**This demo **contains two complete modules. The finished course will be available for review and adoption in July 2021.

**Course Content:**

**Note that course content is being finalized and subject to small changes.*

**Module 1: Functions and Graphs**

-Review of Functions

-Basic Classes of Functions

-Trigonometric Functions

-Inverse Functions

-Exponential and Logarithmic Functions

**Module 2: Limits**

-A Preview of Calculus

-The Limit of a Function

-The Limit Laws

-Continuity

-The Precise Definition of a Limit

**Module 3: Derivatives**

-Defining the Derivative

-The Derivative as a Function

-Differentiation Rules

-Derivatives as Rates of Change

-Derivatives of Trigonometric Functions

-The Chain Rule

-Derivatives of Inverse Functions

-Implicit Differentiation

-Derivatives of Exponential and Logarithmic Functions

**Module 4: Applications of Derivatives**

-Related Rates

-Linear Approximations and Differentials

-Maxima and Minima

-The Mean Value Theorem

-Derivatives and the Shape of a Graph

-Limits at Infinity and Asymptotes

-Applied Optimization Problems

-L’Hôpital’s Rule

-Newton’s Method

-Antiderivatives

**Module 5: Integration**

-Approximating Areas

-The Definite Integral

-The Fundamental Theorem of Calculus

-Integration Formulas and the Net Change Theorem

-Substitution

-Integrals Involving Exponential and Logarithmic Functions

-Integrals Resulting in Inverse Trigonometric Functions

**Module 6: Applications Integration**

-Areas between Curves

-Determining Volumes by Slicing

-Volumes of Revolution: Cylindrical Shells

-Arc Length of a Curve and Surface Area

-Physical Applications

-Moments and Centers of Mass

-Integrals, Exponential Functions, and Logarithms

-Exponential Growth and Decay

-Calculus of the Hyperbolic Functions

**Additional Course Features**

These course materials include:

**Online Homework Manager****(OHM):**A flexible, user-friendly math homework system with customizable learning content, assessments, and activities you can tailor to fit your needs. Request an OHM instructor account.**Outcome-aligned OER:**Designed to replace expensive textbooks, this course curates open educational resources (OER) aligned with learning outcomes. Teach as-is or customize to fit your needs.**LMS Integration:**This course may be delivered with seamless LMS integration and automatic grade return for Canvas, Blackboard, Brightspace, and Moodle.**Accessibility:**Lumen is 100% committed to providing learning materials that are accessible to all learners. Lumen course materials are mobile-friendly.