Solving Differential
Equations: Easy
Equations: Easy
y'=2
What is 2x+C?
+C
Reimann Sums.
What is an area solved through the use of rectangles?
Who was Sir Isaac Newton?
y'=5
y=5x+C
A solution without an initial condition.
What is a general solution?
The Ancient Greeks used a method in which the area of a polygon was squeezed between two polygons: one inscribed in the region and one circumscribed about the region.
What is the exhaustion method?
The difference between the values of the integral of a given function f(x) for an upper value b and a lower value a of the independent variable x.
What is a definite integral?
Another man often credited with discovering Calculus (often ignored because of Newton).
Gottfried Leibnitz
y'=6
y=6+C
A solution when given an initial condition.
One simple shape used to determine the area under a curve on a graph.
What is a rectangle?
This must be the case for a definite integral to be determined as an area.
What is the function f must be continuous and nonnegative on [a,b]?
The theorem that connects Leibnitz and Newton's work. It states that differentiation and definite integration are inverse operations.
y'=67
y=67x+C
Σ
What is Sigma?
The lower sum.
What is the area of the inscribed rectangle?
A more difficult shape used to determine the area beneath a line on a graph.
What is a trapezoid?
This man discovered the concept of Riemann Sums.
Who was Bernhard Riemann?
y'=56,789
y=56789x+C
The index of summation is realized via this variable. Often written as, _=x.
What is the letter i?
The upper sum.
What is the area of circumscribed rectangles?
This is used to verify your results using the trapezoidal method.
What is error analysis?
The letter Σ comes from this culture.
What is Greek society?