Calculus I Videos

Review of Functions from Algebra and Trigonometry
Concept Video – 
Review of Graphs
Concept Video – Review of Transformations of Functions

 

Finding average and instantaneous velocity
Concept Video – 
Average & Instantaneous Velocity
    Example - Finding Average and Instantaneous Velocity

 

Limits
Concept Video – 
Limit Definition Intuitive
Concept Video  – Limit Definition Graphically
Concept Video – One Sided Limits
    Example 1 - Determining Limits Graphically
    Example 2 - Sketching Piecewise Functions and Determining Limits
    Example 3 - Sketching a Graph Meeting Given Conditions
    Example 4 - Finding a Limit Near Where Function is Undefined

Concept Video – Limits Numerically
 

Concept Video  – Limit Laws
Concept Video  – The Squeeze Theorem
    Example 1 - Using Limits Laws Given Functions Graphically
    Example 2 - Finding Limits Using Limit Laws (Justifying)
    Example 3 - Examples of Finding Limits
    Example 4 - Sketching With Greatest Integer Function and Finding Limits

 

Concept Video – The Formal Definition of Limit 
    Example 1 - 
Using Definition of Limit, Given Epsilon Find Delta Using a Graph
    Example 2 - Using Definition of Limit, Prove a Given Limit by Finding Delta 1
    Example 3 - Using Definition of Limit, Prove a Given Limit by Finding Delta 2

Concept Video – Continuity
Concept Video  – Continuous Functions
    Example 1 - Sketching a Graph With Given Discontinuity
    Example 2 - Finding & Identifying Points of Discontinuity From a Graph
    Example 3 - Evaluating  a Limit of a Composition of Continuous Functions
    Example 4 - Determining Where a Function it Continuous
    Example 5 - Using the Intermediate Value Theorem

Concept Video – Limits at Infinity
Concept Video – Infinite Limits
    Example 1 - Inverse Tangent at Infinity
    Example 2 - Evaluating Limits at Infinity
    Example 3 - Horizontal Asymptote & Squeeze Theorem
    Example 4 - Infinite Limits, Limits at Infinity and Asymptotes
    Example 5 - Finding Horizontal and Vertical Asymptotes Using Limits

 

Rates of Change and Derivatives
Concept Video – 
Rates of Change
    Example 1 - Finding Tangent Line of Polynomial at a Point 
    Example 2 – Find a Tangent Line of a 3rd Degree Polynomial at a Point
    Example 3 - Finding Tangent Line of Trig Function at a Point 
    Example 4 - 
Finding the Slope of 1/x
    Example 5 - Application Finding Velocity

 

Concept Video – The Derivative as a Function
Concept Video  – Differentiability
Concept Video 3 – Higher Derivatives & Position, Velocity & Acceleration
    Example 1 - Finding Graph of Derivative From Graph of Function
    Example 2 - Application Using Graph and Derivative
    Example 3 - Finding a Function Algebraically for the Derivative
    Example 4 - Reasons a Function is Not Differentiable at a Point
    Example 5 - Determining Graphs of Position, Velocity and Acceleration

 

Rules of Derivatives
Concept Video – 
Derivatives of Polynomials
    Example 1 – Differentiating with Power Rule
    Example 2 – Algebra Before Differentiating
    Example 3 – Finding Tangent to a Curve Using Rules for Derivatives
    Example 4 – Finding Acceleration From Position
    Example 5 – Finding a 6th Derivative

 

Concept Video – Derivatives of Exponential Functions
    (No individual example videos---2 examples are given in the content video)

 

Concept Video – The Product Rule
    Example – Using the Product Rule

 

Concept Video – The Quotient Rule
    Example 1 – Using the Quotient Rule 1
    Example 2 – Using the Quotient Rule 2

 

Concept Video – Derivatives of Trigonometric Functions
    Example 1 – Derivatives of Trig Functions
    Example 2 – Simple Harmonic Motion
    Example 3 – Derivative of Trig Function and Horizontal Tangents
    Example 4 – Finding A Limit Involving Trig Functions

 

Concept Video  – The Chain Rule
Concept Video  – Derivatives of Exponential Functions Revisited
    Example 1 – Examples Using the Chain Rule
    Example 2 – More Examples Using the Chain Rule 
    Example 3 – Patterns with Derivatives & the Chain Rule

 

Concept Video – Implicit Differentiation
    Example 1 – Example Using Implicit Differentiation
    Example 2 – Finding the 2nd Derivative Using Implicit Differentiation

 

Concept Video – Derivatives of Inverse Trigonometric Functions
    Example – Finding Derivatives of Inverse Trig Functions

 

Concept Video  – The Derivative of Log Functions & Logarithmic Differentiation
Concept Video  – “e” as a Limit
    Example 1 – Finding the Derivatives of Log Functions
    Example 2 – MONSTER Chain Rule Example
    Example 3 – Using Logarithmic Differentiation 1
    Example 4 – Using Logarithmic Differentiation 2

 

Concept Video - Higher Order Derivatives and Position, Velocity and Acceleration

 

Applications of the Derivative
Concept Video – 
Applications With Rates of Change Part 1
Concept Video – Applications With Rates of Change Part 2
    Note:  There are no examples listed as the examples are included in the content video

Concept Video – Related Rates
    Example 1 – Related Rates Circular Oil Spill 
    Example 2 – Related Rates Conical Tank     
    Example 3 – Related Rates Shadow 

 

Concept Video – Linear Approximations
Concept Video – Differentials
    Note:  There are no examples listed as the examples are included in the content video

 

Content Video - Hyperbolic Functions

 

Concept Video  – Extreme Values Definitions
Concept Video – Finding Extreme Values
Concept Video  – Proof of Fermat’s Theorem
    Example 1 – Finding the Absolute Max and Min on an Interval
    Example 2 – Finding the Max and Min Values of Acceleration
    Example 3 – Sketching Graphs Given Info About Extremes
    Example 4 – Finding the Abs Max and Min on an Interval (2)

 

Concept Video – Rolle’s Theorem
Concept Video – The Mean Value Theorem
Concept Video  – Proof of the Mean Value Theorem
    Example 1 – Showing a Function Has Exactly One Real Root
    Example 2 – Determining if MVT Applies and Finding c When it Does
    Example 3 – Using Theorem:  Functions With Same Derivative Differ By a Constant

 

Concept Video  –Indeterminate Forms and  L’Hopital’s Rule
Concept Video  – L’Hopital’s Rule Applied to Special Cases 
    Example 1 – Indeterminate 0/0 or ∞/∞
    Example 2 – Indeterminate 0 - 0 or ∞ - ∞
    Example 3 – Indeterminate ∞∙0
    Example 4 – Indeterminate 1^∞

 

Concept Video  – The First Derivative Test and Curve Sketching
Concept Video  – The Second Derivative Test and Curve Sketching
Concept Video  – Proof of the Concavity Test
Concept Video 4 – Summary of What Derivatives Tell Us About the Shape of a Graph
Concept Video 5 – Sketching a Curve from the Graphs of the First & Second Derivatives
Concept Video 6 – Guidelines for Sketching a Curve 
    Example 1 – Finding Intervals of Increase and Decrease (1)
    Example 2 -  Finding Intervals of Increase and Decrease (2)
    Example 3 – Sketching a Graph From Given Conditions
    Example 4 – Find Local Max and Mins, Concavity and Graph
    Example 5 – Use the Second Derivative Test to Local Extrema
    Example 6 – Use Sketching Guidelines to Graph Function (1)
    Example 7 – Use Sketching Guidelines to Graph Function (2)

 

Concept Video – Newton’s Method Part I
Concept Video – Newton’s Method Part II

    Example 1 – Using Newton’s Method to Find Roots
    Example 2 – Using Newton’s Method to Solve Equations

 

Concept Video  – Optimization Problems
    Example 1 – Largest Printed Area on a Poster
    Example 2 – Maximum Area Enclosed for a Corral
    Example 3 – Largest Area of Rectangle Inscribed in Semi-Circle
    Example 4 – Minimizing Distance on a G-raph

Antiderivatives, Area Under a Curve & Integrals


Concept Video – Antiderivatives
Concept Video – Differential Equations
    Example 1 – Find a General Antiderivative 1
    Example 2 – 
Find a General Antiderivative 2
    Example 3 – Find a Function Given 2nd Derivative and 2 Initial Values 1
    Example 4 – Find a Function Given 2nd Derivative and 2 Initial Values 2
    Example 5 – Antiderivatives and Motion
    Example 6 – Finding Car Velocity with Deceleration and Skid Marks

 

Concept Video – Area Under a Curve Part 1
Concept Video – Area Under a Curve Part 2
Concept Video – Distance or Displacement
Concept Video – Riemann Sums 
    Example – Estimating and Area Under a Curve Using Rectangles

 

Concept Video – The Definite Integral
Concept Video – Properties of Integrals
    Example 1 – Finding a Definite Integral Using Area (1)
    Example 2 – Finding a Definite Integral Using Area (2)
    Example 3 – Using the Properties of Integrals
    Example 4 – Changing from Limit Notation to Integral Notation
    Example 5 – Finding An Integral Using the Limit Definition

 

Concept Video – The Fundamental Theorem of Calculus Part 1
Concept Video – Proof of the Fundamental Theorem of Calculus Part 1
Concept Video – The Fundamental Theorem of Calculus Part 2

    Example 1 – Finding Area Using Fundamental Theorem (1)
    Example 2 – Finding Area Using Fundamental Theorem (2)

 

Concept Video – Indefinite Integrals
Concept Video – The Net Change Theorem
    Example  – Interpreting Area Found by Integral
   

Concept Video – Substitution
Concept Video – Integrals of Symmetric Functions
    Example 1 – Examples of Definite Integrals and Substitution
    Example 2 – Indefinite Integral and Substitution

 

Concept Video – Area Between Curves
    Example 1 – Area Between Curves (1)
    Example 2 – Area Between Curves (2)
    Example 3 – Area Between Curves (3)
    Example 4 – Area Between Curves (4)

Shawna Haider                   Professor Mathematics                Salt Lake Community College

shawna.haider@slcc.edu