MATH 246 (Differential Equations for Scientists and Engineers)
| DESCRIPTION |
This course is an introduction to ordinary differential
equations.
The course introduces the basic techniques for solving and/or analyzing
first and second order differential equations, both linear and
nonlinear,
and systems of differential equations. Emphasis is placed on
qualitative
and numerical methods, as well as on formula solutions. The use
of
mathematical software system is an integral and substantial part of the
course. Beginning Spring 2003, all sections of the course will use the
software system MATLAB. |
| PREREQUISITES |
Required: MATH 141 or equivalent.
Recommended: MATH240 or ENES102 or PHYS161 or PHYS171.
|
| TOPICS |
Introduction to and Classification of Differential
Equations
First Order Equations
Linear, separable and exact equations
Introduction to symbolic solutions using a
MSS
Existence and uniqueness of solutions
Properties of nonlinear vs. linear equations
Qualitative methods for autonomous equations
Plotting direction fields using a MSS
Models and applications
Numerical Methods
Introduction to a numerical solver in a MSS
Elementary numerical methods: Euler, Improved
Euler, Runge-Kutta
Local and global error, reliability of
numerical
methods
Second Order Equations
Theory of linear equations
Homogeneous linear equations with constant
coefficients
Reduction of order
Methods of undetermined coefficients and
variation
of parameters for non-homogeneous equations
Symbolic and numerical solutions using a MSS
Mechanical and electrical vibrations
Laplace Transforms
Definition and calculation of transforms
Applications to differential equations with
discontinuous forcing functions
Systems of First Order Linear Equations
General theory
Eigenvalue-eigenvector method for systems
with constant coefficients
Finding eigenpairs and solving linear systems
with a MSS
The phase plane and parametric plotting with
a MSS
Nonlinear Systems and Stability
Autonomous systems and critical points
Stability and phase plane analysis of almost
linear systems
Linearized stability analysis and plotting
vector fields using a MSS
Numerical solutions and phase portraits of
nonlinear systems using a MSS
Models and applications
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| TEXT |
Text(s)
typically used in this course.
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