Math 285 Section F1  Fall 2000

Ordinary Differential Equations syllabus

Our textbook is "Differential Equations and Boundary Value Problems:Computing and Modelling" (2-nd Edition), by Edwards and Penney
 
 
 

·Chapter 1:First Order Differential Equations [6 Lectures]

1.1 Differential Equations and Mathematical Models.

1.2 Integrals as general and particular solutions.
1.3 Direction fields and solution curves (Emphasis on existence/uniqueness theorem and the geometric interpretation of slope fields).
1..4Separable equations (exponential growth and decay may be omitted)
1.5 Linear first order equations.
1.6 Substitution methods and exact equations.

·Chapter 2: Mathematical Models and Numerical Methods[2 lectures]

2.1 Population Models (in more detail)

2.3 Acceleration-velocity models (briefly, time permitting)

·First Hourly Exam

·Chapter 3: Linear Equations of Higher Order [14 Lectures]

3.1 Introduction: Second order linear equations [1 Lecture]

3.2 General solutions of linear equations (emphasis on second order equations; introduction of Wronskian and linear independence for higher order equations)[2 Lectures]
3.3 Homogeneous equations with constant coefficients (includes factorization of constant coefficient operators) [2 Lectures]
3.4 Mechanical Vibrations [2 Lectures]
3.5 Inhomogeneous equations and the method of undetermined coefficients (includes variations of parameters) [3 Lectures]
3.6 Forced oscillations and resonance [2 Lectures]
3.8 Boundary value problems and eigenvalues [2 Lectures] (May be covered between 9.4 and 9.5 instead)

·Second Hourly Exam

·Chapter 9: Fourier Series Methods [12 Lectures]

9.1 Periodic functions and trigonometric series (emphasis on orthogonality) [3 Lectures]

9.2 General Fourier series and convergence [1 Lecture]
9.3 Fouriersin and cos series [1 Lecture]
9.4 Applications of Fourier series [1 Lecture]
9.5 Heat conduction and separation of variables[2 Lectures]
9.6 Vibrating strings and 1-D wave equation [2 Lectures]
9.7 Steady-state temperature and Laplace equation (Covers the Dirichlet problem for the disk. Provides an example of substitution methods for PDE) [3 Lectures]

·Third Hourly Exam

·Chapter 10: Eigenvalues and Boundary Value Problems [5 Lectures] 

10.1 Sturm-Liouville problems and eigenfunction expansions [2 Lectures]

10.2 Applications of eigenfunction series [2 Lectures]
10.3 Periodic solutions and natural frequencies [1 Lectures]

·Exams and leeway: 5 Lectures

·Total of 44 Lectures

Slight deviations in speed with which we move through the syllabus are possible. 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.


Back to Ilya Kapovich's homepage