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| Introduction to Partial Differential Equations | |||
| INTRO TO PDES | |||
| CLASS CODE: | MATH 472 | CREDITS: 3 | |
| DIVISION: | PHYSICAL SCIENCE & ENGINEERING | ||
| DEPARTMENT: | MATHEMATICS | ||
| GENERAL EDUCATION: | This course does not fulfill a General Education requirement. | ||
| DESCRIPTION: | Solving linear homogeneous and nonhomogeneous second-order partial differential equations with homogeneous and nonhomogeneous boundary conditions by separation of variables. Sturm-Liouville theory. Applications of partial differential equations to diffusion, wave, and other phenomena. Fourier series and their applications to solving partial differential equations. Solving first-order partial differential equations using the method of characteristics. | ||
| TAUGHT: | Fall odd years | ||
| CONTENT AND TOPICS: | Boundary value problems, homogeneous and nonhomogeneous partial differential equations, separable equations, LaPlace Transform and other solution methods, wave, heat and potential equations. | ||
| GOALS AND OBJECTIVES: | 1. Classify second order partial differential equations. 2. Know the three kinds of boundary conditions. 3. Model diffusion, wave, and other phenomena using partial differential equations. 4. Solve linear homogeneous and nonhomogeneous partial differential equations with homogeneous and nonhomogeneous boundary conditions using separation of variables. 5. Solve first order partial differential equations using the method of characteristics. 6. Find the Fourier series representation for a piece-wise smooth function. 7. Understand the basic concepts of functional analysis as they apply to partial differential equations. |
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| REQUIREMENTS: | All students must have their own textual materials. Exams are required by all faculty members. Other forms of assessment may include homework exercises, student projects, and anything else the instuctor may require. |
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| PREREQUISITES: | Either Math 316 or Math 371 | ||
| OTHER: | |||
| EFFECTIVE DATE: | August 2001 | ||