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Nov 21, 2024
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MA 235 - Differential Equations for Engineers4 lecture hours 0 lab hours 4 credits
Course Description
This course discusses the solution of first-order differential equations, the solution of higher-order differential equations with constant coefficients, applications of differential equations, and an introduction to the method of Laplace transforms applied to the solution of certain differential equations. (prereq: MA 231 or MA 226 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
• Determine the solution of first-order differential equations by the method of separation of variables
• Determine the solution of first-order differential equations having homogeneous coefficients
• Determine the solution of exact first-order differential equations
• Determine appropriate integrating factors for first-order linear differential equations
• Apply and solve first-order differential equations of selected physical situations
• Determine the general and particular solutions of higher-order linear homogeneous differential equations with constant coefficients
• Determine the general and particular solutions of certain nonlinear second-order homogeneous differential equations with constant coefficients using the methods of Undetermined Coefficients and Variation of Parameters
• Apply and solve second-order differential equations of selected physical situations
• Determine the Laplace transform of selected elementary functions (such as polynomials and exponential and trigonometric functions having linear arguments)
• Determine a function having a given Laplace transform. That is, determine the inverse Laplace transform of a function
• Solve linear differential equation of various orders using the method of Laplace transforms
Prerequisites by Topic
• Determinants
• Solution of algebraic equations
• Limits including L’Hopital’s Rule
• Differentiation of algebraic and transcendental functions
• Integration (especially improper and the method of partial fractions)
• Factoring of polynomials
Course Topics
• Basic concepts (1 class)
• Solution of first-order differential equations by separation of variables (2 classes)
• Solution of exact equations (2 classes)
• Solution of first-order linear differential equations (2 classes)
• Solution of first-order differential equations using numerical methods (1 class)
• Solution of physical situations that can be modeled by first-order differential equations (2 classes)
• Solution of higher order homogeneous differential equations with constant coefficients (3 classes)
• Solution of non-homogeneous higher-order differential equations using the method of Undetermined Coefficients (2 classes)
• Solution of non-homogeneous higher-order differential equations using the method of Variation of Parameters (2 classes)
• Solution of physical situations that can be modeled by higher-order differential equations (5 classes)
• Introduction of Laplace transforms (1 class)
• Laplace transforms of elementary functions (2 classes)
• Inverse Laplace transforms (2 classes)
• Solution of linear differential equations with constant coefficients using Laplace transforms (3-4 classes)
• Applications of Laplace transforms (2 classes)
• Exams (3 classes)
Coordinator
Ron Jorgensen
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