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### Calculus for Engineers

Calculus
Robert Smith, Millersville University of Pennsylvania
Roland Minton, Roanoke College
1228 pages

Open: Calculus
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Preface

The calculus course is a critical course for science, technology, engineering, and math majors. This course sets the stage for many majors and is where students see the beauty of mathematics, encouraging them to take upper-level math courses. In a calculus market-research study conducted in 2008, calculus faculty pointed out three critical components to student success in the calculus.

The most critical is mastery of the prerequisite algebra and trigonometry skills. Our market research study showed that 58 percent of faculty mentioned that students struggled with calculus because of poor algebra skills and 72 percent said because of poor trigonometry skills. This is the number one learning challenge preventing students from being successful in the first calculus course.

The second critical component for student success is a text that presents calculus concepts, especially the most challenging concepts, in a clear and elegant manner. This helps students see and appreciate the beauty and power of mathematics.

TOC

CHAPTER 0 .. Preliminaries 1
CHAPTER 1 .. Limits and Continuity 47
CHAPTER 2 .. Differentiation 107
CHAPTER 3 .. Applications of Differentiation 173
CHAPTER 4 .. Integration 251
CHAPTER 5 .. Applications of the Definite Integral 315
CHAPTER 6 .. Exponentials, Logarithms and Other Transcendental Functions 375
CHAPTER 7 .. Integration Techniques 421
CHAPTER 8 .. First-Order Differential Equations 491
CHAPTER 9 .. Infinite Series 531
CHAPTER 10 .. Parametric Equations and Polar Coordinates 625
CHAPTER 11 .. Vectors and the Geometry of Space 687
CHAPTER 12 .. Vector-Valued Functions 749
CHAPTER 13 .. Functions of Several Variables and Partial Differentiation 809
CHAPTER 14 .. Multiple Integrals 901
CHAPTER 15 .. Vector Calculus 977
CHAPTER 16 .. Second-Order Differential Equations 1073
APPENDIX A .. Proofs of Selected Theorems A-1
APPENDIX B .. Answers to Odd-Numbered Exercises A-13