Introduction to Calculus

Created by: DigitalEd, powered by Möbius

Description

This Introduction to Calculus Content Pack is a full Möbius course developed by the team of content experts at DigitalEd and is designed as an introductory undergraduate online course in single variable differential and integral calculus. 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
  • Concepts are presented across 33 lessons that include 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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