Exam Instructions for MATH-2400, Introduction to Differential Equations
MATH-2400, INTRODUCTION TO
DIFFERENTIAL EQUATIONS
EXAMS
Instructor: Gregor Kovacic
Office: 419 Amos Eaton
Phone: 276-6908
E-mail: kovacg@rpi.edu
Exam 1
Will be given in class on Friday, September 25. It will cover the following material:
first-order linear and separable differential equations; general, implicit, and explicit solutions;
word problems with applications of linear first-order equations; population dynamics and graphical solution
of autonomous first-order equations; second-order liner homogeneous equations with constant coefficients;
method of undetermined coefficients. It will cover problems 1 through 45 on the
suggested homework list.
Exam 2
Will be given in class on Tuesday, November 3.
It will cover the following material: mechanical oscillations (free, damped, overdamped, resonantly
forced, beats, driven and damped), Euler's equation, variation of parameters, Fourier series (Fourier coefficients,
series for odd and even functions, odd and even extensions and half-range sine and cosine series),
eigenvalue problems, the heat conduction equation (separation of variables, bar with cooled ends, bar with insulated ends,
stationary solutions for bar with different temperatures at either end, solution using eigenfucntions and Fourier series),
wave equation. It will cover problems 49 through 100 on the
suggested homework list. Parts of the test
will be somewhat similar to the relevant parts of this test,
this test, and this test.
Exam 3
Will be given in class, on Tuesday, December 8.
It will cover the following material: 2x2 matrices and vectors, linear 2x2 systems of algebraic equations,
eigenvalues and eigenvectors, 2x2 systems of linear 1st order differential equations with constant coefficients,
general solutions for distinct real eigenvalues and for complex-conjugate eigenvalues, particular solutions for given initial points,
plotting trajectories (phase portraits) in the phase plane, sources, sinks, saddles, centers, spiral sources, spiral sinks,
stability type, equilibrium points of nonlinear 2x2 systems of differential equations, linearization, local
phase portraits near equilibrium points, competing species, predator-prey systems. It will cover
problems 101 through 115 on the
suggested homework list. The test
will be somewhat similar to problems 8 through 11 of
this test (except only 2x2 versions of any of the problems),
and problems 10 through 13 of this test. More details
are provided here.
You are allowed one handwritten sheet (8.5 by 11 inches) of notes.
No other aids (books, notes, calculators, laptops, cell phones, etc.) are allowed.
Optional Final Exam
An optional final exam will be given during the finals period.
You are allowed one handwritten sheet (8.5 by 11 inches) of notes.
No other materials (books, notes, calculators, laptops, cell phones, etc.) are allowed.
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