Graphing and Functions
What is a Function: Basics and Key Terms
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All Videos in Graphing and Functions
- 1. What is a Function: Basics and Key Terms
- 2. Graphing Basic Functions
- 3. Compounding Functions and Graphing Functions of Functions
- 4. Understanding and Graphing the Inverse Function
- 5. Polynomials Functions: Properties and Factoring
- 6. Polynomials Functions: Exponentials and Simplifying
- 7. Exponentials, Logarithms & the Natural Log
- 8. Slopes and Tangents on a Graph
- 9. Equation of a Line Using Point-Slope Formula
- 10. Horizontal and Vertical Asymptotes
- 11. Implicit Functions
Continuity in a Function
How to Solve Visualizing Geometry Problems
Understanding Radians and Degrees on a Scientific Calculator
Limits
Using a Graph to Define Limits
All Videos in Limits
Rate of Change
Velocity and the Rate of Change
All Videos in Rate of Change
Calculating Derivatives and Derivative Rules
Using Limits to Calculate the Derivative
All Videos in Calculating Derivatives and Derivative Rules
- 1. Using Limits to Calculate the Derivative
- 2. The Linear Properties of a Derivative
- 3. Calculating Derivatives of Trigonometric Functions
- 4. Calculating Derivatives of Polynomial Equations
- 5. Calculating Derivatives of Exponential Equations
- 6. Using the Chain Rule to Differentiate Complex Functions
- 7. Differentiating Factored Polynomials: Product Rule and Expansion
- 8. When to Use the Quotient Rule for Differentiation
- 9. Understanding Higher Order Derivatives Using Graphs
- 10. Calculating Higher Order Derivatives
- 11. How to Find Derivatives of Implicit Functions
- 12. How to Calculate Derivatives of Inverse Trigonometric Functions
- 13. Applying the Rules of Differentiation to Calculate Derivatives
Graphing Derivatives and L'Hopital's Rule
Graphing the Derivative from Any Function
All Videos in Graphing Derivatives and L'Hopital's Rule
- 1. Graphing the Derivative from Any Function
- 2. Non Differentiable Graphs of Derivatives
- 3. How to Determine Maximum and Minimum Values of a Graph
- 4. Using Differentiation to Find Maximum and Minimum Values
- 5. Concavity and Inflection Points on Graphs
- 6. Understanding Concavity and Inflection Points with Differentiation
- 7. Data Mining: Function Properties From Derivatives
- 8. Data Mining: Identifying Functions From Derivative Graphs
- 9. What is L'Hopital's Rule?
- 10. Applying L'Hopital's Rule in Simple Cases
- 11. Applying L'Hopital's Rule in Complex Cases
Applications of Derivatives
Linearization of Functions
All Videos in Applications of Derivatives
Area Under the Curve and Integrals
Summation Notation and Mathematical Series
All Videos in Area Under the Curve and Integrals
- 1. Summation Notation and Mathematical Series
- 2. How to Use Riemann Sums for Functions and Graphs
- 3. How to Identify and Draw Left, Right and Middle Sums
- 4. What is the Trapezoid Rule?
- 5. How to Find the Limits of Riemann Sums
- 6. Definite Integrals: Definition
- 7. How to Use Riemann Sums to Calculate Integrals
- 8. Linear Properties of Definite Integrals
- 9. Average Value Theorem
- 10. The Fundamental Theorem of Calculus
- 11. Indefinite Integrals as Anti Derivatives
- 12. How to Find the Arc Length of a Function
Integration and Integration Techniques
Calculating Integrals of Simple Shapes
All Videos in Integration and Integration Techniques
- 1. Calculating Integrals of Simple Shapes
- 2. Anti-Derivatives: Calculating Indefinite Integrals of Polynomials
- 3. How to Calculate Integrals of Trigonometric Functions
- 4. How to Calculate Integrals of Exponential Functions
- 5. How to Solve Integrals Using Substitution
- 6. Substitution Techniques for Difficult Integrals
- 7. Using Integration By Parts
- 8. Partial Fractions: How to Factorize Fractions with Quadratic Denominators
- 9. How to Integrate Functions With Partial Fractions
- 10. Understanding Trigonometric Substitution
- 11. How to Use Trigonometric Substitution to Solve Integrals
- 12. How to Solve Improper Integrals
Integration and Dynamic Motion
Differential Equations
Differential Notation in Physics
All Videos in Differential Equations
Lessons in Calculus
Math 104: Calculus is designed to be used to prepare you to earn real college credit by passing the Calculus CLEP Exam. This course covers topics that are included on the exam, such as polynomials, factoring, higher-order derivative and intermediate value theorem. Use it to help you learn what you need to know about calculus topics to help you succeed on the exam.
The calculus instructors are experienced and knowledgeable educators, who have put together comprehensive video lessons in categories ranging from breaking a complex concept down into its basic components to calculating velocity. Each category is broken down into smaller chapters that will cover topics more in-depth. These video lessons make learning fun and interesting. You get the aid of self-graded quizzes and practice tests to allow you to gauge how much you have learned.
| Category | Objectives |
|---|---|
| Applications of Derivatives | Learn how to estimate function values using linearization and how to use Newton's method to find roots of equations. Also, study linearization of functions, optimization and differentiation, optimizing complex systems andoptimizing simple systems. |
| Area Under the Curve and Integrals | Take a look at average value theorem, definite integrals, indefinite integrals as anti-derivatives, linear properties of definite integrals, the fundamental theorem of calculus, sum notation and the trapezoid rule. Learn how to find the arc length of a function, find the limits of Riemann sums, to identify and draw left, right and middle sums, use Riemann sums for functions and graphs and use Riemann sums to calculate integrals. |
| Calculating Derivatives and Derivative Rules | Discover how to apply the rules of differentiation to calculate derivatives, calculate derivatives of exponential equations and find derivatives of implicit functions. Additionally, take a look at derivatives of polynomial equations, derivatives of trigonometric functions, higher-order derivatives, derivatives of inverse trigonometric functions and linear properties of a derivative. |
| Continuity | Study continuity in a function, discontinuities in functions and graphs, intermediate value theorem, intermediate value theorem and regions of continuity in a function. |
| Differential Equations | Find out about differential notation in physics, separation of variables to solve system differential equations and calculating rate and exponential growth. |
| Geometry and Trigonometry in Calculus | Learn to find distance with the Pythagorean theorem, calculate the volumes of basic shapes and solve visualizing geometry problems. Also study sine and cosine. |
| Graphing and Functions | Discover concepts that include compounding functions and graphing functions of functions, figuring the equation of a line using point-slope formula, graphing exponentials and logarithms and graphing basic functions. Additionally, study horizontal and vertical asymptotes, implicit functions, exponents, slopes and tangents. |
| Graphing Derivatives and L'Hopital's Rule | Learn to apply L'Hopital's Rule and about concavity and inflection points on graphs, function properties from derivatives, identifying functions from derivative graphs, graphing the derivative from any function, determining maximum and minimum values of a graph and non-differentiable graphs of derivatives. |
| Integration and Integration Techniques | Examine anti-derivatives, integrals of simple shapes, integrals of exponential functions, integrals of trigonometric functions and improper integrals. Also take a look at how to solve integrals using substitution, how to use trigonometric substitution to solve integrals and how to factorize fractions with quadratic denominators. |
| Integration Applications | Learn how to calculate volumes using single intervals, find area between functions with integration, find simple areas with root finding and integration and find volumes of revolution with integration. |
| Limits | Study concepts including asymptotes, infinity, limits, continuity and the squeeze theorem, Also learn to determine the limits of functions and use a graph to define limits. |
| Rate of Change | Examine derivatives, Rolle's theorem, velocity and the rate of change. Additionally, look at the definition of mean value theorem and 'differentiable.' |
| Using Scientific Calculators for Calculus | Discover how to use a scientific calculator, solve equations on a scientific calculator and understand radians and degrees on a scientific calculator. Also study trigonometry functions and exponentials on a calculator. |
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Education Portal Instructors
Education Portal's 53 instructors bring a diverse array of experience and expertise to each course. From teaching philosophy in Athens, Greece, to exploring the mystery of genetics, each instructor is uniquely qualified to bring students the best online learning experience possible. Meet them now!
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Jessica Bayliss, M.S.
Jessica is our Director of Education and leads the development of Education Portal's free courses. She has 10 years of experience in education and online teaching. Her work with students of all age levels drives
her belief in the power of free online resources to make higher education more affordable and efficient. Jessica's favorite part of the day is
reading feedback from Education Portal's students. She has a bachelor's degree from the University of Illinois and a master's degree in
instructional technology from Texas A&M - Kingsville.
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Greg Chin, Ph.D.
Greg has taught genetics, molecular biology, and general biology to
high school, collegiate, and post-graduate students at Stanford University, the University of California, Los Angeles, Santa Clara
University and the Dolan DNA Learning Center at Cold Spring Harbor Laboratory. He has also taught science workshops for the general
public and led biology teacher enrichment workshops throughout the U.S. He received a B.S. in Genetics from the University of
California, Davis, and a Ph.D. from Stanford University. Find out how your genes work in Greg's introduction to genetics video lesson!
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Max Pfingsten, M.Ed.
Max has taught classics, history and philosophy
at a variety of levels at the Dikemes Academy in Athens, the Boulder Valley School District, University of Colorado at Boulder and
the Illinois Mathematics and Science Academy (IMSA). His work is noteworthy for its synthesis of technology and simulation with more
traditional teaching approaches. He received a B.A. in Classics from Depauw University, a M.A. in Classics from University of
Colorado at Boulder, and a M.Ed. from Jones International University. See Socrates come to life in Max's lesson on the life, death,
and philosophy of the great Socrates.
- Meet all 53 of our instructors
Contact Information
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The videos were a great study tool. I aced the CLEP exam and earned 3 college credits!
Claire Steiner, Nursing Student More success stories
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