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Calculus 1 | R
Calculus answers two main questions about functions. (1) How steep is a function at a point? (2) What is the area under the graph over some region? The first question is answered using the derivative and to answer the second question we use the integral.
http://qindex.info/d.php?c=5028#5076

Calculus 2 | R
Whether differential or integral both concepts involve the idea that we can do something infinitely many times and get a finite answer that is useful.
http://qindex.info/d.php?c=5028#5196

Derivative | R
When x increases by h, the ratio of a change in F(x) to the change in x that caused it, is equal to [ F(x+h) - F(x) ] / h. As h approaches 0, the limit of the ratio becomes a value. A function that maps x to this limit is called the derivative of F(x).
http://qindex.info/d.php?c=5028#5197

Integral 1 - A(x), The integral of f(x) | R
Suppose a function A(x) that maps x to the area under the graph of f(x) from a sufficiently far point on the left side to x on the right side. Such a function is called the integral of f(x).
http://qindex.info/d.php?c=5028#5198

Integral 2 - The derivative of A(x) is f(x). | R
When x increases by sufficiently small h, the change in A(x) is between h*f(x) and h*f(x+h). So the ratio of a change in A(x) to the change in x that caused it, is between f(x) and f(x+h). As h approaches 0, the limit of the ratio becomes f(x).
http://qindex.info/d.php?c=5028#5199

Integral 3 - Let F(x) be an antiderivative of f(x). | R
The differentiation makes the constant term zero. So the antidifferentiation cannot recover the constant term of the original function from the derivative. Let F(x) be an antiderivative of f(x). Then F(x) and A(x) differ only by a constant c. 
http://qindex.info/d.php?c=5028#5200

Integral 4, A(b) - A(a) = F(b) - F(a) | R
The area under the graph of f(x) from a to b is as follows: A(b) - A(a) = [ F(b) + c ] - [ F(a) + c ] = F(b) - F(a) This is called the fundamental theorem of calculus.
http://qindex.info/d.php?c=5028#5201

01 Essence of calculus | R
Essence of calculus, chapter 1
http://qindex.info/d.php?c=5028#5182

01 The Greeks, Newton and Leibniz | R
Whether differential or integral both concepts involve the idea that we can do something infinately many times and get a finite answer that is useful.
http://qindex.info/d.php?c=5028#5032

01 What Is a Derivative? | R
What Is a Derivative?
http://qindex.info/d.php?c=5028#5205

01 What is Calculus? | R
In calculus you start with two big questions about functions. First how steep is a function at a point? Second what is the area underneath the graph over some region?
http://qindex.info/d.php?c=5028#5121

02 The paradox of the derivative | R
The paradox of the derivative | Essence of calculus, chapter 2
http://qindex.info/d.php?c=5028#5183

02 The Slope of a Tangent Line | R
Understanding Differentiation Part 1: The Slope of a Tangent Line
http://qindex.info/d.php?c=5028#5033

02 The Tangent Line and the Derivative | R
A tangent line to a point A is the limit of the secant lines as P approaches A.
http://qindex.info/d.php?c=5028#5122

03 Derivative formulas through geometry | R
Derivative formulas through geometry | Essence of calculus, chapter 3
http://qindex.info/d.php?c=5028#5185

03 Product Rule for Derivatives | R
Product Rule for Derivatives (Calculus)
http://qindex.info/d.php?c=5028#5124

03 Rates of Change | R
Galileo had already discovered some years prior that the distance traveled by a falling object is represented by a function of time. Newton wondered how one could calculate the velocity of the object at any particular instance during the fall.
http://qindex.info/d.php?c=5028#5034

04 Limits and Limit Laws in Calculus | R
Limits and Limit Laws in Calculus
http://qindex.info/d.php?c=5028#5029

04 The Quotient Rule | R
The Quotient Rule (Calculus)
http://qindex.info/d.php?c=5028#5125

04 Visualizing the chain rule and product rule | R
Visualizing the chain rule and product rule | Essence of calculus, chapter 4
http://qindex.info/d.php?c=5028#5186

05 Derivatives of exponentials | R
Derivatives of exponentials | Essence of calculus, chapter 5
http://qindex.info/d.php?c=5028#5184

05 What is a Derivative? | R
What is a Derivative? Deriving the Power Rule
http://qindex.info/d.php?c=5028#5051

06 Derivatives of Polynomial Functions | R
Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule
http://qindex.info/d.php?c=5028#5052

06 Implicit differentiation, what's going on here? | R
Implicit differentiation, what's going on here? | Essence of calculus, chapter 6
http://qindex.info/d.php?c=5028#5187

07 Derivatives of Trigonometric Functions | R
Derivatives of Trigonometric Functions
http://qindex.info/d.php?c=5028#5053

07 Limits | R
Limits | Essence of calculus, chapter 7
http://qindex.info/d.php?c=5028#5188

08 Derivatives of Composite Functions: The Chain Rule | R
Derivatives of Composite Functions: The Chain Rule
http://qindex.info/d.php?c=5028#5054

08 Integration and the fundamental theorem of calculus | R
The integral equals the antiderivative evaluated at the top bound, minus its value at the bottom bound. This fact is called 'the fundamental theorem of calculus'.
http://qindex.info/d.php?c=5028#5189

09 Derivatives of Logarithmic and Exponential Functions | R
Derivatives of Logarithmic and Exponential Functions
http://qindex.info/d.php?c=5028#3387

09 What does area have to do with slope? | R
What does area have to do with slope? | Essence of calculus, chapter 9
http://qindex.info/d.php?c=5028#5190

10 Higher order derivatives | R
Higher order derivatives | Essence of calculus, chapter 10
http://qindex.info/d.php?c=5028#5191

11 Taylor series | R
Taylor series | Essence of calculus, chapter 11
http://qindex.info/d.php?c=5028#5192

Taylor and Maclaurin Series | R
Taylor and Maclaurin Series
http://qindex.info/d.php?c=5028#5104

The fundamental theorem of calculus | R
If f is Riemann integrable on [a,b] and F(x) is the integral of f(t) from a to b then F is continuous on [a,b]. Furthermore, if f is continuous on [a,b] then F is differentiable on [a,b] and F' = f.
http://qindex.info/d.php?c=5028#5193

What Is a Derivative? | R
What Is a Derivative?
http://qindex.info/d.php?c=5028#5204

What is Integration? | R
What is Integration? Finding the Area Under a Curve
http://qindex.info/d.php?c=5028#5123
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