Chapters from Strauss’ PDE text:
Twelfth week (November 24, 26, 28):
Lecture 30. (lecture notes)
Convergence of the Fourier Series I
Lecture 31. (lecture notes)
Convergence of the Fourier Series II (Application of the Fourier method to the resonance)
Lecture 32. (lecture notes)
Laplace equation.
Eleventh week (November 17, 19, 21):
Lecture 27. (lecture notes)
Fourier Integral. Applications of the Fourier Integral.
Lecture 28. (lecture notes)
On different types of the convergence of the Fourier Series.
Lecture 29. (lecture notes)
Complex Fourier Series.
Some notes of the eleventh week lectures.
Tenth week (November 12, 14):
Lecture 25. (lecture notes)
Problem solving (Midterm Test II review).
Lecture 26. (5.1 – 5.4)
Sine, Cosine, Full Fourier Series.
Fourier method and separation of variables.
Ninth week (November 3, 5, 7):
Lecture 22. (5.6, 2.3, lecture notes)
Inhomogeneous heat equation (finite domain). Maximum principle.
Lecture 23. (2.3, lecture notes)
Diffusion model. Applications of the energy method to the heat equation.
Lecture 24. (2.4, lecture notes)
On uniqueness of the solution of the heat equation. (infinite domain)
Some notes of the ninth week lectures.
Eighth week (October 27, 29, 31):
Lecture 19. (4.2, 4.3, lecture notes)
Heat (diffusion) equation. Fourier method (finite domain, BVP).
Lecture 20. (5.3, lecture notes)
Heat (diffusion) equation. Fourier method (finite domain, IVP with Robin boundary conditions).
Lecture 21. (5.3, lecture notes)
Heat (diffusion) equation. Fourier method (finite domain, IVP with periodic boundary conditions).
Some notes of the eighth week lectures.
Seventh week (October 20, 22, 24):
Lecture 16. (4.1, lecture notes)
Separation of variables.
Lecture 17. (4.1 (last page), lecture notes)
Application of the Spectral decomposition method (Fourier method) to wave equation.
Lecture 18. (2.2, lecture notes )
Applications of the energy method to wave equations.
Some notes of the seventh week lectures.
Sixth week (October 15, 17):
Lecture 15. (lecture notes)
Stability of the D’Alembert solution. General hyperbolic second order PDE with constant coefficients.
Lecture 16. (lecture notes)
Initial value problem for the inhomogeneous wave equation (finite domain).
Some notes of the sixth week lectures.
Fifth week (October 8, 10):
Lecture 13. (3.4 + lecture notes)
General solution of the inhomogeneous wave equation (infinite domain). Different methods.
Lecture 14. (4.1 + lecture notes)
The intial value problem for the inhomogeneous wave equation (infinite domain). Different methods.
Some notes of the fifth week lectures.
Fourth week (September 29, October 1, 3):
Lecture 10. (2.1 + lecture notes)
The wave equation.
Lecture 11. (2.1-2.2 + lecture notes)
Solving the initial value problem for a wave equation using method of characteristics.
Lecture 12. (1.3 + lecture notes)
Vibrating string model. D’Alembert method of the solution of the initial value problem for a hyperbolic PDE with constant coefficients.
Some notes of the fourth week lectures.
Third week (September 22, 24, 26):
Lecture 7. (1.6 + lecture notes)
Classification of second order PDE.
Lecture 8. (lecture notes)
Transformation of second-order PDE with constant coefficients to canonical forms.
Lecture 9. (2.1 + lecture notes)
Transformation of second-order PDE with non-constant coefficients to canonical forms.
Some notes of the third week lectures.
Second week (September 15, 17, 19):
Lecture 4. (1.2, 1.5 + lecture notes)
First order PDE with non-constant coefficients.
Lecture 5. ( 1.5 + lecture notes)
Method of characteristics for first order linear PDE with non-constant coefficients. Well-posedness of IVP problems.
Lecture 6. (lecture notes)
Stability of solutions of IVP.
Some notes of the second week lectures.
First week (September 8, 10, 12):
Lecture 1. (1.1 + lecture notes)
Introduction. Classifications of PDE. (linear, nonlinear, order of PDE, homogeneous, non-homogeneous)
Lecture 2. (1.2, 1.3 + lecture notes)
Eikonal and transport equations. Geometric methods of solutions. (models, directional derivative, geometric properties of a gradient )
Lecture 3. (1.2, 1.5 + lecture notes)
Linear wave equation. Well and ill-posed initial value problems. Method of characteristics. (existence of the general solution, existence of the IVP solution, uniqueness of the IVP solution in a domain )