Calculus Problems

ISBN-13: 9783319154275 / Angielski / Miękka / 2016 / 366 str.

Filippo De Mari; Marco Baronti; Robertus Putten

Opis

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.

Spis treści

1 Manipulation of Graphs.- 2 Invertible Mappings.- 3 Sequences.- 4 Maxima, minima, least upper bound, greatest lower bound.- 5 Limits of functions.- 6 Continuous Functions.- 7 Differentiable Functions.- 8 Taylor Expansions.- 9 Geometry of functions: extrema and convexity.- 10 Indefinite and Definite Integrals.- 11 Improper Integrals and Integral Functions.- 12 Numerical Series.- 13 Separation of Variables.- 14 First Order Linear Differential Equations.- 15 Constant Coefficient Differential Equations.

O autorze

Marco Baronti was born in Genova in 1956. Since 1990 he is Associate Professor in Mathematical Analysis at the University of Genova. His scientific interests are mainly in Functional Analysis and in particular in Geometry of Banach Spaces. 

Filippo De Mari was born in Genova in 1959. In 1987 he received his Ph.D. from Washington University in St. Louis, USA. Since 1998 he is Associate Professor in Mathematical Analysis at the University of Genova. His scientific interests are mainly in Harmonic Analysis, Representation Theory and Lie Groups.

Robertus van der Putten was born in Sanremo in 1959. In 1989 he received his Ph.D. from the University of Milan. Since 1990 he is Researcher in Mathematical Analysis at the University of Genova. His scientific interests are mainly in Calculus of Variations. 

Irene Venturi was born in Viareggio in 1978. In 2009 she received her Ph.D. from the University of Genova and in 2011 a Masters in Security Safety and Sustainibility in Transportation Systems. She is a teacher in Mathematics and has several editorial collaborations.

Blurb

This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. 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.