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### Calculus I: Differential Calculus

**Developed by** the University of Waterloo

**Available for:** Möbius
Courseware

**Pricing and implementation:** Contact DigitalEd

This interactive course contains all materials needed for a standard course in Differential Calculus, including functions, limits, derivatives, and an introduction to integration. It provides numerous opportunities for interactive exploration, drill and practice, and assessment, integrated with careful explanations of the materials. While providing a strong mathematical foundation, the emphasis of these courses is on applying calculus to scientific models, making it particularly relatable to students in the sciences.

**FUNCTIONS**

- Introduction to Calculus

- Functions

- Combining Functions

- Inverse Functions

- Modelling with Functions

- Exponential Functions

- Trigonometric Functions

**LIMITS**

- Limits of Sequences

- Instantaneous Velocity

- Limit of a Function at a Point

- Continuity

**DERIVATIVES**

- The Derivative

- Differentiation Rules

- The Chain Rule

- Implicit Differentiation

**APPLICATIONS OF DERIVATIVES**

- Modelling with Derivatives

- Exponential Processes

- Linearization

- Newton's Method

- Indeterminate Forms

- Extreme Values

- Shapes of Graphs

- Optimization

**INTEGRATION**

- Anti-derivatives

- Sigma Notation

- Riemann Sums

- Definite Integrals

- The Fundamental Theorem of Calculus

- Indefinite Integrals

- Integration by Substitution

- Areas Between Curves

### Calculus II: Integral Calculus

**Developed by** the University of Waterloo

**Available for:** Möbius
Courseware

**Pricing and implementation:** Contact DigitalEd

This interactive course contains all materials needed for a standard course in Integral Calculus, including integration methods, series, differential equations, parametric curves and vector-valued functions, and an introduction to multivariate calculus. It provides numerous opportunities for interactive exploration, drill and practice, and assessment, integrated with careful explanations of the materials. While providing a strong mathematical foundation, the emphasis of these courses is on applying calculus to scientific models, making it particularly relatable to students in the sciences.

**INTEGRATION**

- Review of Integration

- Integration by Parts

- Trigonometric Integrals

- Trigonometric Substitutions

- Integration by Partial Fractions

- Improper Integrals

- Areas and Volumes

- Volumes by Shells

- Arc Length

- Surface Area

**SERIES**

- Intro to Power Series

- Sequences

- Series

- Integral Test, p-series

- Comparison Test

- Alternating Series, AST, Remainder

- Ratio Test

- Power Series and Convergence

- Working With Power Series

- Taylor Series

- Taylor Polynomials and Taylor's Inequality

- Taylor Approximations in Science

**DIFFERENTIAL EQUATIONS**

- Intro to Differential Equations

- Linear DEs

- Nonlinear

- Separation of Variables

- Euler's Method and Direction Fields

**PARAMETRIC CURVES and VECTOR-VALUED FUNCTIONS**

- Parametric Curves

- Polar Coordinates

- Arc Length and Area

- Vector-Valued Functions

- Derivatives: Velocity and Acceleration

**MULTIVARIATE CALCULUS**

- Multivariable Functions

- 2D, 3D Integrals

- Change of Variables

### College Algebra

**Senior Contributing Author:** Jay Abramson, Arizona State
University

**Published by** OpenStax

**Available for:** Möbius
Courseware

**Pricing and implementation:** Contact DigitalEd

*College Algebra* provides a comprehensive exploration of
algebraic principles and meets scope and sequence requirements for a typical
introductory algebra course. The modular approach and richness of content ensure
that this content meets the needs of a variety of courses. *College Algebra*
offers a wealth of examples with detailed, conceptual explanations, building a
strong foundation in the material before asking students to apply what they’ve
learned.

**Prerequisites**

- Real Numbers: Algebra Essentials

- Exponents and Scientific Notation

- Radicals and Rational Expressions

- Polynomials

- Factoring Polynomials

- Rational Expressions

**Equations and Inequalities**

- The Rectangular Coordinate Systems and Graphs

- Linear Equations in One Variable

- Models and Applications

- Complex Numbers

- Quadratic Equations

- Other Types of Equations

- Linear Inequalities and Absolute Value Inequalities

**Functions**

- Functions and Function Notation

- Domain and Range

- Rates of Change and Behavior of Graphs

- Composition of Functions

- Transformation of Functions

- Absolute Value Functions

- Inverse Functions

**Linear Functions**

- Linear Functions

- Modeling with Linear Functions

- Fitting Linear Models to Data

**Polynomial and Rational Functions**

- Quadratic Functions

- Power Functions and Polynomial Functions

- Graphs of Polynomial Functions

- Dividing Polynomials

- Zeros of Polynomial Functions

- Rational Functions

- Inverses and Radical Functions

- Modeling Using Variation

**Exponential and Logarithmic Functions**

- Exponential Functions

- Graphs of Exponential Functions

- Logarithmic Functions

- Graphs of Logarithmic Functions

- Logarithmic Properties

- Exponential and Logarithmic Equations

- Exponential and Logarithmic Models

- Fitting Exponential Models to Data

**Systems of Equations and Inequalities**

- Systems of Linear Equations: Two Variables

- Systems of Linear Equations: Three Variables

- Systems of Nonlinear Equations and Inequalities: Two Variables

- Partial Fractions

- Matrices and Matrix Operations

- Solving Systems with Gaussian Elimination

- Solving Systems with Inverses

- Solving Systems with Cramer's Rule

**Analytic Geometry**

- The Ellipse

- The Hyperbola

- The Parabola

- Rotation of Axis

- Conic Sections in Polar Coordinates

**Sequences, Probability and Counting Theory**

- Sequences and Their Notations

- Arithmetic Sequences

- Geometric Sequences

- Series and Their Notations

- Counting Principles

- Binomial Theorem

- Probability

### Developmental and Intermediate Algebra

**Authors:** Dr. Shubhangi Stalder, University of Wisconsin Waukesha •
Dr. Paul Martin, University of Wisconsin Marathon

**Available for:** Möbius
Courseware

**Pricing and implementation:** Contact DigitalEd

The aim of this course is to teach problem solving skills that will prepare students for college algebra, but also eventually to solve life problems. Inspired by research on math education, brain plasticity, and growth mindsets, it employs both traditional and non-traditional approaches in presenting material.

**Module 0: Mindfulness of Learning Mathematics**

**Module 1: Introduction to Mathematical Objects**

- A Brief History of Numbers

- Number Sets

- Geometric Shapes

- Visualizations of Rational and Decimal Numbers

- Representing Real Numbers on a Number Line and Complex Numbers in the Complex Plane

- Natural Number Exponents and Properties of Exponents

- Negative and Zero Exponents

- Rational Exponents and Radicals

- Polynomials

- Functions

**Module 2: Arithmetic of Algebraic Objects**

- Addition as Combining “Like” Units

- Multiplication

- Subtraction as the Inverse of Addition

- Factoring

- Factoring Trinomials and a Geometric Interpretation

- Multiplication of Rational and Radical Expressions

- Division

- Order of Operations

**Module 3: Solving Equations and Inequalities**

- A Brief History of Equations and Inequalities

- Solving Equations and Inequalities

- Factoring and the Zero Property of Equality

- Radical and Power Equations

- Quadratic Equations

**Module 4: Applications and Graphing**

- Coordinate Plane Geometry

- Graphing Solutions to Equations in Two Variables

- Graphs of Linear Equations in Two Variables

- Interpreting Graphs and Linear Models

- Other Applications

- Rate Problems

- Using Formulas from a Variety of Fields

**Developed by** the Mathematical Association of America (MAA)

**Available for:** Möbius
Courseware, Möbius Assessment

**Pricing and implementation:** Contact DigitalEd

Place your incoming students in the right mathematics courses quickly and painlessly using the renowned Mathematical Association of America (MAA) placement tests offered online exclusively through the Möbius Courseware and Möbius Assessment testing environments.

Learn more### CÉGEP

**Authors:** Louise Pellerin, enseignante au Département de
mathématiques et intervenante en recherché au Cégep de
Chicoutimi • Diane Bergeron, coordonnatrice et enseignante dans le programme de
Présciences de la santé à la Cité collégiale

**Available for:** Möbius
Courseware, Möbius Assessment

**Pricing and implementation:** Contact DigitalEd

Les modules de cours et banques de données pour les cours des mathématiques, créés pour les étudiants francophones du Cégep.

En savoir plus