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Calculus Lectures in Videos




 

Looking for free Calculus help?
We have a series of free Calculus Video Lessons from UMKC - The University of Missouri-Kansas City. The Topics are: Functions, Limits of a Function, The Derivative of a Function, Some Special Derivatives, The Derivative Applied, The Integral of a Function and The Integral Applied.

We also have a series of free Calculus 2 Video Lessons from UNSW - University of New South Wales, Sydney.

Unit 0 - Functions: A Review of Precalculus

Beginning Definition of a Function
Visualizing Functions: Graphs
Domain (& Range) of Functions
Some Exercises
Graphing Technology Viewing Windows
Zooming In or Out Errors in Resolution
New Functions From Old Operations on Functions
How Operations Affect Function Graphs
Functions with Symmetric Graphs
Some Exercises
Families of Functions The Power Function Family y = xp
The Polynomial Function, and Rational Function Families
Trigonometry for Calculus Right Triangle Trigonometry
Trigonometric Graphs
Handy Trigonometric Identities
Laws of Sine and Cosine
Trigonometric Families
Inverse Functions A Function Inverse to Another Function When do Inverse Functions (& Their Graphs) Exist? Inverse Trigonometric Functions
Exponential & Logarithmic Functions The Exponential Function Family
The Logarithmic Function Family
Solving Exponential & Logarithmic Equations
 

Unit 1 - Limits of Functions: Approach & Destination

Intuitive Beginning A New Tool: The "Limit"
Some Limit Examples
Two-sided & One-sided Limits
Limits that Fail to Exist: When f(x) grows without bound
Limits at Infinity: When x grows without bound
More Limits that Fail to Exist: Infinity & Infinite Indecision
An Exercise on Limits
The Algebra of Limits as x ->a Basic Limits
Limits of Sums, Differences, Products, Quotients, & Roots
Limits of Polynomial Functions
Limits of Rational Functions & the Apparent Appearance of 0/0
Limits of Piecewise-Defined Functions: When One-sided Limits Matter!
Some Exercises
The Algebra of Limits as x -> +/- inf : End Behavior  Basic Limits
Limits of Sums, Differences, Products, Quotients, & Roots
Limits of Polynomial Functions: Two End Behaviors
Limits of Rational Functions: Three Types of End Behavior
Limits of Functions with Radicals
Some Exercises
Limits of ln(x), ex, and More
Continuous Functions Functions Continuous (or not!) at a Single Point x=c
Functions Continuous on an Interval
Properties & Combinations of Continuous Functions
The Intermediate Value Theorem & Approximating Roots: f(x) = 0
Some Exercises
Trigonometric Functions The 6 Trigonometric Functions: Continuous on Their Domains
When Inverses are Continuous
Finding a Limit by "Squeezing"
Sin(x)/x -> 1 as x -> 0, and Other Limit Tales
Some Exercises
 



Unit 2 - The Derivative of a Function

Measuring Rates of Change Slopes of Tangent Lines
One-Dimensional Motion
Average Velocity
Instantaneous Velocity
General Rates of Change
Some Exercises
What is a Derivative? Definition of the Derived Function: The "Derivative", & Slopes of Tangent Lines
Instantaneous Velocity
Functions Differentiable (or not!) at a Single Point
Functions Differentiable on an Interval
A Function Differentiable at a point is Continuous at that point
Other Derivative Notations
Some Exercises
Finding Derivatives I: Basic Rules The Power Rule
Constant Multiple, Sum, & Difference Rules
Notation for Derivatives of Derivatives
Some Exercises
Finding Derivatives II The Product Rule
The Quotient Rule
Some Exercises
Finding Derivatives III The Sine Function
The Other Trigonometric Functions
Some Applications
Finding Derivatives IV The Chain Rule: Derivatives of Compositions of Functions
Generalized Derivative Formulas
Some Exercises
When Rates of Change are Related Differentiating Equations to "Relate Rates"
A Strategy
An Exercise
More on Derivatives Local Linear Approximations of Non-Linear Functions
Defining "dx" and "dy" Alone


 

Unit 3 - Some Special Derivatives

Implicit Differentiation Functions Defined Implicitly
Derivatives of Functions Defined Implicitly
The Derivative of Rational Powers of x
Some Exercises
Derivatives Involving Logarithms  Derivatives of Logarithmic Functions
The "Logarithmic Differentiation" Technique
The Derivative of Irrational Powers of x
Some Exercises
Derivatives Involving Inverses Derivatives of Inverse Functions
Derivatives of Exponential Functions
Derivatives of Inverse Trigonometric Functions
Some Exercises
Finding Limits Using Differentiation  Limits of Quotients that appear to be "Indeterminate": The Rule of L'Hopital
Some Examples
Finding Other "Indeterminate" Limits


Unit 4 - The Derivative Applied

Analyzing the Graphs of Functions I Increasing & Decreasing Functions: The 1st Derivative Applied
Functions Concave Up or Concave Down: The 2nd Derivative Applied
When Concavity Changes: Inflection Points
Logistic Growth Curves: A Brief Look
Some Exercises
Analyzing the Graphs of Functions II  Local Maximums & Minimums
The 1st Derivative Test for Local Maximums & Minimums
The 2nd Derivative Test for Local Maximums & Minimums
Polynomial Function Graphs
Some Exercises
Analyzing the Graphs of Functions III What to Look For in a Graph
Rational Function Graphs
Functions Whose Graphs have Vertical Tangents or Cusps
Some Exercises
Analyzing the Graphs of Functions IV Global Maximums & Minimums
Global Extrema on (finite) Closed Intervals
Global Extrema on (finite or infinite) Open Intervals
When a Single Local Extremum must be Global
Some Exercises
Optimization Problems Applied Maximum & Minimum Problems
Optimization over a (finite) Closed Interval: Maximizing Area or Volume, Minimizing Cost
Optimization over Other Intervals: Minimizing Materials or Distance
An Economics Application: Cost, Revenue, Profit, & Marginal Analysis
Some Exercises
Newton's Method for Approximating Roots of Equations Development of the Method
Strength & Weaknesses of the Method
The Mean Value Theorem for Derivatives A Special Case of the Mean Value Theorem: Rolle's Theorem
The (Full) Mean Value Theorem for Derivatives
Direct Consequences of This Mean Value Theorem
Some Exercises
One-Dimensional Motion & the Derivative Rectilinear Motion Revisited
Velocity, Speed, & Acceleration
Analyzing a Position Graph
An Exercise




 

Unit 5 - The Integral of a Function

The Indefinite Integral "Undo-ing" a Derivative: Antiderivative = Indefinite Integral
Finding Antiderivatives
The Graphs of Antiderivatives: Integral Curves & the Slope Field Approximation
The Antiderivative as Solution of a Differential Equation
Some Exercises
Indefinite Integration by Substitution The Substitution Method of Indefinite Integration: A Major Technique
Straightforward Substitutions
More Interesting Substitutions
Some Exercises
Area Defined as a Limit The Sigma Shorthand for Sums
Summation Properties & Handy Formulas
Definition of Area "Under a Curve"
Net "Area"
Approximating Area Numerically
Some Exercises
The Definite Integral The Definite Integral Defined
The Definite Integral of a Continuous Function = Net "Area" Under a Curve
Finding Definite Integrals
A Note on the Definite Integral of a Discontinuous Function
Some Exercises
The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus, Part 1
Definite & Indefinite Integrals Related
The Mean Value Theorem for Integrals
The Fundamental Theorem of Calculus, Part 2
Differentiation & Integration are Inverse Processes
Some Exercises
One-Dimensional Motion & the Integral Position, Velocity, Distance, & Displacement
Uniformly Accelerated Motion
The Free Fall Motion Model
An Exercise
Definite Integration by Substitution Extending the Substitution Method of Integration to Definite Integrals
Some Exercises
 


Unit 6 - The Definite Integral Applied

Plane Area Area Between Two Curves [One Floor, One Ceiling]
Area Between Two Curves [One Left, One Right]
An Exercise
Volumes I  Volumes by Slicing
Volumes of Solids of Revolution: Disks
Volumes of Solids of Revolution: Washers
Some Exercises
Volumes II  Volumes of Solids of Revolution: Cylindrical Shells
An Exercise
Length of a Plane Curve  Finding Arc Lengths
Finding Arc Lengths of Parametric Curves
Average Value of a Function  Average (Mean) Value of a Continuous Function Work  Work Done by a Constant Force
Work Done by a Variable Force
Do-It-Yourself Integrals: Pumping Fluids
Work as Change in Kinetic Energy
An Exercise


 

Calculus 2

Surfaces and Partial Derivatives Tangent plane and error estimation Chain rule for functions of two variables
Integrals of trig functions and reduction formulae Integration by trig substitution and partial fractions
Integration + Partial Fractions
Integration via rationalizing substitutions and other substitutions
Partial derivatives and integration Introduction to Separable Differential Equations
Linear and Exact Differential Equations
How to solve 2nd order differential equations? What is a Taylor polynomial? Sequences and their limits
Introduction to series + the integral test
Integration and differential equations
Series, comparison + ratio tests Alternating series and absolute convergence
What is a Taylor series?
What is a Power series?
Arc length + average value of a function Surface area of revolution of functions
Calculus revision lecture
Hydrostatic Force More Free Videos on Calculus

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