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Calculus II

Overview

Starting from the definition of the Riemann integral, this course explores some practical applications of integration, as well as the techniques commonly employed to find closed-form antiderivatives. The focus shifts briefly to countably infinite sequences and recursion equations, thereby providing the background for a multifaceted treatment of differential equations (graphically, verbally, symbolically, and numerically).

Selected learning outcomes

Evaluate integrals by using the appropriate techniques.
Set up, evaluate, and interpret integrals that represent arc length, area, volume, and average value.
Determine the convergence or divergence of sequences and series.
Represent functions with power series and approximate functions with Taylor polynomials.
Solve selected differential equations using graphical, numerical, and analytic methods.
Model with differential equations the phenomena of population growth, mixing problems, and other applications.

Resources

Course structure and syllabus excerpts

Sample lesson: applications of formal power series (PDF)

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