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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