MTH163: Ordinary Differential Equations I

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Cross Listed:
Offered:
Fall and Spring
Prerequisites:
MTH143 or MTH162 or MTH172
This course is a prerequisite or co-requisite for:
Two years of the calculus sequence MTH161--MTH164 or MTH141-143 and MTH163--MTH164 or MTH171--174 is required to major in mathematics. Among the engineering courses, EE231 Fields, EE232 Waves, and EE241 Signals all require MTH163. There are many others. This course does NOT satisfy the prerequisite for MTH235 (linear algebra). All math majors and others interested in taking linear algebra should take MTH165 or the MTH170's series instead.
Description:
This is an introduction to the subject of ordinary differential equations, a subject which serves as a corner stone of problem solving techniques in the physical sciences and engineering. Certain aspects of it have also become important in the biological sciences and in economics. The study of ordinary differential equations, particularly nonlinear differential equations, continues to be a vital part of modern mathematics, and includes the study of dynamical systems and of chaotic behavior. This course concentrates on the older aspects of the subject, emphasizing those techniques which are important in physics and engineering. The emphasis in this course, as in the other calculus courses, is on learning techniques for solving certain equations (which occur frequently in physics and engineering), rather than on the theoretical aspects of the subject. Laplace transform techniques are discussed in several engineering 200 level courses. The treatment in this course will give an introduction to the use of these techniques and some indication of its mathematical basis. The practical applications of the technique and extensive practice in its use will take place in the engineering courses.
Topics covered:
Usually MTH164 (multidimensional calculus) is taken before MTH163 (differential equations) since its subject matter is more closely related to MTH162. However some engineering majors require MTH163 to be completed by the end of the fall semester of the sophomore year. Elementary methods, linear equations, and systems with constant coefficients, solutions in series, special functions, phase plane analysis and stability, Laplace transform, extremal problems.
Related courses:
  • MTH263 is an upper level course in ordinary differential equations which deals more with the qualitative behavior of the solutions to differential equations. This is important in many applications, where the exact solution of the differential equation cannot be calculated.
  • MTH281 deals with partial differential equations, which are important in mathematics and in physical applications.
  • ME 201 discusses ordinary and partial differential equations. It covers material similar to that in MTH281.
  • ME401 discusses ordinary differential equations.
  • EE212 includes some work with Laplace transform methods of solving ODEs.
  • EE213 includes some work with Laplace transform methods of solving ODEs.
  • EE410 includes material on dynamical systems (as does MTH263).