Description
Book SynopsisCalculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear - or higher order - approximation is at the heart of calculus. Emphasizing the role of approximations in calculus, this book addresses topics such as derivatives, integrals, and sequences.
Table of ContentsPatterns and induction Divisibility Primes Derivatives and approximations of functions Antiderivatives and integration Distribution of primes Log, exponential, and the inverse trigonometric functions The mean value theorem and approximations Linearization topics Defining integrals, areas, and arclengths Improper integrals and techniques of integration The prime number theorem Local approximation of functions and integral estimations Sequences and series Power series and Taylor series More on series Limits of functions Differential equations Logical arguments Hints for selected problems Bibliography Index.
