Lecture #
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Notes and Supplemental Materials
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1 (Sept. 7)
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Lecture 1: Introduction ; Exercises and Problems
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2 (Sept. 9)
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Lecture 2: Conservation Laws I; Exercises and Problems
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3 (Sept. 14)
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Lecture 3: Conservation Laws II; Exercises and Problems
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4 (Sept. 16)
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Lecture 4: Conservation Laws III; Exercises and Problems
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5 (Sept. 21)
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Lecture 5: Fully Nonlinear 1st Order Equations; Exercises and Problems
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6 (Sept. 23)
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Lecture 6: Hopf-Lax Formula; Exercises and Problems
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7 (Sept. 28)
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Lecture 7: H-J Equation Weak Solution; Exercises and Problems
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8 (Sept. 30)
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Midterm 1 (Lec1-Lec6)
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9 (Oct. 5)
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Lecture 9: Poisson Equations: Explicit Formulas; Exercises and Problems
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10 (Oct. 12)
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Lecture 10: Harmonic Functions; Exercises and Problems
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11 (Oct. 14)
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Lecture 11: Regularity for Poisson Equation; Exercises and Problems
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12 (Oct. 19)
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Lecture 12: Weak Solution; Exercises and Problems
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13 (Oct. 21)
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Lecture 13: Sobolev Spaces; Exercises and Problems
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14 (Oct. 26)
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Lecture 14: Poisson Equation in Sobolev Spaces; Exercises and Problems
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15 (Nov. 4)
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Lecture 15: Heat Equations: Explicit Formulas; Exercises and Problems
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16 (Nov. 9)
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Lecture 16: Heat Equations: Maximum Principles; Exercises and Problems
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17 (Nov. 18)
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Lecture 17: Asymptotic Behavior and Energy Method; Exercises and Problems
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18 (Nov. 23)
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Lecture 18: Wave Equations: Explicit Formulas; Exercises and Problems
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19 (Nov. 25)
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Lecture 19: Wave Equations: Uniqueness and Asymptotics; Exercises and Problems
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20 (Dec. 2)
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Lecture 20: Wave Equations: Asymptotics (cont.)
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