Applied Differential Equations and Vector Calculus MATH 4499

Upon successful completion of this course, the student will be able to:

• Model physical processes using higher-order differential equations. [1, 2]
• Use eigenvalue methods to analytically solve homogeneous higher-order linear differential equations with constant coefficients and use the methods of undetermined coefficients and variation of parameters to extend this to the inhomogeneous case. [1, 2]
• Analytically solve first- and second-order linear systems of differential equations in both the homogeneous and inhomogeneous cases. [1]
• Solve higher-order linear differential equations using series methods about ordinary and regular singular points. [1, 2]
• Use Laplace transform methods, including partial fractions and convolutions, to solve differential equations expressing initial value problems. [1, 2]
• Use Fourier integral methods to solve initial and boundary value problems involving separable partial differential equations. [1, 2]
• Apply vector differential and integral operations to vector fields, such as in fluid flow, solid mechanics and electric fields, and to scalar fields such as fluid density. [1]
• Interpret the physical meaning of curl and divergence operations when applied to the dynamics of fluid flow. [1]
• Distinguish between conservative and non-conservative fields and the implication for calculations. [1]
• Use vector theorems - Gauss' Divergence, Green's and Stokes' theorems - to transform between different vector calculus calculations in order to solve most efficiently. [1, 2]
• Demonstrate proficiency with the mathematics for fluid dynamics and mechanics of solids. [1, 2]

Effective as of Fall 2018