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Contains solutions to the odd-numbered problems from the end-of-section exercises and Chapter Review Tests. Solutions are given for the full version of the student text. (Student Solution Manual, Brief features Chapters 1-7 of the full text.)
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An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.
The only text on the market that truly integrates calculus with precalculus and algebra in a two-semester course appropriate for math and science majors, Integrated Calculus uses a student-friendly approach without sacrificing rigor. Students learn about logic and proofs early in the text then apply these skills throughout the course to different types of functions.This combined approach allows students to eliminate a pure precalculus course and focus on calculus, with a "point-of-use" presentation of necessary algebra and precalculus concepts. Algebra and precalculus topics are integrated into the text to provide instruction and review just prior to using these concepts in a calculus context. This helps students see the relevance and connectedness of the mathematics. Because of the text's integration of algebra, limits, and derivatives, students are able to fully review all the components of a specific function. Concept Questions begin each exercise set and test students' understanding of definitions, theorems, and concepts from the reading. The remaining exercises are divided into Skills, Applications, and Proofs sections.
A high-school mathematics teacher who learned how to sequence and present ideas during his 30-year career presents a bridge for beginning calculus students to study independently in preparation for a traditional calculus curriculum or as supplemental material for students who are currently in a calculus class.
This text embraces the reform being called for in calculus teaching and learning. All key concepts are presented following the Rule of Three: from a graphical, numerical, and algebraic viewpoint, encouraging students to visualise, verbalise and write.
Applied Calculus embraces the reform being called for in calculus teaching and learning. All key concepts are presented following the Rule of Three: from a graphical, numerical, and algebraic viewpoint, encouraging students to visualize, verbalize and write.