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Handbook 1997 : Faculty of Science : Mathematics

618-130 Applied Mathematics

Note:

Students may not gain credit for both 618-130 and 618-132.

Credit Points:

12.5

Coordinator:

Dr J Clark

Prerequisite/s:

618-101 (1995 Handbook) or 618-111 or 618-121 or 618-142; or 618-100 (1995 Handbook), with 618-142 as corequisite; or 618-141, with 618-142 as corequisite; or 618-162, with 618-142 as corequisite.

Timetable:

Second semester, repeated in first semester of the following year

Contact:

39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving

Objectives:

On completion of this subject, students should:

Comprehend:

  • the terminology of ordinary differential equations;

  • the principles and essential information regarding first and second ordinary differential equations;

  • eigenvalues and eigenvectors;

  • linear systems of first and second order ordinary differential equations and their application primarily in the field of mechanics.

Have developed:

  • the ability to solve analytically: first order ordinary differential equations (ODEs) of linear, separable or homogeneous type; second order linear ODEs, including the method of reduction of order, with special emphasis on constant coefficient equations; systems of two or three linear first order ODEs using eigenvalue/eigenvector techniques;

  • the ability to apply the above techniques to simple problems in particle dynamics, including projectile motion.

Appreciate:

  • the role of differential equations in applied mathematics and their use in modelling the dynamics of single particles and small systems of particles.

Content:

Differential equations: first-order differential equations (separable, linear via integrating factor, homogeneous) and applications; second-order differential equations (reducible to first-order, linearly independent solutions), second-order linear differential equations (particular integrals, complementary functions) and applications; numerical solution of first-order equations.Mechanics: Straight-line motion; motion of a projectile; motion in a circle; simple harmonic motion; momentum; impulse; work and energy; pendulum; friction; connected bodies; springs.Systems of differential equations Eigenvalues and eigenvectors; systems of first-order differential equations and applications; phase portraits; systems of second-order linear differential equations and applications.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.
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Handbook 1997 : Faculty of Science : Mathematics 
Status:                   OFFICIAL 1997
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Copyright © University of Melbourne 1997.