Calculus for Sciences I & II

Created by: University of Waterloo, powered by Möbius

Description

The Calculus for Sciences I & II Content Pack is a Möbius course developed by the University of Waterloo that you can use as a customizable starting point to a complete calculus course in Möbius. This Content Pack spans two semesters of calculus and covers applications in the sciences. Topics covered include: functions, limits, differentiation, integration, series and sequences, differential equations, parametric curves, vector functions, and introduces multivariate calculus. This customizable resource contains 12 units of sectioned lessons and assignments enhanced with Möbius capabilities including in-lesson questions, adaptive questions, Math Apps, interactive narratives, immediate feedback, and end-of-lesson assignments.

How does Möbius take the University of Waterloo’s content to the next level?

  • Lessons contain interactive elements like Interactive Narratives, HTML objects, Math Apps, or Geogebra applications to help solidify difficult STEM concepts.

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

  • Work with over 50 configurable assessment properties when modifying existing or building your own assessments.

Course Structure

  • All content is organized into 12 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 73 lessons that promote Active Learning by including illustrative visualizations, interactive elements, and example problems with immediate feedback
  • Different forms of assessment materials are distributed across 86 assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 1980 questions that you can use to create your own lessons and assignments or supplement existing ones
12 units
73 lessons
86 assignments
1980+ questions

Unit 1: Functions

  • 1.1 Introduction to Calculus

  • 1.2 Functions

  • 1.3 Combining Functions

  • 1.4 Reversing a Function

  • 1.5 Modeling with Functions

  • 1.6 Exponential Functions

  • 1.7 Logarithmic Functions

  • 1.8 Trigonometric Functions

Unit 2: Limits

  • 2.1 Limits

  • 2.2 Instantaneous Velocity

  • 2.3 Limit of a Function at a Point

  • 2.4 Continuity

Unit 3: Differentiation

  • 3.1 The Derivative

  • 3.2 Differentiation Rules

  • 3.3 The Chain Rule

  • 3.4 Implicit Differentiation

Unit 4: Applications of Differentiation

  • 4.1 Modeling With Derivatives

  • 4.2 Exponential Processes

  • 4.3 Linearization

  • 4.4 Newton's Method

  • 4.5 Indeterminate Forms

  • 4.6 Extreme Values

  • 4.7 Shapes of Graphs

  • 4.8 Optimization

Unit 5: Introduction to Integration

  • 5.1 Anti-derivatives

  • 5.2 Sigma Notation

  • 5.3 Riemann Sums

  • 5.4 Definite Integrals

  • 5.5 The Fundamental Theorem of Calculus

  • 5.6 Indefinite Integrals

  • 5.7 Integration by Substitution

  • 5.8 Areas Between Curves

Unit 6: Integration

  • 6.1 Review of Integration

  • 6.2 Surface Area

  • 6.3 Arc Length

  • 6.4 Volumes by Shells

  • 6.5 Areas and Volumes

  • 6.6 Improper Integrals

  • 6.7 Integration by Partial Fractions

  • 6.8 Trigonometric Substitutions

  • 6.9 Integration by Parts

  • 6.10 Trigonometric Integrals

Unit 7: Series

  • 7.1 Introduction to Taylor Polynomials

  • 7.2 Sequences

  • 7.3 Series

  • 7.4 Working with Power Series

  • 7.5 Integral Test

  • 7.6 Comparison Test

  • 7.7 Power Series and Convergence

  • 7.8 Ratio Test

  • 7.9 Alternating Series Test

  • 7.10 Taylor Polynomials

  • 7.11 Taylor Approximations in Science

  • 7.12 Taylor Series

Unit 8: Differential Equations

  • 8.1 Differential Equations

  • 8.2 Linear Differential Equations

  • 8.3 Separation of Variables

  • 8.4 Euler's Method and Direction Fields

  • 8.5 Linear Differential Equations: Solution Behaviour

  • 8.6 Non-Linear Differential Equations: Solution Behaviour

Unit 9: Parametric Curves and Vector-Valued Functions

  • 9.1 Vector-valued Functions

  • 9.2 Arc Length and Area

  • 9.3 Polar Coordinates

  • 9.4 Parametric Curves

Unit 10: Vector-Valued Functions

  • 10.1 Vector-Valued Functions

  • 10.2 Calculus of Vector-Valued Functions

  • 10.3 Polar Coordinates

Unit 11: Multivariable Calculus

  • 11.1 Functions of Multiple Variables

  • 11.2 Partial Derivatives

  • 11.3 Applications of Partial Derivatives

  • 11.4 Double Integrals

  • 11.5 Double Integrals in Polar Coordinates

Bi-Weekly Assignments

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