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 | Syllabus:
Click here for details in a
PDF file |
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Course: Math
415, Ordinary and Partial Differential Equations, MWF 11:30am |
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Texts:
(1) Elementary Differential Equations & Boundary Value Problems (7th Ed) by
Boyce and Diprima |
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Topics: Solutions to first order, second order and higher order ordinary differential equations and
partial differential equations; Phase plane analysis; Fourier series; Boundary value problems. |
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Office Hours: MWF 10:30-11:30am
@MW410 and by
appointment |
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Grading: first midterm
(Fri. Oct 5, 20%), second midterm (Fri. Nov. 2, 25%), final exam( Mon. Dec
3 11:30am, 30%), class participation (5%), and homework (20%). The letter
grade will be with an approximately 90(A)-80(B)-70(C)-60(D) scale. |
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Policy:
NO make-up exams without doctor's excuse. Late Homework will be no credit. |
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Tentative Schedule: updated regularly |
The HW problems need to
be turned in. HW due every Wednesday in class. It includes all assignments given in the
previous week (Mon, Wed, Fri).
| Monday |
Wednesday |
Friday |
| Sept 17 |
Sept
19 (Autumn Classes Begin)
Chapter 1:Introduction
HW: 1.1 (11), 1.2(11),1.3(13,28)
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Sept 21
Chapter 2.1 & 2.2
Linear Equation: Method of Integrating Factors
Separable Equations
HW: 2.1 (6,10,15,18,28)
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| Sept 24 Chapter 2.2,2.3
Separable Equations
Modeling with First Order Equations
2.2(4,11,25,33)
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Sept 26
Chapter 2.3,2.4
HW:2.3(4,9,16,21,24)
Differences Between Linear and Nonlinear Equations |
Sept 28
Chapter 2.4, 2.5
HW:2.4(11,17,22,28)
Autonomous Equations and Population Dynamics
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| Oct 1
Chapter 2.5
HW:2.5(3,7,9,17) |
Oct 3
Chapter 2.6
HW2.6(7,9,19,26,27)
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Oct 5
Chapter 2.6
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| Oct 8
Chapter 2.7
Numerical Approximations and Population Dynamics
HW2.7(3,15,18(too much computation, I decide not to give this question as HW))
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Oct 10
First Exam |
Oct 12
2.8 The Existence and Uniqueness Theorem
HW 2.8(4,7,11)
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| Oct 15
Chapter 3.1
Homogeneous Equations with Constant Coefficients
Fundamental Solutions of Linear Homogeneous Equations
HW: 3.1 (6 13 19 20)
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Oct 17
Chapter 3.2
Linear Independence and the Wronskian
HW: 3.2 (2,8,11,13,23)
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Oct 19
Chapter 3.3
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| Oct 22
Chapter 3.4, 3.5
HW: 3.3 (2,3,4,15,16,20) HW 3.4 (2,3,21)
Complex Roots of the Characteristic Equation |
Oct 24
Chapter 3.5
HW: 3.5 (3,11,12,20,25,30)
Repeated Roots; Reduction of Order
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Oct 26
3.6,3.7
HW 3.6 (3,8,14,24), HW 3.7(2,5,14,17)
Nonhomogeneous Equations: Method of Undetermined Coefficients
Variation of Parameters
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| Oct 29
3.8,3.9
Mechanical and Electrical Vibrations
HW 3.8 (2,6,9,13), HW 3.9(5,7,10)
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Oct 31
Supplement Material:
Systems of ODEs
HW 3.2 supplement (11(a),16,19
Click here for a PDF file of supplement material
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Nov 2
Supplement Material:
3.3 Homogeneus Linear Systems with constant coefficient
HW 3.3 supplement (3,14 without drawing the direction field and phase portrait)
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| Nov 5
Supplement Material:
Stability
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Nov 7
Second Exam
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Nov 9
Supplement: Chapter 3.4 Complex eigenvalues
HW:Solve (1)y''+9y=0 and (2) 16y''-8y'+145y=0 y(0) = -2 and y'(0)=1 by reformulating (a) and (b) to first order system equations and draw the phase portrait |
| Nov 12 (Veteran's Day. No Classes) |
Nov 14
Chapter 10.1,Two-Point Boundary Value Problems
HW 10.1: 2,3,4,11,13
Chapter 10.2 Fourier Series |
Nov 16
Chapter 10.2, Fourier Series
HW 10.2: 3,4,15,18
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| Nov 19
Chapter 10.3
The Fourier Convergence Theorem
HW 10.3: 2,3
Chapter 10.4 Even and Odd Functions |
Nov 21
Chapter 10.4 Even and Odd Functions
HW 10.4: 3,6,7,15,18,35
Chapter 10.5
Separation of Variables; Heat Conduction in a Rod
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Nov 23 (Columbus Day. No Classes)
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| Chapter 10.5,10.6
Other Heat Conduction Problems
HW 10.5: 3,5,8,10
HW 10.6: 2,3,9(a)
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Nov 28
Chapter 10.7: 1(a),6(a)
The Wave Equation : Vibrations of an Elastic String |
Nov 30
Chapter 10.8: 1(a,b),2,5
Laplace's Equation
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| Dec 3 Final Exams Week
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Dec 5 Final Exams Week
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Dec 7 Final Exams Week
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