10. A general view of rate-independent systems

11. Introduction

12. The Fokker–Planck Equation

13. Linear Response Theory for Diffusion Processes

14. Derivation of the Langevin Equation

15. Exit Problems for Diffusion Processes and Applications

16. Modeling with Stochastic Differential Equations

17. Diffusion Processes

18. The Langevin Equation

19. Introduction to Stochastic Differential Equations

20. Introduction to Stochastic Processes

21. The Heat Equation

22. Inverse Boundary Value Problems

23. Singular Boundary Integral Equations

24. Riesz Theory

25. Iterative Solution and Stability

26. Dual Systems and Fredholm Alternative

27. Operator Approximations

28. Potential Theory

29. Sobolev Spaces

30. Regularization by Discretization

31. Equations of the First Kind

32. Regularization in Dual Systems

33. Bounded and Compact Operators

34. Introduction and Basic Functional Analysis

35. Degenerate Kernel Approximation

36. Tikhonov Regularization

37. Quadrature Methods

38. Projection Methods

39. Narrow Escape in

40. Brownian Models of Chemical Reactions in Microdomains

41. Mathematical Brownian Motion

42. Interfacing at the Stochastic Separatrix

43. The First Passage Time to a Boundary

44. Brownian Simulation of Langevin’s

45. Narrow Escape in

46. Euler’s Scheme and Wiener’s Measure

47. Bifurcation in Symmetric FDEs

48. Degree Theory

49. Lyapunov–Schmidt Reduction

50. Normal Form Theory

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