Calculus Problems

Description

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. Front Matter....Pages i-xiii Manipulation of Graphs....Pages 1-28 Invertible Mappings....Pages 29-40 Maximum, Minimum, Supremum, Infimum....Pages 41-51 Sequences....Pages 53-64 Limits of Functions....Pages 65-87 Continuous Functions....Pages 89-103 Differentiable Functions....Pages 105-130 Taylor Expansions....Pages 131-145 The Geometry of Functions....Pages 147-165 Indefinite and Definite Integrals....Pages 167-189 Improper Integrals and Integral Functions....Pages 191-216 Numerical Series....Pages 217-235 Separation of Variables....Pages 237-258 First Order Linear Differential Equations....Pages 259-273 Constant Coefficient Linear Differential Equations....Pages 275-296 Miscellaneous....Pages 297-306 Back Matter....Pages 307-366