Instructor
Dr. Iuliana Oprea, Weber 123
Office Hours: Mo 121PM, Tu 34pm
and by
appt., Phone:
4916751 Office
Email:
juliana"at"math.colostate.edu; www: http://www.math.colostate.edu/~juliana/M345.html
Class Time and Room: MTWF
2:002:50PM in EE 203
The general course page for M340: M340, sections
16
Homework 




Lab Section: This
course is formally split in a lecture and a lab session, which in
practice will not be separated.
Required Textbook:
J. Polking, A. Boggess, D. Arnold: Differential Equations (2nd
edition), Prentice Hall 2006, 2001, ISBN 0131437380
Course Objectives:
The construction of mathematical models to address realworld
problems
is one of the most important aspects of each of the branches of
science.
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.
Synopsys: First
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
methods.
Homework:
Homework is collected at the beginning of every Wednesday
lecture and
is returned the next lecture. Late homework is not
accepted.
Examinations: There will be two inclass exams, on March 3
and April 14
and a Final Exam
Grading: Graded Homework,
quizzes: 25%; Two Hourly Exams: 20%
each; Final Exam: 35%.
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.
Content:
• Chapter 1: Introduction to Differential Equations. 1.1, 1.2, 1.3
• Chapter 2: Firstorder 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
method. 6.1
• Chapter 4: SecondOrder Equations. Homogenous and inhomogenous equations, variation of parameters and undetermined coefficients methods, forced and unforced harmonic motion. 4.2, 4.3, 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  short review
• Chapter 8: Introduction to Systems. Definition, geometric interpretation, linear systems, phaseplane portraits. 8.1, 8.2, 8.3, 8.4, 8.5
• Chapter 9: Linear Systems with
Constant Coefficients. Eigenvalueeigenvector solutions of
homogeneous systems and matrix exponential, phaseplane portraits and
tracedeterminant 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
Part IV: Linear Higher Order Equations
• Chapter 9.8: Higher Order Equations. Linear Dependence/Independence, Wronskian, fundamental set of solutions. 9.8, 4.3 revisited
• Chapter 10: Nonlinear Systems.
Linearization, longterm behaviour of solutions, mechanical systems,
population models.