Concise Modular Calculus 39 97

Defines improper integrals near vertical asymptotes. Finishes the discussion of the Gamma function. Introduces convergence tests ...

Computes areas under curves and areas between curves with the Fundamental Theorem of

2/2 on Change of Variables & Surface Area) Discusses the multivariable change of variable formula. Explains how to encode a ...

Introduces definite integrals as limits of Riemann sums. Shows how definite integrals are used to compute areas, displacements ...

Explains what

Introduces power series as a way to represent functions. Explains the radius of convergence, the algebra, derivatives and ...

Visually illustrates the typical ways in which limits are used: Divisions by zero, defining derivatives, defining integrals and ...

Justifies one sided limits through "failure modes" for limits. Analyzes one sided limits and vertical asymptotes graphically and ...

(Alternative 1b/5 on Series) Introduces infinite series as a vehicle to simulate the "summation of infinitely many numbers." Explains ...

Introduces the alternating series test and the limit comparison test. Shows how, for the partial sums of certain series, to estimate ...

Incorporates major concepts of

Presents the derivative form of the fundamental theorem of

Demonstrates that the Mean Value Theorem is the tool that connects slopes (a microscopic concept) with growth behavior (a ...