Calculus Volume 2

Created by: OpenStax, powered by Möbius

Description

The Calculus Volume 2 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 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?

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 650 questions that you can use to create your own course materials or supplement existing ones
9 units
59 lessons
0 assignments
650+ questions

Introductory Materials

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

Appendices

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