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.

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 = x^{p}
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 |

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=cFunctions Continuous on an Interval Properties & Combinations of Continuous Functions The Intermediate Value Theorem & Approximating Roots: f(x) = 0Some 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 |

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 |

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 |

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 |

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
FunctionSome 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 |

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 |

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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