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Calculus II
Calculus II 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 I 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 II 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 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 II 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
Module 1: Use basic integration techniques to calculate area
- Apply summation rules
- Interpret definite integrals
- Explain the Fundamental Theorem of Calculus
- Use the net change theorem
- Apply substitution to indefinite and definite integrals
- Integrate functions involving exponential and logarithmic functions
- Integrate functions resulting in inverse trigonometric functions
- Approximate integrals when the antiderivative is impossible to calculate
Module 2: Apply integrals to geometric application, physical application, and modeling problems
- Calculate the areas of curved regions by using integration methods
- Find the volume of a solid of revolution using various methods
- Compare different integration methods for determining volume
- Calculate the arc length of a curve and the surface area of a solid of revolution
- Quantify mass, density, work, force, and pressure using integration
- Determine the center of mass in various dimensions
- Apply integration and derivatives to exponential and natural logarithmic functions
- Apply the exponential growth model to explain real world concepts
- Use integrals and derivatives to evaluate hyperbolic functions
Module 3: Perform additional integration calculations and approximations
- Apply the integration-by-parts formula to solve indefinite and definite integrals
- Solve integration problems involving trigonometric functions
- Solve integration problems involving trigonometric substitution
- Identify linear and quadratic factors in rational functions
- Solve integration problems using alternative strategies
- Use numerical integration techniques to determine the accuracy of integrals
- Evaluate improper integrals
Module 4: Develop methods to solve differential equations
- Analyze differential equations and their solutions
- Evaluate direction fields of first-order differential equations
- Apply separation of variables to differential equations
- Interpret the results and solution curves of logistic equations
- Solve first-order linear equations
Module 5: Understand infinite series and how to use them to evaluate functions
- Evaluate sequences by determining the formula, the limit, and the divergence
- Interpret infinite, geometric, and telescoping series
- Use the divergence and integral tests to determine the convergence or divergence of a series
- Use the comparison test to determine the convergence of a series
- Assess alternating series by testing for convergence and estimating the sum
- Apply the ratio and root tests to a series
Module 6: Represent functions using power series
- Use power series to represent functions and determine convergence
- Apply the properties of a power series
- Examine Taylor and Maclaurin series
- Apply Taylor series to solve differential equations and nonelementary integrals
Module 7: Describing curves through parametric equations and polar coordinates
- Identify parametric equations
- Apply calculus to parametric equations
- Understand polar coordinates and their application
- Determine area and arc length in polar coordinates
- Distinguish properties of parabolas, ellipses, and hyperbolas
Teaching with Lumen Course Materials
- 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.
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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