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Calculus I

Released on July 26, 2024!

Lumen Learning recently updated Calculus I with an eye on relevance, meaning, and representation of today’s diverse students. Each module begins with a readiness check inviting students to revisit critical skills from Precalculus and College Algebra. Essential math concepts appear throughout the text to help students who need further learning support. Calculus I includes embedded algorithmically generated practice questions that have feedback and embedded hints, worked-example videos, and self-check assessments. For even more practice opportunities, there are problem sets and an in-class activity for each module.

Keeping student engagement in mind, we have created a full suite of thought-provoking assignments: discussion prompts, Desmos interactives, application based assignments related to economics, computer science, biology, physics, and engineering, flipped classroom options, and a capstone project.

Faculty can adapt and use these materials in a variety of ways depending on their class structure and institutional requirements. All content is constructed around the goal of helping students master the learning outcomes for this course.

This course is designed to be used as part one of a three-part calculus sequence: Calculus I covers functions, limits, derivatives, and integration, Calculus II covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. Calculus III covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integrations, and second-order differential equations. 

 

Lumen Learning’s Calculus I consists of the following resources:

  • Online Homework Manager (OHM): A flexible, user-friendly math homework system with customizable learning content, assessments, and activities you can tailor to fit your needs. Request an OHM instructor account.
  • Outcome-aligned OER: Designed to replace expensive textbooks, this course curates open educational resources (OER) aligned with learning outcomes. Teach as-is or customize to fit your needs.
  • LMS Integration: This course may be delivered with seamless LMS integration and automatic grade return for Canvas, Blackboard, Brightspace, and Moodle.
  • Accessibility: Lumen is 100% committed to providing learning materials that are accessible to all learners. Lumen course materials are mobile-friendly.

Lumen Learning applies learning science research to the design of affordable digital courseware to engage students and empower them in building a strong foundation in Mathematics. OHM has fully digital course materials focused on hands-on practice, customizable template courses, interactive full e-text with immediate feedback that stands alone or integrates seamlessly into Brightspace, Canvas, Blackboard, or Moodle.

Contributors: Lumen Learning vetted and improved sources from Calculus Volume 1 by OpenStax.

Course Content

Basic Functions and Graphs  

  • Review of Functions
  • Basic Classes of Functions

More Basic Functions and Graphs

  • Trigonometric Functions
  • Inverse Functions
  • Exponential and Logarithmic Functions

Understanding Limits

  •  A Preview of Calculus
  •  Introduction to the limit of a function

Limits and Continuity 

  • The Limit Laws
  • Continuity
  • The Precise Definition of a Limit

Introduction to Derivatives

  • Defining the Derivative
  • The Derivative as a Function
  • Differentiation Rules
  • Derivatives as Rates of Change

Techniques for Differentiation

  • Derivatives of Trigonometric Functions
  • The Chain Rule
  • Derivatives of Inverse Functions
  • Implicit Differentiation
  • Derivatives of Exponential and Logarithmic Functions

Analytical Applications of Derivatives

  • Related Rates
  • Linear Approximations and Differentials
  • Maxima and Minima 
  • The Mean Value Theorem
  • Derivatives and the Shape of a Graph

Contextual Applications of Derivatives

  • Limits at Infinity and Asymptotes
  • Applied Optimization Problems
  • L’Hôpital’s Rule
  • Newton’s Method
  • Antiderivatives

Introduction to Integration

  • Approximating Areas
  • The Definite Integral
  • The Fundamental Theorem of Calculus
  • Integration Formulas and the Net Change Theorem

Techniques for Integration

  • Integration using Substitution
  • Integrals Involving Exponential and Logarithmic Functions   
  • Integrals Resulting in Inverse Trigonometric Functions
  • Approximating Integrals

Application of Integration

  • Areas Between Curves
  • Determining Volumes by Slicing
  • Volumes of Revolution: Cylindrical Shells
  • Arc Length of a Curve and Surface Area

Physical Applications of Integration

  • Physical Applications
  • Moments and Centers of Mass

Integration of Exponential, Logarithmic, and Hyperbolic Functions

  • Integrals, Exponential Functions, and Logarithms
  • Exponential Growth and Decay
  • Calculus of the Hyperbolic Functions

What People Are Saying

  • “OHM is fantastic for providing students with immediate feedback and remediation. It has helped my students improve their precision in answers.” – Royce Shelley, Salt Lake Community College

 

  • “Since using OHM, my students have a better understanding of the course topics.” – Bethzabeth Berrios, SUNY Rockland

 

  • “Since using OHM, I have achieved greater efficiency in giving feedback to students. OHM helps me to quickly let students know how well they are progressing through the course.” – Noel Whelchel, Atlanta Metropolitan State College

 

  • “Since using OHM, I have been able to hold students accountable for their homework. It is extremely comprehensive for the students and it saves me an immense amount of time.” – Mac Psachie, Hunter College CUNY

 

  • “OHM has greatly reduced the cost of an online homework program for our students.” – Jim Smart, Tallahassee Community College

 

Teaching with Lumen Course Materials

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  • Replace expensive textbooks | Ready-to-adopt open educational resources (OER) include text, videos, simulations, self-checks, and other interactives.
  • Choose affordability | Low cost to students.
  • Use better content | Continuous, data-driven improvements make OER content more effective at supporting learning.
  • Simplify access | Easy access to course materials in your LMS (Blackboard, Canvas, D2L, and Moodle) plus automatic grade return.
  • Improve student outcomes | Research shows Lumen course materials can improve academic performance, passing rates, and course completion.

FOR INSTRUCTORS

  • Connect with students | Instructor and student tools designed to help strengthen communication.
  • Save time | Start with curated, outcome-aligned OER and supplemental instructor resources like quiz banks, assignments, slide decks, etc. 
  • Customize your course | Freedom to tailor course content to fit your learning outcomes and instructional approach.
  • Enjoy awesome support | Faculty-friendly onboarding, training, and support. 
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FOR STUDENTS

  • Learn by doing | Online homework, self-check activities, and other interactive tools strengthen learning.
  • Engage from day one | Avoid falling behind with access to course materials from the first day of class.
  • Retain materials | Download a digital copy of course content to keep forever.
  • Become a better learner | Real-time feedback guides students on where to focus and how to improve.

Are you ready to get started with Lumen Learning digital courseware?

Great! Fill out our Explore a Course form, and our team will contact you promptly.

  • Sidney Tate, Ensign College
  • Daniel Breuer, Mitchell Community College
  • Ryan Melton, Kilgore College
  • Katie Christensen, Kennesaw State University
  • Dr. Lydia Maynard, Shenandoah University
  • Matthew Simmons, Florida State College at Jacksonville
  • Dr. Jackie Johnston, Northeast Texas Community College
  • Ariel Cintrón-Arias, East Tennessee State University
  • William Lindsey