Introduction to Calculus - volume 1 in pdf

This is the first volume of an introductory calculus presentation intended for future scientists and engineers. Volume I contains five chapters emphasizing fundamental concepts from calculus and analytic geometry and the application of these concepts to selected areas of science and engineering. Chapter one is a review of fundamental background material needed for the development of differential and integral calculus together with an introduction to limits. Chapter two introduces the differential calculus and develops differentiation formulas and rules for finding the derivatives associated with a variety of basic functions. Chapter three introduces the integral calculus and develops indefinite and definite integrals. Rules for integration and the construction of integral tables are developed throughout the chapter. Chapter four is an investigation of sequences and numerical sums and how these quantities are related to the functions, derivatives and integrals of the previous chapters. Chapter five investigates many selected applications of the differential and integral calculus. The selected applications come mainly from the areas of economics, physics, biology, chemistry and engineering.

Contents

• Chapter 1 Sets, Functions, Graphs and Limits
• Chapter 2 Differential Calculus
• Chapter 3 Integral Calculus
• Chapter 4 Sequences, Summations and Products
• Chapter 5 Applications of Calculus