MA 241 - Analytic Geometry and Calculus II

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Additional Integration Techniques – Trig Integrals, Partial Fractions – Trig Substitution – Long Division – Trapezoidal Rule, Simpsons Rule – Simpsons Rule Cont, Error Bound – Infinite Intervals – Discontinuous Integrands, Comparison Theorem – Area between curves, Area enclosed by Parametric Curves – Area enclosed by Parametric Curves – Solids of Revolution – Solids of Revolution review, Cylindrical Shells – Arc Length – Average Value of a Function Mean Value Theorem for Integrals – Applications to Physics and Engineering – Hooke’s Law – Spring Problem – Pumping Problem – Moments and Centers of Mass – Modeling with Differential Equations – Direction Fields and Euler’s Method – Separable Differential Equations – Orthogonal Trajectories – Exponential Growth and Decay – Compound Interest – Newton’s Law of Cooling – The Logistic Equation – 2nd Order Linear Differential Equations – Terms Auxiliary equation

Nonhomogeneous Linear Equations – Sequences – Convergence and Divergence – Alternating signs – Fibonacci sequence – Geometric Progression – Series – Geometric Progression Convergence and Value – Derivation and Integration – Telescoping – Harmonic – Divergence Test – Convergence Rules – Taylor and MacLaurin Series – Binomial Series Derivation –

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