Math 285 Section
C1 Spring 2004
Ordinary
Differential Equations Syllabus
(very approximate, especially since I still only have
the second edition of the textbook)
Our textbook is "Differential Equations
and Boundary Value Problems:Computing and Modelling" (3-d
Edition), by Edwards and Penney
·Chapter
1:First Order Differential Equations
1.1 Differential Equations and Mathematical
Models.
1.2 Integrals as general and particular solutions.
1.3 Direction fields and solution curves
1.4
Separable equations
1.5 Linear first order equations.
1.6 Substitution methods and exact equations.
·Chapter
2: Mathematical Models and Numerical Methods
2.2 Equilibrium solutions and stability
2.4-2.5 Numerical Methods (briefly, time
permitting)
·Chapter
3: Linear Equations of Higher Order
3.1 Introduction: Second order linear equations
3.2 General solutions of linear equations.
Wronskian and linear independence.
3.3 Homogeneous equations with constant coefficients
3.4 Mechanical Vibrations
3.5 Inhomogeneous equations and the method
of undetermined coefficients (includes variations of parameters)
3.6 Forced oscillations and resonance
3.8 Boundary value problems and eigenvalues
·Chapter
9: Fourier Series Methods
9.1 Periodic functions and trigonometric series
(emphasis on orthogonality)
9.2 General Fourier series and convergence
9.3 Fourier
Sine and Cosine series
9.4 Applications of Fourier series
9.5 Heat conduction and separation of variables
9.6 Vibrating strings and 1-D wave equation
9.7 Steady-state temperature and Laplace
equation.
·Chapter
10: Eigenvalues and Boundary Value Problems
10.1 Sturm-Liouville problems and eigenfunction
expansions
10.2 Applications of eigenfunction series
10.3 Periodic solutions and natural frequencies
Some topics may have to be omitted or covered in less detail. However,
under no circumstances will we cover any material not included in the above
syllabus. Also, only material covered in class will be included in the
midterm and the final exams.
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