Descrição do livro
This textbook is intended for a streamlined one-semester calculus course. Calculus is the science of change, but it can also be interpreted more narrowly as a study of motion. From the very beginning of calculus, its peculiar challenge has been to study continuous motion. Skillful manipulation of those formulas is what solves calculus problems. We take a different approach. Later, we supplement the incremental part with a study of continuous phenomena and the quantities infinitely divisible either by their nature or by assumption: time, space, mass, temperature, money, some commodities, etc. The order is opposite to that of the traditional approach, which relies on discretization: Motion through multi-dimensional spaces is considered in parallel.
Initially, we limit ourselves to incremental phenomena and the quantities indivisible by their very nature: people, animals, and other organisms, moments of time, locations of space, particles, some commodities, digital images and other man-made data, etc. Computers excel at handling these incremental processes.
Contents
Chapter 1: The differences and the sums
Chapter 2: The difference quotients and the Riemann sums
Chapter 3: The derivatives and the integrals
Chapter 4: Limits and continuity
Chapter 5: Additional topics
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