# Calculus with Vectors

• Jay S. Treiman
Textbook

1. Front Matter
Pages i-ix
2. Jay S. Treiman
Pages 1-32
3. Jay S. Treiman
Pages 33-67
4. Jay S. Treiman
Pages 69-85
5. Jay S. Treiman
Pages 87-120
6. Jay S. Treiman
Pages 121-168
7. Jay S. Treiman
Pages 169-201
8. Jay S. Treiman
Pages 203-230
9. Jay S. Treiman
Pages 231-288
10. Jay S. Treiman
Pages 289-334
11. Jay S. Treiman
Pages 335-380
12. Back Matter
Pages 381-399

### Introduction

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.

### Keywords

L’Hopital’s Rule Newton's method inverse trigonometric functions one-sided limits vector-valued functions

#### Authors and affiliations

• Jay S. Treiman
• 1
1. 1.Department of MathematicsWestern Michigan UniversityKalamazooUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-09438-0
• Copyright Information Springer International Publishing Switzerland 2014
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-319-09437-3
• Online ISBN 978-3-319-09438-0
• Series Print ISSN 1867-5506
• Series Online ISSN 1867-5514
• Buy this book on publisher's site