Prep for GRE® Subject Math Exam-Module2:Single Var Calculus

Explore limits of sequences, convergence criteria, and partial limits, and apply arithmetic operations, the sandwich and pizza theorems, and the connection to limits of functions.

Explore limits of functions through epsilon-delta and sequence definitions, including left and right limits, one-sided limits, infinity limits, continuity, and the sandwich theorem with visual intuition.

Master limits of irrational functions, analyzing polynomial over polynomial forms, identifying continuity away from denominator roots, and using derivatives to resolve 0/0 and determine infinity by leading powers.

Examine continuity and differentiability, including sharp edges like absolute value at zero, and use the derivative to assess maxima, minima, and inflection via the mean value theorem.

Explore basics of integration, including antiderivatives and continuity conditions, and apply techniques like substitution, integration by parts, partial fractions, and polynomial division to evaluate complex integrals.

Apply definite integrals via Riemann sums, using upper and lower bounds to converge to the Riemann integral for bounded, piecewise continuous functions and to compute area under the graph.

solve a polar integration problem by converting to r(θ), recognizing a cardioid, and integrating over θ from 0 to 2π to find the area.

Apply Leibniz rule for differentiating under the integral with variable limits, use the fundamental theorem, and analyze improper integrals at infinity along with convergence criteria for power and geometric series.

Explore limits of integrals and sums, convergence criteria, and tools like the sandwich theorem, absolute convergence, limit comparison, and root and ratio tests.

Examine function sequences, pointwise and uniform convergence, and the role of power series. Apply Taylor expansions, term-by-term differentiation and integration, and error estimation to GRE single-variable calculus problems.

Tackle the final quiz with a few questions, each appearing for about half a minute; pace yourself, note that answers are in the next lecture, and good luck.

Cover substitution and anti-derivative techniques, convergence criteria for improper integrals, monotone function discontinuities, series expansions, and applications to Riemann sums and volumes of revolution.

Review the handouts for single variable calculus to reinforce key concepts and problem-solving strategies for the GRE subject math exam module 2.

Complete this module, one of eight in our GRE subject math prep course, and reinforce mastery with full practice exams, study plan, handouts, and updates via mailing list and Facebook.