Topics Covered:
First-order differential equations:WRITING UP HOMEWORK SOLUTIONS: You are expected to show all essential steps in solving a problem. Draw appropriate figures. If in doubt, PUT IT IN! Make your solution flow. Ask yourself the question: "If I were the reader, how would I score this problem?'' Numerical answers alone, single words "yes" or "no", etc., are NEVER, EVER acceptable as complete answers. One of the skills you are expected to learn in this class is that of communicating mathematics clearly and completely in writing. Writing up homework exercises is your opportunity to hone these skills. Your grade depends on it!
Separable variables, homogeneous equations, exact equations, linear
equations, orthogonal trajectories, applications of linear equations.
Linear differential equations of higher order:
Initial-value and boundary-value problems, linear dependence and
independence, solutions, constructing a second solution from a known
solution, homogeneous linear equations with constant coefficients,
undetermined coefficients, variation of parameters, applications to:
simple harmonic motion, damped, and forced motion.
Differential equations with variable coefficients:
Power series solutions, ordinary and singular points.
The Laplace Transform:
The transform and its inverse; operational properties: translation
theorems, derivatives of a transform, transforms of derivatives and
integrals, periodic functions; applications
Systems of linear differential equations:
Laplace transform method, systems, use of matrices, homogeneous
linear systems.
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