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Interactive Applied Calculus, 1st edition

Published by Pearson (September 7, 2019) © 2020

  • Nathan P. Ritchey Edinboro University of PA , Youngstown State University
  • Darin Kapanjie Temple University
  • Katharine Fisher University of Toledo

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For courses in Applied Calculus.

Students learn calculus by seeing and doing calculus

Written in MyLab® Math, Interactive Applied Calculus weaves video, text and MyLab Math assessment questions into a seamless learning experience that helps more students master calculus and succeed in the course. Rather than introducing concepts all at once on a printed page, this unique online product uses Interactive Assignments that take a “watch a little, do a little” approach. Concepts are explained to students who then practice them immediately, leading to deeper understanding. The authors cover all key concepts in a way that students will find accessible and engaging. 

Hallmark features of this title

  • A “watch a little, do a little” learning experience:
    • 1) Students GET READY for the chapter by taking a Skills Check Quiz which populates a personalized Skills Review Homework that addresses prerequisite skills gaps.
    • 2) Students LEARN by working through Interactive Assignments and an accompanying Homework assignment for each section of the chapter.
  • Short, dynamic videos deliver concepts to unfold gradually; students learn at their own pace. Videos use visual and auditory cues, interactive figures, animations and more, and are authored and narrated by mathematicians who are active in the classroom.
  • The Implementation Guide provides course set-up and activity suggestions for multiple course formats.

Features of MyLab Math

  • Personal Inventory Assessments are online exercises designed to promote self-reflection and engagement. These 33 assessments include topics such as a Stress Management Assessment, Diagnosing Poor Performance and Enhancing Motivation, and Time Management Assessment. 
  • Learning Catalytics is a student response tool that uses students' smartphones, tablets, or laptops to engage them in more interactive tasks and thinking during lecture. Learning Catalytics fosters student engagement and peer-to-peer learning with real-time analytics. Use pre-built exercises created specifically for calculus.  
  • Interactive Figures illustrate key concepts and allow manipulation. They have been designed to be used in lecture and independently by students.
  • Setup & Solve exercises require students to show how they set up a problem as well as the solution, better mirroring what is required of students on tests.
  • Additional Conceptual Questions provide support for assessing concepts and vocabulary. Many of these questions are application oriented.
  • Study skills modules help students with the life skills that can make the difference between passing and failing. MathTalk videos highlight applications of the content of the course to business. The videos are supported by assignable exercises.

1. Linear Functions

  • 1-1 Slopes and Equations of Lines
  • 1-2 Linear Functions and Applications
  • 1-3 The Least Squares Line

2. Nonlinear Functions

  • 2-1 Properties of Functions
  • 2-2 Quadratic Functions; Translation and Reflection
  • 2-3 Polynomial and Rational Functions
  • 2-4 Exponential Functions
  • 2-5 Logarithmic Functions
  • 2-6 Applications: Growth and Decay; Mathematics of Finance

3. The Derivative

  • 3-1 Limits
  • 3-2 Continuity
  • 3-3 Rates of Change
  • 3-4 Definition of the Derivative
  • 3-5 Graphical Differentiation

4. Calculating the Derivative

  • 4-1 Techniques for Finding Derivatives
  • 4-2 Derivatives of Products and Quotients
  • 4-3 The Chain Rule
  • 4-4 Derivatives of Exponential Functions
  • 4-5 Derivatives of Logarithmic Functions

5. Graphs and the Derivative

  • 5-1 Increasing and Decreasing Functions
  • 5-2 Relative Extrema
  • 5-3 Higher Derivatives, Concavity, and the Second Derivative Test
  • 5-4 Curve Sketching

6. Applications of the Derivative

  • 6-1 Absolute Extrema
  • 6-2 Applications of Extrema
  • 6-3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand
  • 6-4 Implicit Differentiation
  • 6-5 Related Rates
  • 6-6 Differentials: Linear Approximation

7. Integration

  • 7-1 Antiderivatives
  • 7-2 Substitution
  • 7-3 Area and the Definite Integral
  • 7-4 The Fundamental Theorem of Calculus
  • 7-5 The Area Between Two Curves
  • 7-6 Numerical Integration

8. Further Techniques and Applications of Integration

  • 8-1 Integration by Parts
  • 8-2 Volume and Average Value
  • 8-3 Continuous Money Flow
  • 8-4 Improper Integrals

9. Multivariable Calculus

  • 9-1 Functions of Several Variables
  • 9-2 Partial Derivatives
  • 9-3 Maxima and Minima
  • 9-4 Lagrange Multipliers
  • 9-5 Total Differentials and Approximations
  • 9-6 Double Integrals

R. Algebra Reference

  • R-1 Polynomials
  • R-2 Factoring
  • R-3 Rational Expressions
  • R-4 Equations
  • R-5 Inequalities
  • R-6 Exponents
  • R-7 Radicals

Tables

  • Table 1. Formulas of Geometry
  • Table 2. Integrals
Answers to Selected Exercises
Photo Acknowledgements
Index

About our authors

Nathan P. Ritchey earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is former chair of the Department of Mathematics and Statistics at Youngstown State University and is currently a professor in the Department of Mathematics at Kent State University. He has published articles in economics, honors education, medicine, mathematics, operations research and student recruitment. Nate is a Consultant / Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations.

In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's "People Who Make a Difference Award," the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program.

Darin Kapanjie joined the Fox School of Business at Temple University in 2003. He has served as Managing Director of Online & Digital Learning and the Academic Director of Online MBA and BBA Programs. Darin helped build and manage the interactive and collaborative Fox Online model adopted for Temple's online business courses.

Darin is committed to teaching beyond the physical classroom. He is known for using cutting-edge teaching technologies, and was an early adopter of Class Capture, Wireless Tablet Annotation, and Pearson MyLabs; he was the first to use WebEx web conferencing tools to teach synchronous online classes at Temple. Darin has been honored with Philadelphia Business Journal's Top 40 Under 40 Award, the Musser Award for Leadership in Teaching, the Andrisani-Frank Excellence in Undergraduate Teaching Award, the Fox Online MBA Professor of the Year, the Innovation in Teaching Award at Temple's Classroom Engagement Through Technology Conference, a two-time winner of the Fox Business Honors Teacher of the Year and was the inaugural recipient of the John DeAngelo Innovative Leader in Technology Award. 

Katharine Fisher has taught mathematics at the college level for 25 years in Canada and the U.S. and is currently a Senior Lecturer at the University of Toledo. She completed her graduate and undergraduate studies in pure mathematics. In 2016 she received the College of Natural Sciences and Mathematics Excellence in Teaching Award from her university.

When Katharine was asked to develop a technology-rich applied calculus course for her university 10 years ago, she began making hundreds of videos to incorporate into her classes and received enthusiastic responses from her students. She has taught in a variety of course formats including hybrid, lab-based, online, and traditional lecture environments. When not teaching or developing course materials, she can be found running, cycling, or traveling with her husband and kids.

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