Calculus I
Here you will find 150+ Calculus I videos that cover every main concept you will see in a typical Calculus I class. Scroll through the gallery below which is sorted in order of topics as they are typically addressed throughout the semester.
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Topics Covered
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How to Succeed in Calculus
Unit Circle Explanation
14 Minutes to Completely Memorize the Unit Circle
Memorize Unit Circle - Longer Version
Unit circle - Quick Quiz
Why Do We Study Limits in Calculus
Limits - Graphically and Numerically
How to Evaluate a Limit Numerically: Example 1
How to Evaluate a Limit Numerically: Example 2
Limit - Evaluate Graphically, Example 1
How to Evaluate Limits Analytically
Properties of Limits in Calculus
Limits - Evaluate Analytically, Example 1
Limits - Evaluate Analytically, Example 2
Limits - Evaluate Analytically, Example 3
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- How to Succeed in Calculus
- Unit Circle Explanation
- 14 Minutes to Completely Memorize the Unit Circle
- Memorize Unit Circle – Longer Version
- Unit circle – Quick Quiz
- Why Do We Study Limits in Calculus
- Limits – Graphically and Numerically
- How to Evaluate a Limit Numerically: Example 1
- How to Evaluate a Limit Numerically: Example 2
- Limit – Evaluate Graphically, Example 1
- How to Evaluate Limits Analytically
- Properties of Limits in Calculus
- Limits – Evaluate Analytically, Example 1
- Limits – Evaluate Analytically, Example 2
- Limits – Evaluate Analytically, Example 3
- One Sided Limits
- One Sided Limits – Examples
- One Sided Limits – Examples 2
- Limit of Piecewise Functions
- Infinite Limits
- Introduction to Continuity
- Discontinuity (Calculus)
- Discontinuity – Calculus, Example 1
- Intermediate Value Theorem
- Intermediate Value Theorem – IVT Example 1
- Limit Definition of the Derivative of a Function
- Limit Definition of the Derivative – Example 1
- Limit Definition of the Derivative – Example 2
- Tangent Line Approximation (Calculus)
- Basic Derivative Rules
- Basic Derivative Rules – Lots of Examples
- How to Find the Equation of a Tangent Line (Calculus)
- Tangent Line – Example 1
- Average Rate of Change
- Instantaneous Rate of Change
- Product Rule
- Quotient Rule (Calculus)
- Chain Rule (Calculus)
- Trig Derivatives
- Differentiability
- Derivative Notations
- Derivatives Using TI Calculator
- Higher Order Derivatives
- Implicit Differentiation
- Tangent Line Using Implicit Differentiation
- 2nd Derivative Using Implicit Differentiation
- Related Rates: Introduction and Theory
- Related Rates Example: Falling Ladder
- Related Rates Example: Water In Trough
- Related Rates Example: Fill Balloon With Air
- Critical Point
- Absolute Extrema
- Absolute Extrema Example
- Extreme Value Theorem
- Relative Extrema
- First Derivative Test
- Relative Extrema Example
- Concavity and Inflection Points
- Finding Concave Up/Down Intervals
- Finding a Point of Inflection
- Limits at Infinity
- Concavity Example2
- Curve Sketching: Introduction
- Curve Sketching: Polynomial Example
- Curve Sketching Rational Function Example
- Graphing Derivatives Using Graph of f(x)
- Using a Derivative to Graph f(x)
- Using Derivatives to Find Increasing/Decreasing Intervals
- Using Derivatives to Find Max Min
- Rolles Theorem
- Rolles Theorem Ex
- Rolles Theorem Ex2
- Mean Value Theorem
- Mean Value Theorem Ex
- Solving Optimization Problems
- Optimization: Maximize Volume of a Box
- Optimization: Maximize Area of a Pasture
- Optimization: Maximize Area of Bounded Rectangle
- Optimization: Example 4
- Hallway Problem
- Differentials
- Differentials: Example
- Marginals: Cost, Revenue, Profit
- Marginal Revenue: Example
- Introduction to Antiderivatives
- Basic Integral Rules
- Integral Constant Rule
- Integral Constant Multiple Rule
- Integral Sum Difference Rule
- Integral Power Rule
- Check Answer for Indefinite Integral
- Integral Example Using Long Division
- Initial Conditions Example
- Initial Conditions3
- Introduction to Area Under a Curve
- Approximate Area Under Curve
- Area: Right Hand Sum
- Riemann Sums
- Fundamental Theorem of Calculus: FTC
- 2nd Fundamental Theorem of Calculus
- Why No Plus C For Definite Integrals
- Definite Integral Example 1 – Fundamental Theorem of Calculus
- Definite Integral Example 2 – Fundamental Theorem of Calculus
- Definite Integral Properties
- Definite Integral Absolute Value
- Absolute Value Definite Integral – Example 1
- Definite Integral Using a TI Calculator (Graphing)
- Definite Integral Using a TI Calculator (Nongraphing)
- Signed Area Below x-Axis
- Average Value of a Function Over an Interval
- Average Value of a Function – Example 1
- Differential Equations Introduction
- Introduction to u-Substitution
- Integral u-Substitution Example 1
- Integral u-Substitution Example 2
- Integral u-Substitution Example 3
- Integral u-Substitution Example 4
- Integral u-Substitution Example 5
- Integral u-Substitution Example 6
- Integral u-Substitution Example 7
- Integral u-Substitution Example 8
- Trapezoidal Rule
- Trapezoidal Rule Example
- Exponential Functions
- Why is ‘e’ an Important Base?
- Exponential Derivative
- Exponential Derivative: Chain Rule
- Exponential Tangent Line
- Exponential Growth Model
- Exponential Growth: Example
- Exponential Decay: Half Life
- General Exponential Derivative
- Introduction to Inverse Functions
- Inverse Function Graphical
- Inverse Function Algebraic
- Inverse Functions: Exponentials/Logarithms
- Properties of ln(x)
- Algebraic Properties of Logarithms
- Derivative of ln(x)
- Natural Log Derivative Example
- General Logarithm Derivative
- Log Rule Integral: Introduction
- Log Rule Example
- Log Rule Ex2
- Log Rule/Long Divison
- Area Between Curves
- Disk Method5
- Disk Method Ex1
- Disk Method Ex2
- Washer Method
- Washer Method Example
- Arc Length
- Arc Length Ex1
- Arc Length Function
- Arc Length Function2
- Work HD
- Hookes Law Ex1