Calculus Problems

Authors: Marco Baronti, Filippo De Mari, Robertus van der Putten, Irene Venturi



Several step-by-step (and absolutely to-the-point!) tutorials help the reader to more quickly learn the material

Offers solved problems that are similar to those assigned in actual tests

Combines a self-contained approach with accessible solved problems

This book, intended as a practical working guide for calculus students, includes 450 exercises. It is designed for undergraduate students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, and will greatly benefit anyone seeking a problem-solving approach to calculus. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter.

A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage.

Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-world applicability.

Table of contents (16 chapters)

Front Matter

Manipulation of Graphs

Invertible Mappings

Maximum, Minimum, Supremum, Infimum

Sequences

Limits of Functions

Continuous Functions

Differentiable Functions

Taylor Expansions

The Geometry of Functions

Indefinite and Definite Integrals

Improper Integrals and Integral Functions

Numerical Series

Separation of Variables

First Order Linear Differential Equations

Constant Coefficient Linear Differential Equations

Miscellaneous

Back Matter

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