Calculus problems
著者
書誌事項
Calculus problems
（Collana unitext, v. 101 . La matematica per il 3+2）
Springer, c2016
- : [pbk.]
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注記
Includes bibliographical references (p. 361) and index
内容説明・目次
内容説明
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.
目次
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.
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