Difference between revisions of "Course schedule"

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{|style="border-collapse: collapse;" class="withlines"
 
{|style="border-collapse: collapse;" class="withlines"
 
!style="width:25px;"|Week
 
!style="width:25px;"|Week
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!style="width:80px;"|Chapters/sections (Diffy Qs)
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!style="width:60px;" colspan=2|Chapters/sections
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!style="width:80px;"|Chapters/sections (Boyce and DiPrima)
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!style="width:240px;"|Topics
 
!style="width:240px;"|Topics
 
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|style="border-top: 1px solid #999;"|1: {{LectureDate|1|2}}
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!style="width:20px;"|(Diffy Qs)
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!style="width:20px;"|(B & D)
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|style="border-top: 1px solid #999;"|{{LectureDate|1|2}}
 
|style="border-top: 1px solid #999;"|/ {{LectureDate|1|4}}
 
|style="border-top: 1px solid #999;"|/ {{LectureDate|1|4}}
 
|style="border-top: 1px solid #999;"|0.2
 
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|style="border-top: 1px solid #999;"|Intro to differential equation models
 
|style="border-top: 1px solid #999;"|Intro to differential equation models
 
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|Introduction to solutions of differential equations
 
|Introduction to solutions of differential equations
 
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|Classification of DEs.
 
|Classification of DEs.
 
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|First order linear equations - Method of Integrating Factors
 
|First order linear equations - Method of Integrating Factors
 
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|First order separable equations
 
|First order separable equations
 
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|/ {{LectureDate|2|4}}
 
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|Modeling with First Order DEs
 
|Modeling with First Order DEs
 
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|Linear and nonlinear equations - existence and uniqueness
 
|Linear and nonlinear equations - existence and uniqueness
 
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|Second order linear equations - Homogeneous equations with constant coefficients (real roots of the characteristic equation)
 
|Second order linear equations - Homogeneous equations with constant coefficients (real roots of the characteristic equation)
 
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|Second order linear equations - The Wronskian
 
|Second order linear equations - The Wronskian
 
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|2.2
 
|2.2
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|Second order linear equations - Complex root of the characteristic equation
 
|Second order linear equations - Complex root of the characteristic equation
 
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|Repeated roots; Reduction of order
 
|Repeated roots; Reduction of order
 
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|Nonhomogeneous equations; method of undetermined coefficients
 
|Nonhomogeneous equations; method of undetermined coefficients
 
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|/ {{LectureDate|4|4}}
 
|/ {{LectureDate|4|4}}
 
|2.4
 
|2.4
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|Mechanical and electrical vibrations
 
|Mechanical and electrical vibrations
 
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|Forced vibrations
 
|Forced vibrations
 
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|3.1
 
|3.1
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|Introduction to systems of first order linear equations
 
|Introduction to systems of first order linear equations
 
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|Review of matrices
 
|Review of matrices
 
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|Systems of linear equations;linear independence, eigenvalues, eigenvectors
 
|Systems of linear equations;linear independence, eigenvalues, eigenvectors
 
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|Basic theory of systems of first order linear equations
 
|Basic theory of systems of first order linear equations
 
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|Homogeneous linear systems with constant coefficients
 
|Homogeneous linear systems with constant coefficients
 
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|Complex eigenvalues
 
|Complex eigenvalues
 
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|3.4
 
|3.4
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|Repeated roots
 
|Repeated roots
 
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|Summary of homogeneous 2x2 systems. Nonhomogeneous linear systems (Method of Undetermined Coefficients, constant vector only)
 
|Summary of homogeneous 2x2 systems. Nonhomogeneous linear systems (Method of Undetermined Coefficients, constant vector only)
 
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|/ {{LectureDate|9|4}}
 
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|6.1
 
|6.1
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|Definition of the Laplace Transform
 
|Definition of the Laplace Transform
 
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|Solution of IVPs
 
|Solution of IVPs
 
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|Step functions
 
|Step functions
 
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|DEs with discontinuous forcing functions
 
|DEs with discontinuous forcing functions
 
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|6.4
 
|6.4
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|Impulse functions
 
|Impulse functions
 
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|The convolution integral
 
|The convolution integral
 
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|Fourier series
 
|Fourier series
 
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|4.3
 
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|The Fourier convergence theorem
 
|The Fourier convergence theorem
 
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|Even and odd functions
 
|Even and odd functions
 
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|4.6
 
|4.6
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|Heat conduction in a rod - Fourier series and separation of variables
 
|Heat conduction in a rod - Fourier series and separation of variables
 
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|The wave equation - vibrations of an elastic string
 
|The wave equation - vibrations of an elastic string
 
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|Other heat conduction problems
 
|Other heat conduction problems
 
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Revision as of 23:45, 9 January 2015

This schedule is tentative and may change slightly as the term progresses.

Not included on this schedule: There will be a weekly worksheet handed in during each tutorial session, starting during the second week of class. Pre-lecture WeBWorK assignments will be due before each lecture and a post-lecture assignment will be due each week.

Regarding textbook references below: These references are to Boyce and DiPrima (from last year). I will start add corresponding refs to the new textbook (Diffy Qs).

Week Chapters/sections Topics
(Diffy Qs) (B & D)
1 Jan 3 / Jan 5 0.2 1.1 Intro to differential equation models
0.2, 1.1 1.2 Introduction to solutions of differential equations
-- 1.3 Classification of DEs.
1.4 2.1 First order linear equations - Method of Integrating Factors
1.3 2.2 First order separable equations
2 Jan 10 / Jan 12 -- 2.3 Modeling with First Order DEs
1.2 2.4 Linear and nonlinear equations - existence and uniqueness
2.1, 2.2 3.1 Second order linear equations - Homogeneous equations with constant coefficients (real roots of the characteristic equation)
-- 3.2 Second order linear equations - The Wronskian
3 Jan 17 / Jan 19 2.2 3.3 Second order linear equations - Complex root of the characteristic equation
-- 3.4 Repeated roots; Reduction of order
2.5 3.5 Nonhomogeneous equations; method of undetermined coefficients
4 Jan 24 / Jan 26 2.4 3.7 Mechanical and electrical vibrations
2.6 3.8 Forced vibrations
5 Jan 31 Flex day
Feb 2 Midterm 1
6 Feb 7 / Feb 9 3.1 7.1 Introduction to systems of first order linear equations
3.2 7.2 Review of matrices
3.2 7.3 Systems of linear equations;linear independence, eigenvalues, eigenvectors
3.3 7.4 Basic theory of systems of first order linear equations
3.4 7.5 Homogeneous linear systems with constant coefficients
3.4 7.6 Complex eigenvalues
Feb 14 / Feb 16 Reading break
7 Feb 21 / Feb 23 3.4 7.8 Repeated roots
3.9 7.9 Summary of homogeneous 2x2 systems. Nonhomogeneous linear systems (Method of Undetermined Coefficients, constant vector only)
8 Feb 28 / Mar 2 6.1 6.1 Definition of the Laplace Transform
6.2 6.2 Solution of IVPs
6.2 6.3 Step functions
-- 6.4 DEs with discontinuous forcing functions
9 Mar 7 / Mar 9 6.4 6.5 Impulse functions
6.3 6.6 The convolution integral
4.1, 4.2 10.2 Fourier series
10 Mar 14 4.3 10.3 The Fourier convergence theorem
4.4 10.4 Even and odd functions
Mar 16 Midterm 2
11 Mar 21 / Mar 23 4.6 10.5 Heat conduction in a rod - Fourier series and separation of variables
4.7, 4.8 10.7 The wave equation - vibrations of an elastic string
12 Mar 28 / Mar 30 -- 10.6 Other heat conduction problems
Apr 4 Flex day
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