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• 01 The Greeks, Newton and Leibniz

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/i.php?f=5028#5032

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/i.php?f=5028#5032

• 01 What is Calculus?

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/i.php?f=5028#5121

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/i.php?f=5028#5121

• 02 The paradox of the derivative

The paradox of the derivative | Essence of calculus, chapter 2

http://qindex.info/i.php?f=5028#5183

The paradox of the derivative | Essence of calculus, chapter 2

http://qindex.info/i.php?f=5028#5183

• 02 The Slope of a Tangent Line

Understanding Differentiation Part 1: The Slope of a Tangent Line

http://qindex.info/i.php?f=5028#5033

Understanding Differentiation Part 1: The Slope of a Tangent Line

http://qindex.info/i.php?f=5028#5033

• 02 The Tangent Line and the Derivative

A tangent line to a point A is the limit of the secant lines as P approaches A.

http://qindex.info/i.php?f=5028#5122

A tangent line to a point A is the limit of the secant lines as P approaches A.

http://qindex.info/i.php?f=5028#5122

• 03 Derivative formulas through geometry

Derivative formulas through geometry | Essence of calculus, chapter 3

http://qindex.info/i.php?f=5028#5185

Derivative formulas through geometry | Essence of calculus, chapter 3

http://qindex.info/i.php?f=5028#5185

• 03 Product Rule for Derivatives

Product Rule for Derivatives (Calculus)

http://qindex.info/i.php?f=5028#5124

Product Rule for Derivatives (Calculus)

http://qindex.info/i.php?f=5028#5124

• 03 Rates of Change

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/i.php?f=5028#5034

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/i.php?f=5028#5034

• 04 Limits and Limit Laws in Calculus

Asymptote: a straight line approached by a given curve as one of the variables in the equation of the curve approaches infinity

http://qindex.info/i.php?f=5028#5029

Asymptote: a straight line approached by a given curve as one of the variables in the equation of the curve approaches infinity

http://qindex.info/i.php?f=5028#5029

• 04 Visualizing the chain rule and product rule

Visualizing the chain rule and product rule | Essence of calculus, chapter 4

http://qindex.info/i.php?f=5028#5186

Visualizing the chain rule and product rule | Essence of calculus, chapter 4

http://qindex.info/i.php?f=5028#5186

• 05 Derivatives of exponentials

Derivatives of exponentials | Essence of calculus, chapter 5

http://qindex.info/i.php?f=5028#5184

Derivatives of exponentials | Essence of calculus, chapter 5

http://qindex.info/i.php?f=5028#5184

• 05 What is a Derivative?

What is a Derivative? Deriving the Power Rule

http://qindex.info/i.php?f=5028#5051

What is a Derivative? Deriving the Power Rule

http://qindex.info/i.php?f=5028#5051

• 06 Derivatives of Polynomial Functions

Power Rule, Product Rule, and Quotient Rule

http://qindex.info/i.php?f=5028#5052

Power Rule, Product Rule, and Quotient Rule

http://qindex.info/i.php?f=5028#5052

• 06 Implicit differentiation, what's going on here?

Implicit differentiation, what's going on here? | Essence of calculus, chapter 6

http://qindex.info/i.php?f=5028#5187

Implicit differentiation, what's going on here? | Essence of calculus, chapter 6

http://qindex.info/i.php?f=5028#5187

• 07 Derivatives of Trigonometric Functions

Derivatives of Trigonometric Functions

http://qindex.info/i.php?f=5028#5053

Derivatives of Trigonometric Functions

http://qindex.info/i.php?f=5028#5053

• 08 Derivatives of Composite Functions: The Chain Rule

Derivatives of Composite Functions: The Chain Rule

http://qindex.info/i.php?f=5028#5054

Derivatives of Composite Functions: The Chain Rule

http://qindex.info/i.php?f=5028#5054

• 08 Integration and the fundamental theorem of calculus

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/i.php?f=5028#5189

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/i.php?f=5028#5189

• 09 Derivatives of Logarithmic and Exponential Functions

Derivatives of Logarithmic and Exponential Functions

http://qindex.info/i.php?f=5028#3387

Derivatives of Logarithmic and Exponential Functions

http://qindex.info/i.php?f=5028#3387

• 09 What does area have to do with slope?

What does area have to do with slope? | Essence of calculus, chapter 9

http://qindex.info/i.php?f=5028#5190

What does area have to do with slope? | Essence of calculus, chapter 9

http://qindex.info/i.php?f=5028#5190

• 10 Higher order derivatives

Higher order derivatives | Essence of calculus, chapter 10

http://qindex.info/i.php?f=5028#5191

Higher order derivatives | Essence of calculus, chapter 10

http://qindex.info/i.php?f=5028#5191

• 11 Taylor series

Taylor series | Essence of calculus, chapter 11

http://qindex.info/i.php?f=5028#5192

Taylor series | Essence of calculus, chapter 11

http://qindex.info/i.php?f=5028#5192

• 18 The Fundamental Theorem of Calculus

Redefining Integration

http://qindex.info/i.php?f=5028#3415

Redefining Integration

http://qindex.info/i.php?f=5028#3415

• 19 Properties of Integrals and Evaluating Definite Integrals

Properties of Integrals and Evaluating Definite Integrals

http://qindex.info/i.php?f=5028#3416

Properties of Integrals and Evaluating Definite Integrals

http://qindex.info/i.php?f=5028#3416

• 20 Evaluating Indefinite Integrals

Evaluating Indefinite Integrals

http://qindex.info/i.php?f=5028#3417

Evaluating Indefinite Integrals

http://qindex.info/i.php?f=5028#3417

• 21 Evaluating Integrals With Trigonometric Functions

Evaluating Integrals With Trigonometric Functions

http://qindex.info/i.php?f=5028#3418

Evaluating Integrals With Trigonometric Functions

http://qindex.info/i.php?f=5028#3418

• 22 Integration Using The Substitution Rule

Integration Using The Substitution Rule

http://qindex.info/i.php?f=5028#3419

Integration Using The Substitution Rule

http://qindex.info/i.php?f=5028#3419

• 24 Integration by Trigonometric Substitution

Integration by Trigonometric Substitution

http://qindex.info/i.php?f=5028#3421

Integration by Trigonometric Substitution

http://qindex.info/i.php?f=5028#3421

• 25 Advanced Strategy for Integration in Calculus

Advanced Strategy for Integration in Calculus

http://qindex.info/i.php?f=5028#3422

Advanced Strategy for Integration in Calculus

http://qindex.info/i.php?f=5028#3422

• 26 Evaluating Improper Integrals

Evaluating Improper Integrals

http://qindex.info/i.php?f=5028#3423

Evaluating Improper Integrals

http://qindex.info/i.php?f=5028#3423

• 27 Finding the Area Between Two Curves by Integration

Finding the Area Between Two Curves by Integration

http://qindex.info/i.php?f=5028#3424

Finding the Area Between Two Curves by Integration

http://qindex.info/i.php?f=5028#3424

• 28 Calculating the Volume of a Solid of Revolution by Integration

Calculating the Volume of a Solid of Revolution by Integration

http://qindex.info/i.php?f=5028#3425

Calculating the Volume of a Solid of Revolution by Integration

http://qindex.info/i.php?f=5028#3425

• 29 Calculating Volume by Cylindrical Shells

Calculating Volume by Cylindrical Shells

http://qindex.info/i.php?f=5028#3426

Calculating Volume by Cylindrical Shells

http://qindex.info/i.php?f=5028#3426

• 30 The Mean Value Theorem For Integrals: Average Value of a Function

The Mean Value Theorem For Integrals: Average Value of a Function

http://qindex.info/i.php?f=5028#3427

The Mean Value Theorem For Integrals: Average Value of a Function

http://qindex.info/i.php?f=5028#3427

• The fundamental theorem of calculus

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/i.php?f=5028#5193

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/i.php?f=5028#5193