Professor Iuliana Oprea, Weber 123
Office Hours: MW 9:10-10:00AM, and by appt., Phone: 491-6751 Office
Email: juliana"at"math.colostate.edu; www: http://www.math.colostate.edu/~juliana/M340.html
Class Time and Room: MTWF 8:00-8:50AM in EE 203
Lab Section: This
course is formally split in a lecture and a lab session, which in
practice will not be separated. You should register, however, for both
lecture (338813) and Lab (338814).
J. Polking, A. Boggess, D. Arnold: Differential Equations (2nd edition), Prentice Hall 2006, 2001, ISBN 0-13-143738-0
J. Polking, D. Arnold: Ordinary Differential Equations using Matlab (available shrink-wrapped with the textbook at no extra costs)
The construction of mathematical models to address real-world
is one of the most important aspects of each of the branches of
It is often the case that these mathematical models are formulated in
terms of equations involving functions as well as their derivatives,
called differential equations. When only one derivative is involved,
they are called ordinary differential equations - ODEs. The course will
demonstrate the usefulness of ODEs for modelling physical, biological
and other phenomena. Complementary mathematical approaches for their
solutions will be presented, including analytical methods, graphical
analysis and numerical techniques.
order equations, mathematical models, linear equations of second
order, the Laplace Transform, linear systems of arbitrary order and
matrices, nonlinear systems and phase plane analysis, numerical
Homework is collected at the beginning of every Wednesday
is returned the next lecture. Late homework is not accepted. Each
homework you hand in should have a header at the top of the first page
with your name, the date you hand in the homework, and the number of
homework (e.g. Homework 1 etc).
Examinations: There will be two in-class exams: February 22 (Wed), April 12 (Wed),
and a Final Exam on May 9( Tues)
Grading: Graded Homework,
quizzes: 25%; Two Hourly Exams: 20%
each; Final Exam: 35%. Grades will
be published on WebCT.
Computer use: Some of the Tuesday class sessions will take place in the computer lab in Weber 205. The dates in question will be announced in advance in the lecture.
Tutoring: free tutoring for M340 is available at http://www.colostate.edu/Depts/NatSci/html/Tutorial.html
• Chapter 1: Introduction to Differential Equations. 1.1, 1.2, 1.3
• Chapter 2: First-order Equations. Solution techniques for linear and separable equations, exact equations, models of motion, autonomous equations and stability of equilibrium solutions. 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 2.9
• Chapter 3: Modeling and Applications. Personal finance. 3.3
• Chapter 6: Numerical Methods. Euler
• Chapter 4: Second-Order Equations. Homogenous and inhomogenous equations, variation of parameters and undetermined coefficients methods, forced and unforced harmonic motion. 4.2, 4.4, 4.5, 4.6, 4.7
• Chapter 5: The Laplace Transform.
Definition and properties, application to differential equations,
discontinuous forcing terms, Delta function, convolution. 5.1, 5.2,
5.3, 5.4, 5.5, 5.6, 5.7
• Chapter 7: Matrix Algebra. Vectors, matrices, linear systems of equations, subspaces, determinants. 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7
• Chapter 8: Introduction to Systems. Definition, geometric interpretation, linear systems, phase-plane portraits. 8.1, 8.2, 8.3, 8.4, 8.5
• Chapter 9: Linear Systems with
Constant Coefficients. Eigenvalue-eigenvector solutions of
homogeneous systems and matrix exponential, phase-plane portraits and
trace-determinant plane, qualitative analysis and stability,
inhomogenous systems. 9.1, 9.5, 9.6 (9.2: planar
systems), 9.3, 9.4, 9.7, 9.9
• Chapter 10: Nonlinear Systems.
Linearization, long-term behaviour of solutions, mechanical systems,
Part V: Linear Higher Order Equations
• Chapter 9.8: Higher Order Equations. Linear Dependence/Independence, Wronskian, fundamental set of solutions. 9.8, 4.3