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Week of
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Topics
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Assignments
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Jan 22
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Introduction and Review : Chapter 1
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Jan 29
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First Order Differential Equations
Methods of Solving Differential Equations : 2.1, 2.2, 2.6
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Section 2.1: 15, 16, 17, 28
Section 2.2: 4, 6, 10, 25
Section 2.6: 4, 6, 18, 19, 24, 27
due February 8th
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Feb 5
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Second Order Differential Equations
Homogeneous Equations
Fundamental Solutions : 3.1, 3.2
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Section 3.1: 5, 6, 11, 12, 22, 28
Section 3.2: 4, 9, 14, 19, 24, 31
due February 15th
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Feb 12
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Constant Coefficient Equations
Complex Roots : 3.4,
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Section 3.3: 4, 8, 10, 17, 21, 25
Section 3.4: 10, 12, 18, 19
Section 3.5: 6, 14, 20, 25
Section 3.6: 3, 7
due February 22nd
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Feb 19
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Repeated Roots 3.5
Non-homogeneous Equations : 3.6, 3.7
Practice problems
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Section 3.4: 34*, 37
Section 3.5: 28, 31
Section 3.6: 13, 15, 17, 32*, 33
Section 3.7: 2, 9, 14, 17, 28*, 30
due March 1st
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Feb 26
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MIDTERM 1 (Monday 26th February)
Power Series Solutions
Review of Series : 5.1
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Mar 5
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Series Solutions
Ordinary Points : 5.2, 5.3
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Section 5.2: 9, 12, 17
Section 5.3: 3, 7
due March 15th
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Mar 11
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Series Solutions
Regular Singular Points and Euler's Equation: 5.4, 5.5
The Laplace Transform
Definition and solution of IVPs : 6.1, 6.2
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Section 5.4: 8, 9, 18, 19, 21, 24
Section 5.5: 4, 6, 15, 19, 21, 23
due March 22nd
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Mar 18
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The Laplace Transform
Discontinuous functions : 6.3, 6.4
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Section 6.1: 5, 7, 17, 19
Section 6.2: 5, 8, 14, 16, 22
Section 6.3: 2, 9, 14, 18
due March 29th
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Mar 25
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Spring Break
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April 8
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MIDTERM 2 (Wednesday 11th April)
Practice midterm, Solutions
to the practice midterm (Note: There won't be problems about Bessel's
equation. Instead there will be more problems about the Laplace
transform.)
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Section 6.4: 3, 7, 9, 15
Section 6.5: 4, 6, 16 (part (d) is optional)
Section 6.6: 6, 7, 9, 10, 13, 16
due April 19th
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Apr 16
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The Laplace Transform
Impulse functions and convolution : 6.5, 6.6
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Section 10.1: 3, 8, 13
Section 10.2: 11, 14, 16, 17
due April 24th
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Apr 23
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Fourier Series
Boundary value problems and Fourier series : 10.1, 10.2
Fourier series, even and odd functions : 10.3, 10.4
Partial Differential Equations
The heat equation and separation of variables : 10.5
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Sec. 10.3: 4, 5, 8, 9, 12
Sec. 10.4: 8, 9, 17, 18, 24, 35
Sec. 10.5: 2, 5, 8, 10, 12
due May 3rd
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Apr 30
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Other Heat Conduction problems : 10.6
The Wave Equation: Vibration of an elastic string : 10.7
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Section 10.6: 2, 4, 9, 12
Section 10.7: 2, 6, 9 (ignore part (d) in 2, 6)
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May 9
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Final from 2003
Practice topics and problems.
Practice set : 2.6-27, 3.5-30, 3.6-17,
3.7-17, 5.2-6, 5.5-20*,
6.4-9, 6.5-6, 10.4-25(a),(b), 10.5.10* ( * =extra credit)
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