Calculus 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.

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 Includes supplementary material: sn.pub/extras

Autorentext
Marco Baronti was born and grew up in Genova (Italy) where he got his Laurea in Mathematics in 1979. He won a scholarship from the C.N.R. in Genoa and subsequently a research grant from I.N.D.A.M. at the University of Bologna. In 1984 he became a researcher at the University of Parma and then associate professor in 1987 at the University of Ancona. In 1991 he returned to Genova, where he presently holds a position as associate professor in Mathematical Analysis. Enrico Calcagno was born and grew up in Genova (Italy) where he got his Laurea in Mathematics. He started his tenured position at the University of Genova in 1981. His scientific interests are mainly in Differential Geometry and Algebraic Topology. He has been involved for about forty years in a wide teaching activity for mathematicians, physicists, chemists, biologists, computer scientists, geologists and engineers. Filippo De Mari was born and grew up in Genova (Italy) where he got his Laurea in Mathematics in 1983. He obtained his Ph.D. in 1987 from Washington University in St. Louis (USA) and then held two post-doctoral positions in Bremen (Germany) 1988-89 and Torino (Italy) 1990-92. In 1992 he returned to Genova, where he presently holds a position as full professor in Mathematical Analysis. Robertus van der Putten was born and grew up in Sanremo (Italy). He got his Laurea in Mathematics in 1984 at the University of Genova. He obtained his Ph.D. in 1989 from the University of Milan. Since 1990, he is a researcher in Mathematical Analysis at the University of Genoa. His scientific interests are mainly in the Calculus of Variations. His main scientific interests may be grouped into following main areas. The first concerns the properties of energy functional integrals in the setting of nonlinear elasticity and the existence of the minimum in Sobolev spaces.

Inhalt
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.