Overview:
This course introduces the math, science, and engineering student to the beginnings of the theory and application of differential equations.  After beginning with begin with some motivational settings, we will proceed to

• A qualitative introduction to DE applications such as projectile motion, population growth, radioactive decay, heating and cooling, and periodic motion.  
• Theory of solutions including slope fields and domains of solutions.
• Applications and solution techniques for first order equations – separable, linear, exact, and integral equations
• Numerical techniques and approximate solutions, including computer (Maple) implementation of Euler and Runge-Kutta methods
• Linear second order applications and solutions.  We will cover periodic motion (springs and pendula), the mathematics of RLC circuits, characteristic equations, undetermined coefficients, and variation of parameters.
• Series solutions to DE.
• LaPlace Transforms, inverse transforms, IVPs, and convolutions. 
• Linear systems of equations, with applications, matrix techniques, the theory of solutions and homogeneous systems.
• If time permits we begin Boundary Value Problems and Fourier Series.