Introduction to Calculus

Created by: DigitalEd, powered by Möbius

Description

The Introduction to Calculus Content Pack is a Möbius course developed by the team of content experts at DigitalEd that you can use as a customizable starting point to a complete calculus course in Möbius. This Content Pack explores: limits, derivatives, applications of derivatives, integrals, and application of integrals. This customizable resource contains 5 units of sectioned lessons and assignments enhanced with Möbius capabilities including text-based course material, images, plots and graphs, Interactive Narratives, Math Apps, both inline and algorithmic questions, and pre-built assessments.

How does Möbius take this Content Pack to the next level?

Course Structure

  • All content is organized into 5 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 33 lessons with illustrative visualizations, unlimited practice, helpful hints, and immediate feedback to promote Active Learning
  • Different forms of assessment materials are distributed across 24 assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 560 questions that you can use to create your own lessons and assignments or supplement existing ones
5 units
33 lessons
24 assignments
560+ questions

Unit 1: Limits

  • 1.1 Introduction to Limits

  • 1.2 One-sided Limits

  • 1.3 Computing Limits

  • 1.4 Infinite Limits

  • 1.5 Limits at Infinity

  • 1.6 Continuity

  • 1.7 Precise Definition of a Limit

Unit 2: Derivatives

  • 2.1 Definition and Properties

  • 2.2 Product and Quotient Rule

  • 2.3 Chain Rule

  • 2.4 Trigonometric Derivatives

  • 2.5 Exponential and Logarithmic Derivatives

  • 2.6 Implicit Differentiation

  • 2.7 Higher Order Derivatives

Unit 3: Applications of Derivatives

  • 3.1 Rate of Change, Extrema and Concavity

  • 3.2 Mean Value Theorem

  • 3.3 Sketching

  • 3.4 Linear Approximation

  • 3.5 Related Rates

  • 3.6 Optimization

  • 3.7 L'Hôpital's Rule

Unit 4: Integrals

  • 4.1 Indefinite Integrals

  • 4.2 Differential Equations

  • 4.3 Riemann Sums

  • 4.4 Definite Integrals

  • 4.5 Fundamental Theorem of Calculus

  • 4.6 Integration Using Substitution

  • 4.7 Numerical Integration

Unit 5: Applications of Integrals

  • 5.1 Area of a Region

  • 5.2 Mean Value Theorem for Integrals

  • 5.3 Arclength

  • 5.4 Volume of a Solid

  • 5.5 Work

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