This demo contains two complete modules. The finished course will be available for review and adoption in July 2021.
*Note that course content is being finalized and subject to small changes.
Module 1: Functions and Graphs
-Review of Functions
-Basic Classes of Functions
-Exponential and Logarithmic Functions
Module 2: Limits
-A Preview of Calculus
-The Limit of a Function
-The Limit Laws
-The Precise Definition of a Limit
Module 3: Derivatives
-Defining the Derivative
-The Derivative as a Function
-Derivatives as Rates of Change
-Derivatives of Trigonometric Functions
-The Chain Rule
-Derivatives of Inverse Functions
-Derivatives of Exponential and Logarithmic Functions
Module 4: Applications of Derivatives
-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
Module 5: Integration
-The Definite Integral
-The Fundamental Theorem of Calculus
-Integration Formulas and the Net Change Theorem
-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
-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.