Calculus with Vectors

ISBN-13: 9783319094373 / Angielski / Twarda / 2014 / 399 str.

Jay S. Treiman

Opis

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises.The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.

Recenzje

"This book is useful to university students in pure and applied mathematics, engineering, etc. The theoretical part is well presented in each chapter. The applications - solved problems and proposed problems - are gradually presented in order to obtain a good understanding of the theoretical notions." (Cristinel Mortici, zbMATH, Vol. 1325.00003, 2016)

Spis treści

​Preface.- 1. Points and Vectors.- 2. Limits and Derivatives.- 3. More on Limits.- 4. Rules for Finding Derivatives.- 5. Applications of Limits and Derivatives.- 6. Integration.- 7. The Cross Product.- 8. More Techniques of Integration.- 9. Applications of Integration.- 10. Series.- Index.

O autorze

Jay Treiman is a Professor of Mathematics at Western Michigan University.

Blurb

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes.

The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.