Description

The Calculus Volume 2 Content Pack is the second of three OpenStax Calculus offerings that have been transformed into a turn-key Möbius online course. OpenStax Calculus guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, OpenStax Calculus with Möbius is offered as a typical two- or three-semester general calculus course, with Volume 2 covering: integration, differential equations, sequences and series, and parametric equations and polar coordinates. This customizable resource includes all traditional OpenStax features such as chapter introductions, sections, review material, and practice tests, and has been enhanced with Möbius capabilities including algorithmic questions, in-lesson questions with unlimited practice, helpful hints, and immediate feedback.

How does Möbius take OpenStax to the next level?

  • All chapter sections delivered as Möbius lessons with checkpoint questions embedded right inside of lessons.

  • Learn how Möbius’ unique STEM question types provide the best STEM learning experience.

  • Deliver OpenStax exercises using over 50 configurable assessment properties.

Course Structure

  • All content is organized into 9 Units for easy navigation
  • Concepts are presented across 59 Lessons that include illustrative visualizations, unlimited practice, helpful hints, and immediate feedback to promote Active Learning
  • Different forms of assessment materials are distributed across 6 Assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 600 questions that you can use to create your own lessons and assignments or supplement existing ones
9 units
59 assignments
6 lessons
600+ questions

Unit 1: Integration

  • 1.1 Approximating Areas

  • 1.2 The Definite Integral

  • 1.3 The Fundamental Theorem of Calculus

  • 1.4 Integration Formulas and the Net Change Theorem

  • 1.5 Substitution

  • 1.6 Integrals Involving Exponential and Logarithmic Functions

  • 1.7 Integrals Resulting in Inverse Trigonometric Functions

Unit 2: Applications of Integration

  • 2.1 Areas between Curves

  • 2.2 Determining Volumes by Slicing

  • 2.3 Volumes of Revolution: Cylindrical Shells

  • 2.4 Arc Length of a Curve and Surface Area

  • 2.5 Physical Applications

  • 2.6 Moments and Centers of Mass

  • 2.7 Integrals, Exponential Functions, and Logarithms

  • 2.8 Exponential Growth and Decay

  • 2.9 Calculus of the Hyperbolic Functions

Unit 3: Techniques of Integration

  • 3.1 Integration by Parts

  • 3.2 Trigonometric Integrals

  • 3.3 Trigonometric Substitution

  • 3.4 Partial Fractions

  • 3.5 Other Strategies for Integration

  • 3.6 Numerical Integration

  • 3.7 Improper Integrals

Unit 4: Introduction to Differential Equations

  • 4.1 Basics of Differential Equations

  • 4.2 Direction Fields and Numerical Methods

  • 4.3 Separable Equations

  • 4.4 The Logistic Equation

  • 4.5 First-order Linear Equations

Unit 5: Sequences and Series

  • 5.1 Sequences

  • 5.2 Infinite Series

  • 5.3 The Divergence and Integral Tests

  • 5.4 Comparison Tests

  • 5.5 Alternating Series

  • 5.6 Ratio and Root Tests

Unit 6: Parametric Equations and Polar Coordinates

  • 6.1 Power Series and Functions

  • 6.2 Properties of Power Series

  • 6.3 Taylor and Maclaurin Series

  • 6.4 Working with Taylor Series

Unit 7: Parametric Equations and Polar Coordinates

  • 7.1 Parametric Equations

  • 7.2 Calculus of Parametric Curves

  • 7.3 Polar Coordinates

  • 7.4 Area and Arc Length in Polar Coordinates

  • 7.5 Conic Sections

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