 trustle > EngliSea > M > Math > 60 Calculus Calculus Summary
http://qindex.info/i.php?f=5028#3679 Calculus Summary
http://qindex.info/i.php?f=5028#3660 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 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 02 The paradox of the derivative
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 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 03 Derivative formulas through geometry
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 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 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 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 05 Derivatives of exponentials
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 06 Derivatives of Polynomial Functions
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 07 Limits
Limits | Essence of calculus, chapter 7
http://qindex.info/i.php?f=5028#5188 08 Derivatives of Composite Functions: The Chain Rule
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 09 Derivatives of Logarithmic and Exponential Functions
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 10 Higher order derivatives
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 19 Properties of Integrals and Evaluating Definite Integrals
Properties of Integrals and Evaluating Definite Integrals
http://qindex.info/i.php?f=5028#3416 21 Evaluating Integrals With Trigonometric Functions
Evaluating Integrals With Trigonometric Functions
http://qindex.info/i.php?f=5028#3418 25 Advanced Strategy for Integration in Calculus
Advanced Strategy for Integration in Calculus
http://qindex.info/i.php?f=5028#3422 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 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 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 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.
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