APEX Calculus

(4 reviews)


Gregory Hartman, Virginia Military Institute
Brian Heinold, Mount St. Mary’s University
Troy Siemers, Virginia Military Institute
Dimplekumar Chalishajar, Virginia Military Institute

Pub Date: 2014

ISBN 13: 978-1-5142251-5-8

Publisher: Independent

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Reviewed by Bethany Downs, Mathematics Instructor, Portland Community College, on 6/20/2018.

This a is a comprehensive text that covers all the basic material presented in a standard calculus sequence. It is clearly written, with … read more



Reviewed by Bryan Faulkner, Associate Professor, Ferrum College, on 2/9/2017.

The text covers material for a first semester course in differential calculus and begins integral calculus with antiderivatives and Riemann sums. The … read more



Reviewed by Samuel Horelick, instructor, J. Sargeant Reynolds Community College, on 2/9/2017.

The text covers all areas and skills of Calculus I, Calculus II, and Calculus III. This is an excellently written standard Calculus text that … read more



Reviewed by Anne Nelson Fisher, Mathematics Instructor, Central Lakes College, on 1/8/2016.

The text covers all necessary topics for Calculus I and II. However, no justification or proof for the derivatives of the natural exponential and … read more


Table of Contents

  • Chapter 1: Limits
  • Chapter 2: Derivatives
  • Chapter 3: The Graphical Behavior of Functions
  • Chapter 4: Applications of the Derivative
  • Chapter 5: Integration
  • Chapter 6: Techniques of Antidifferentiation
  • Chapter 7: Applications of Integration
  • Chapter 8: Sequences and Series
  • Chapter 9: Curves in the Plane
  • Chapter 10: Vectors
  • Chapter 11: Vector Valued Functions
  • Chapter 12: Functions of Several Variables
  • Chapter 13: Multiple Integrations

About the Book

This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 13. All three are available separately for free at www.vmi.edu/APEX.

About the Contributors


Gregory Hartman, PhD. Author. Associate Professor of Mathematics at Virginia Military Institute, where he has been on faculty since 2005. He earned his PhD in Mathematics from Virginia Tech in 2002.

Brian Heinold, PhD. Contributor. Associate Professor, Mathematics and Computer Science Department, Mount St. Mary's University. Heinold came to Mount St. Mary's in 2006, after receiving his doctorate from Lehigh University. Since then he has taught a variety of math and computer science courses. He has mentored several honors projects, coordinated the department's Smalltalk colloquium series and advised a number of COMAP teams. He has given presentations on fractals and mathematical imagery, teaching and graph theory.

Troy Siemers, PhD. Contributor. Head of the Applied Mathematics program at VMI. He earned his Ph. D. from the University of Virginia and previously led a summer program abroad in Lithuania.

Dimplekumar Chalishajar, PhD. Contributor. Assoicate Professor, Department of Applied Mathematics and Computer Science, Virginia Military Institute.


Jennifer Bowen, PhD. Associate Professor and Department Chair of Mathematics and Computer Science, The College of Wooster. Bowen earned a BA in Mathematics with Honors from Boston College, and both an MS and PhD in Mathematics from The University of Virginia. Bowen teaches a range of courses, including Math in Contemporary Society, Basic Statistics, Calculus I, Calculus II, Multivariate Calculus, Transition to Advanced Mathematics, and Abstract Algebra.