MTH 267 Differential Equations (3 cr.)
Introduces ordinary differential equations. Includes first order differential equations, second and higher order ordinary differential equations with applications, and numerical methods. Replaces MTH 279 or MTH 291. Prerequisite: Completion of MTH 264 with a grade of C or better. Lecture 3 hours per week.
Major Topics:
First Order Differential Equations
Numerical Approximations
Higher Order Differential Equations
Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
Series Solutions to Differential Equations
Laplace Transforms
Systems of Linear First-Order Differential Equations
Objectives and Skills:
Classify a differential equation as linear or nonlinear.
Understand and create a directional field for an arbitrary first-order differential equation.
Determine the order, linearity or non-linearity, of a differential equation.
Solve first order linear differential equations.
Solve Separable differential equations.
Solve initial value problems.
Use the Euler or tangent line method to find an approximate solution to a linear differential equation.
Solve second order homogenous linear differential equations with constant coefficients.
Determine the Fundamental solution set for a linear homogeneous equation.
Calculate the Wronskian.
Use the method of Reduction of order.
Solve nonhomogeneous differential equations using the method of undetermined coefficients.
Solve nonhomogeneous differential equations using the method of variation of parameters.
Solve applications of differential equations as applied to Newton’s Law of cooling, population dynamics, mixing problems, and radioactive decay.
Solve springs-mass-damper, electrical circuits, and/or mixing problems (2nd order)
Solve application problems involving external inputs (non-homogenous problems).
Use the definition of the Laplace transform to find transforms of simple functions
Find Laplace transforms of derivatives of functions whose transforms are known
Find inverse Laplace transforms of various functions.
Use Laplace transforms to solve ODEs.