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Calculus 2

Calculus 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. Each module begins with a prerequisite material review section, in which critical skills from Precalculus, College Algebra, and Calculus 1 are revisited. Additionally, just-in-time reviews of essential math concepts appear throughout the text to help those students who need further learning support. Calculus 2 includes embedded algorithmically generated practice questions, worked-example videos, and a complete set of outcome aligned online assessments in OHM.

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 1 covers functions, limits, derivatives, and integration, Calculus 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. Calculus 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integrations, and second-order differential equations.

Lumen Learning’s Calculus 2 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 2 by OpenStax.

 

Course Content

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

Advanced Integration Techniques

  • Integration by Parts
  • Trigonometric Integrals
  • Partial Fractions
  • Other Strategies for Integration

Numerical and Improper Integration

  • Numerical Integration Methods
  • Error Analysis in Numerical Integration
  • Improper Integrals

Introduction to Differential Equations

  • Basics of Differential Equations
  • Direction Fields and Euler’s Method
  • Separation of Variables
  • First-Order Linear Equations and Applications

Sequences and Series Foundations

  • Sequences and Their Properties
  • Introduction to Series
  • The Divergence and Integral Tests
  • Comparison Tests
  • Alternating Series
  • Ratio and Root Tests

Power Series and Applications

  • Introduction to Power Series
  • Operations with Power Series
  • Taylor and Maclaurin Series
  • Applications of Series

Parametric Curves and Their Applications

  • Fundamentals of Parametric Equations
  • Calculus with Parametric Curves

Polar Coordinates and Conic Sections

  • Understanding Polar Coordinates
  • Area and Arc Length in Polar Coordinates
  • Conic Sections

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.

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  • Ryan Melton, Kilgore College
  • Matthew Simmons, Florida State College at Jacksonville
  • William Lindsey
  • Kaiwen Amrein, Portland Community College
  • Brenna Wragge
  • Katie Christensen, Kennesaw State University
  • Sidney Tate, Ensign College