Mathematical Methods
Fall semester of 2019-2020
Course code: UCSCIMAT21
TEXTBOOK: N.H. Asmar, Partial Differential Equations with Fourier Series and Boundary value problems, THIRD Edition, Dover Publications, Inc.
Week 36
DAY 1: Monday 2-9-'19, 13:45-15:30
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Lecture on: ordinary differential equations, initial value problems, intro to partial differential equations and initial boundary value problems
Lecture notes [Lecture 1]
Reading: A.1, A.2, 1.2 and 3.1 (book Asmar)
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DAY 2: Thursday 5-9-'19, 9:00-10:45
Exercises: A.1 (1, 3, 5, 11, 20), A.2 (3, 7, 10, 25, 37, 40), 1.2 (15, 17, 19), 3.1 (1, 3, 5, 7) (book Asmar)
Solutions: [pdf]
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Week 37
DAY 3: Monday 9-9-'19, 13:45-15:30
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Lecture on: linear systems of ODEs.
Lecture notes [Lecture 2]
Reading: chapters 10.1-10.4 in [this] document .
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DAY 4: Thursday 12-9-'19, 9:00-10:45
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Exercises: 10.1.5, 10.1.6, 10.2.1(a), 10.2.2(a), 10.2.3(a), 10.2.4(a), 10.3.1, 10.3.7, 10.3.8, 10.4.1, 10.4.3, 10.4.9 in [this] document.
Solutions: [pdf]
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Week 38
DAY 5: Monday 16-9-'19, 13:45-15:30
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Lecture on: series methods for ordinary differential equations
Lecture notes [Lecture 3]
Reading: A4 and A5 (Asmar).
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DAY 6: Thursday 19-9-'19, 9:00-10:45
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Cancelled.
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Week 39
DAY 7: Monday 23-9-'19, 13:45-15:30
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Lecture on: periodic functions and Fourier series
Lecture notes [Lecture 4]
Reading: 2.1, 2.2, 2.3, 2.3, 2.4 and 2.6 (Asmar)
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DAY 8: Thursday 26-9-'19, 9:00-10:45
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Exercises: A4.1, A4.2, A4.3, A4.4, A4.13, A4.14, A4.33, A4.34, A5.1, A5.3, A5.5, A5.7, A5.24(a,b,c) (book Asmar).
Solutions: [pdf]
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Week 40
DAY 9: Monday 30-9-'19, 13:45-15:30
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Lecture on: PDEs and separation of variables
Lecture notes [Lecture 5]
Reading: 3.3, 3.5 and 3.6 (Asmar)
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DAY 10: Thursday 3-10-'19, 9:00-10:45
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Exercises: 2.1 (2, 10), 2.2 (5, 7, 9, 15, 17, 24), 2.3 (1, 2), 2.4 (9, 13, 15) (Asmar).
Solutions: [pdf]
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Week 41
DAY 11: Monday 7-10-'19, 13:45-15:30
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Exercises: 3.3 (1, 2, 4), 3.5 (1, 2, 3, 9), 3.6 (1, 2)
Solutions: [pdf]
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DAY 12: Thursday 10-10-'19, 9:00-10:45
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Rehearsal and Mock Midterm
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Week 42
DAY 13: Monday 14-10-'19, 13:45-15:30
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MIDTERM
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DAY 14: Thursday 17-10-'19, 9:00-10:45
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no class
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Week 43
DAY 15: Monday 21-10-'19; FALL BREAK!
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DAY 16: Thursday 24-10-'19; FALL BREAK!
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Week 44
DAY 17: Monday 28-10-'19, 13:45-15:30
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Lecture on: Fourier integrals
Lecture notes [Lecture 6]
Reading: 7.1
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DAY 18: Thursday 31-10-'19, 9:00-10:45
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Exercises: 7.1 (1, 3, 5, 13, 14, 15)
Solutions: [pdf]
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Week 45
DAY 19: Monday 4-11-'19, 13:45-15:30
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Lecture on: Fourier transform
Lecture notes [Lecture 7]
Reading: 7.2
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DAY 20: Thursday 7-11-'19, 9:00-10:45
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Exercises: 7.2 (1, 3, 10, 17, 19, 20, 21, 23)
Solutions: [pdf]
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Week 46
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DAY 21: Monday 11-11-'19, 13:45-15:30
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Lecture on: Fourier transform applied to PDEs
Lecture notes [Lecture 8]
Reading: 7.3 and 7.4
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DAY 22: Thursday 14-11-'19, 9:00-10:45
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Exercises: 7.3 (1, 3, 9, 14) and 7.4 (1, 3, 8, 10)
Solutions: [pdf]
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Week 47
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DAY 23: Monday 18-11-'19, 13:45-15:30
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Lecture on: Laplace transform
Lecture notes [Lecture 9]
Reading: 8.1 and 4.7 (=> the Gamma function)
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DAY 24: Thursday 21-11-'19, 9:00-10:45
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Exercises: 8.1 (1, 3, 4, 6, 8, 9, 11, 14, 26, 27, 31, 32)
Solutions: [pdf]
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Week 48
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DAY 25: Monday 25-11-'19, 13:45-15:30
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Lecture on: Laplace transform applied to DEs
Lecture notes [Lecture 10]
Reading: remaining part of 8.1 and (8.2 and 8.3: optional)
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DAY 26: Thursday 28-11-'19, 9:00-10:45
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Exercises: 8.1 (39, 40, 42, 43) and optional: 8.2 (1, 2, 7, 8, 23, 26)
Solutions: [pdf]
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Week 49
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DAY 27: Monday 2-12-'19, 13:45-15:30
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Rehearsal and Mock Final Exam
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Week 49
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DAY 28: Thursday 5-12-'19, 9:00-10:45
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no class
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Week 50
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DAY 29: Monday 9-12-'19, 13:45-15:30
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FINAL EXAM
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Week 50
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DAY 30: Thursday 12-12-'19, 9:00-10:45
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no class
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