Differential Equations. Advanced coursework in Physics requires skills in working with differential equations. Therefore, it is recommended that students take a course in differential equations as part of their Associates degree program. Differential Equations is a recommendation only. Students are not required to complete the course as part of the major or the articulation Agreement, and therefore, will not be penalized for not completing the course prior to transferring into the parallel bachelor degree.
Differential Equations a minimum of 3 credits Completion of comparable coursework will at the minimum yield competency in: o Classifying differential equations as ordinary and partial; classifying ordinary differential equations (ODEs) by linearity and by order. o Understanding the concept of solutions and verify solutions by substitution. o Explaining the difference of the general solutions of ODEs and the solutions to initial value problems (IVPs). o Understanding the concepts of direction fields associated with first order ODEs and integral curves. o Sketching the direction fields and some typical integral curves for such ODEs. o Recognizing various types of first order ODEs and find their general solutions by elementary integration. o Finding the solution of an IVP of such equations by determining the appropriate constant. Such equations should include linear first order and separable ODEs, Bernoulli equations, homogeneous equations, and exact equations. o Identifying simple integral factors for certain non-exact equations. o Developing a sense of solving an ODE using appropriate substitutions. o Determining if a first order linear IVP has a unique solution and the interval of existence. o Understanding the result on existence/uniqueness/interval of existence of solutions of an IVP of a general first order ODE. o Recognizing the differences between linear and nonlinear ODEs. o Setting up and solving IVPs for various applied problems such as those involving exponential growth/decay, mixing, and mechanics/physics. o Understanding the logistic model in population dynamics. o Understanding stability properties of equilibrium solutions of first order autonomous equations and determine their stability properties using linear stability criteria.
