Understanding Calculus II: Problems, Solutions, and Tips

Learning what distinguishes Calculus II from Calculus I; embarking on a three-episode review; the top 10 student pitfalls from precalculus; a refresher on basic functions and their graphs, which are essential tools for solving calculus problems.

Reviewing the concept of derivatives while recalling the derivatives of trigonometric, logarithmic and exponential functions; applying the knowledge of derivatives to the analysis of graphs; closing by reversing a problem.

Covering the basic facts of integration; an example of integration by substitution; turning to definite integrals and the area problem; the fundamental theorem of calculus; the second fundamental theorem of calculus; solving a differential equation.

Learning various techniques for solving differential equations; separation of variables; Euler's method, which is the simplest numerical technique for finding approximate solutions; looking at growth and decay models, with two applications.

Examining orthogonal trajectories, which are curves that intersect a given family of curves at right angles; these occur in thermodynamics and other fields; developing the logistic differential equation, which is widely used in mathematical biology.

Investigating linear differential equations; the key to their solution is what Professor Edwards calls the "magic integrating factor"; trying several examples and applications; returning to an equation involving Euler's method.