The Calculus Volume 3 Content Pack is one of three OpenStax Calculus offerings that you can use as a customizable starting point to a complete calculus course in Möbius. OpenStax Calculus covers the core concepts of calculus and helps students 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 3 covering: parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations. 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?

Course Structure

  • All content is organized into 9 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 59 lessons with illustrative visualizations, unlimited practice, helpful hints, and immediate feedback to promote Active Learning
  • Create different forms of assessment materials to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 550 questions that you can use to create your own course materials or supplement existing ones
9 units
59 lessons
0 assignments
550+ questions

Introductory Materials

Unit 1: Parametric Equations and Polar Coordinates

  • 1.1 Parametric Equations

  • 1.2 Calculus of Parametric Curves

  • 1.3 Polar Coordinates

  • 1.4 Area and Arc Length in Polar Coordinates

  • 1.5 Conic Sections

Unit 2: Vectors in Space

  • 2.1 Vectors in the Plane

  • 2.2 Vectors in Three Dimensions

  • 2.3 The Dot Product

  • 2.4 The Cross Product

  • 2.5 Equations of Lines and Planes in Space

  • 2.6 Quadric Surfaces

  • 2.7 Cylindrical and Spherical Coordinates

Unit 3: Vector-Valued Functions

  • 3.1 Vector-Valued Functions and Space Curves

  • 3.2 Calculus of Vector-Valued Functions

  • 3.3 Arc Length and Curvature

  • 3.4 Motion in Space

Unit 4: Differentiation of Functions of Several Variables

  • 4.1 Functions of Several Variables

  • 4.2 Limits and Continuity

  • 4.3 Partial Derivatives

  • 4.4 Tangent Planes and Linear Approximations

  • 4.5 The Chain Rule

  • 4.6 Directional Derivatives and the Gradient

  • 4.7 Maxima/Minima Problems

  • 4.8 Lagrange Multipliers

Unit 5: Multiple Integration

  • 5.1 Double Integrals over Rectangular Regions

  • 5.2 Double Integrals over General Regions

  • 5.3 Double Integrals in Polar Coordinates

  • 5.4 Triple Integrals

  • 5.5 Triple Integrals in Cylindrical and Spherical Coordinates

  • 5.6 Calculating Centers of Mass and Moments of Inertia

  • 5.7 Change of Variables in Multiple Integrals

Unit 6: Vector Calculus

  • 6.1 Vector Fields

  • 6.2 Line Integrals

  • 6.3 Conservative Vector Fields

  • 6.4 Green’s Theorem

  • 6.5 Divergence and Curl

  • 6.6 Surface Integrals

  • 6.7 Stokes’ Theorem

  • 6.8 The Divergence Theorem

Unit 7: Second-Order Differential Equations

  • 7.1 Second-Order Linear Equations

  • 7.2 Nonhomogeneous Linear Equations

  • 7.3 Applications

  • 7.4 Series Solutions of Differential Equations


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