209 MATH

1. Sequences limit of a sequence (definition and theorems), infinite series, geometric series, convergent and divergent series, tests for convergence (integral, comparison and ratio tests), alternating series, absolute convergence, conditional convergence, Definition of Power Series,  representation of functions by power series, differentiation and Integration of power Series, Taylor and Maclaurin series
2. Definition of a Diff Eq , Classification of Diff Eq ,initial value problems, existence and uniqueness theorem, Separable equations (Separable variable). Linear equations, exact equations, Integrating factor. Solutions by substitution: Homogeneous equations. Bernoulli equation, equations with linear coefficients. Linear Models: Growth and decay, Newton’s Law of cooling/ warming.  Cauchy-Euler Equation. Orthogonal functions and Fourier Series. Fourier cosine and sine series.