ELEMENTARY CALCULUS: AN INFINITESIMAL APPROACH PDF

Book Description:

This primary-year calculus book is centered round using infinitesimals, an approach largely neglected till lately for causes of mathematical rigor. It exposes college students to the instinct that initially led to the calculus, simplifying their grasp of the central ideas of derivatives and integrals. The creator additionally teaches the standard method, giving college students the advantages of both methods.

The book received major critical acclaim although the first review of the book was a bit harsh.

One of the author’ students based her thesis on the teachings of the book and found elementary calculus to be more helpful in solving problems than the standard method for doing these sums.

Editorial

Real and Hyperreal Numbers

Differentiation

Continuous Functions

Integral

Limits, Analytic Geometry, and Approximations

Applications of the Integral

Trigonometric Functions

Exponential and Logartihmic Functions

Exponential Functions

Logarithmic Functions

Derivatives of Exponential Functions and the Number e

Some Uses of Exponential Functions

Natural Logarithms

Some Differential Equations

Derivatives and Integrals Involving ln x

Integration of Rational Functions

Methods of Integrations

Extra Problems for Chapter 8

Infinite Series

Vectors

Vector Algebra

Vectors and Plane Geometry

Vectors and Lines in Space

Product of Vectors

Planes in Space

Vector Valued Functions

Vector Derivatives

Hyperreal Vectors

Extra Problems for Chapter 10Partial Differentiation

Multiple Integrals

Vector Calculus

Differential Equations

Year: 2013