Quick Statistics Using Microsoft(TM) Excel

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Limits and Derivatives

Introduction to Limits
Limit Examples
Limit Examples 2
Limit Examples 3
Limit Examples 4
The Squeeze Therom
Proof lim (Sin x / x) = 1
More limit problems
Epsilon Dela Limit Definition 1
Delta Limit Definition 2

Calculus: Derivatives 1 (new version) or Calculus Derivatives 1

Derivatives 2 New or Calculus Derivatives 2
Derivatives 2.5

Calculus Derivatives 3

Calculus: Derivatives 4: The Chain Rule
Calculus: Derivatives 5

Calculus: Derivatives 6
Derivatives part 7 Product Rule
Calculus Derivative 8
Calculus Derivatives 9

Proof: d/dx(x^n)

Proof: d/dx(sqrt(x))

Proof: d/dx(ln x) = 1/x
Proof: d/dx(e^x) = e^x

Proofs of Derivatives of Ln(x) and e^x

Derivative of x^(x^x)

Extreme Derivative Word Problem (advanced)

Implicit Differentiation

Implicit Differentiation (part 2)

More implicit differentiation

More chain rule and implicit differentiation intuition

Trig Implicit Differentiation Example

Maxima Minima Slope Intuition
Inflection Points and Concavity Intuition

Monotonicity Theorem

Maximum and minimum values on an interval

Graphing Using Derivatives

Graphing with Calculus

Calculus Graphing with Derivatives Example

Optimization with Calculus 1
Optimization with Calculus 2
Optimization with Calculus 3
Optimization Example 4

Introduction to rate-of-change problems
Rates-of-change (part 2)
Ladder rate-of-change problem

Mean Value Theorem

Calculus Video Lectures from MIT

AP Calculus BC Exam Problems
2008 1 a

2008 1 b&c

2008 1 d

2008 2 a
2008 2 b &c
2008 2d

Integrals and
Differential Equations

The Indefinite Integral or Anti-derivative

Indefinite integrals (part II)
Indefinite Integration (part III)
Indefinite Integration (part IV)

Indefinite Integration (part V)

Integration by Parts (part 6)

Indefinite Integration (part 7)
Another u-substation example

Introduction to definite integrals
Definite integrals 2

Definite Integrals 3 (area under a curve)

Definite Integrals 4

Definite Integrals 5

Definite integral with substitution

Integrals: Trig Substitution 1

Integrals: Trig Substitution 2

Integrals: Trig Substitution 3 (long problem)
Introduction to differential equations

Separable Differential Equations
Separable differential equations 2

Exact Equations Example 1
Exact Equations Example 2

Exact Equations Example 3

Integrating factors 1
Integrating factors 2

First order homogenous equations

First order homogenous equations 2

2nd Order Linear Homogeneous Equations 1

2nd Order Linear Homogeneous Equations 2

2nd Order Linear Homogeneous Equations 3

2nd Order Linear Homogeneous Equations 4

Complex roots of the characteristic equations 1

Complex roots of the characteristic equations 2

Complex roots of the characteristic equation 3

Repeated roots of the characteristic equation

Repeated roots of the characteristic equations part 2

Undetermined Coefficients 1

Undetermined Coefficients 2

Undetermined Coefficients 3

Undetermined Coefficients 4

Laplace Transform 1
Laplace Transform 2
Laplace Transform 3 (L{sin(at)})

Laplace Transform 4

Laplace Transform 5

Laplace Transform 6

Laplace Transform to solve an equation

Laplace Transform 2

Laplace Transform 3 (L{sin(at)})

Laplace Transform 4

Laplace Transform 5

Laplace Transform 6

Laplace Transform to solve an equation

Laplace Transform solves an equation 2

More Laplace Transform tools
Laplace Transform to solve a nonhomogenous equation

Laplace Transform of : L{t}

Laplace Transform of t^n: L{t^n}

Laplace Transform of the Unit Step Function

Inverse Laplace Examples

Laplace/Step Function Differential Equation

Dirac Delta Function

Laplace Transform of the Dirac Delta Function

Introduction to the Convolution

The Convolution and the Laplace Transform

Using the Convolution Theorem for Initial Value Prob

Introduction to L'Hopital's Rule
L'Hopital's Rule Example 1
L'Hopital's Rule Example 2L'
Hopital's Rule Example 3

Sequences and Series (part 1)

Sequences and series (part 2

Advanced Topics

Solid of Revolution 1

Solid of Revolution 2

Solid of Revolution 3

Solid of Revolution 4
Solid of Revolution 5

Solid of Revolution 6

Solid of Revolution 7
Solid of Revolution 8

Polynomial approx of functions 1

Polynomial approx of functions 2

Approx functions with polynomials 3

Polynomial approx of functions 4

Polynomial approxi of functions 6

Polynomial approxi of functions 7

Advanced Proof
Field from infinite plate 1

Field from infinite plate 2

Taylor Polynomials

Exponential Growth

Partial Derivatives

Partial Derivatives 2

Gradient of a scalar field

Divergence 1

Divergence 2

Divergence 3

Curl 1

Curl 3

Double Integral 1

Double Integrals 2

Double Integrals 3

Double Integrals 4

Double Integrals 5

Double Integrals 6

Triple Integrals 1

Triple Integrals 2

Triple Integrals 3

∫(2^ln x)/x dx Antiderivative Example

Introduction to the Line Integral

Line Integral Example 1

Line Integral Example 2 (part 2)

Line Integral Example 2 (part 1)

Position Vector Valued Functions

Derivative of a position vector valued function

Differential of a vector valued function

Vector valued function derivative example

Introduction to the Line Integral

Line Integral Example 1

Line Integral Example 2 (part 1)

Line Integral Example 2 (part 2)

Position Vector Valued Function

Derivative of a position vector valued function

Differential of a vector valued function

Vector valued function derivative example

Line Integrals and Vector Fields

Using a line integral to find the work done
by a vector field example

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End

Parameterization of a Reverse Path

Scalar Field Line Integral Independent
of Path Direction

Vector Field Line Integrals Dependent
on Path Direction

Path Independence for Line Integrals

Closed Curve Line Integrals of
Conservative Vector Field

Example of Closed Line Integral
of Conservative Vector Field

Second Example of Line Integral
of Conservative Vector Field

Green's Theorem Proof Part 1

Green's Theorem Proof (part 2)

Green's Theorem Example 1

Green's Theorem Example 2

Introduction to Parametrizing a
Surface with Two Parameters

Determining a Position Vector-Valued Function
for a Parameterization of Tow Parameters

Partial Derivatives of Vector-Valued Functions

Introduction to the Surface Integral

Example of calculating a surface integral part 1

Example of calculating a surface integral part 2

Example of calculating a surface integral part 3

Introduction to L'Hopital's Rule

L'Hopital's Rule Example 1

L'Hopital's Rule Example 2

L'Hopital's Rule Example 3