Document
... Last argument is the closest. Here’s the real reason: Suppose that R were countable. In particular, any subset of R, being smaller, would be countable also. So the interval [0,1] would be countable. Thus it would be possible to find a bijection from Z+ to [0,1] and hence list all the elements of [0, ...
... Last argument is the closest. Here’s the real reason: Suppose that R were countable. In particular, any subset of R, being smaller, would be countable also. So the interval [0,1] would be countable. Thus it would be possible to find a bijection from Z+ to [0,1] and hence list all the elements of [0, ...
( )= x
... reality, they can be more difficult and are fraught with dangers. And in calculus, inequalities show up more frequently than solving equations. Solving inequalities are a simple matter if they are based on linear equations. They are solved exactly like linear equations, remembering that if you multi ...
... reality, they can be more difficult and are fraught with dangers. And in calculus, inequalities show up more frequently than solving equations. Solving inequalities are a simple matter if they are based on linear equations. They are solved exactly like linear equations, remembering that if you multi ...
INTRODUCTION TO POLYNOMIAL CALCULUS 1. Straight Lines
... the line to any other point on the line. The law of similar triangles says that this ratio is independent of the two points on the line that are chosen. What about the slope of a curve that is not a straight line? Does this make sense? If so, how do we calculate it? Let's look at an example, say the ...
... the line to any other point on the line. The law of similar triangles says that this ratio is independent of the two points on the line that are chosen. What about the slope of a curve that is not a straight line? Does this make sense? If so, how do we calculate it? Let's look at an example, say the ...
Exponential Growth and Decay
... iii. The term extremum is used to denote either local maximum or a local minimum. iv. The value x = c is called a critical value for a continuous function f if 1. either f 0 (c) = 0 or f 0 (x) fails to exist at x = c and if 2. f (c) is well-defined. ...
... iii. The term extremum is used to denote either local maximum or a local minimum. iv. The value x = c is called a critical value for a continuous function f if 1. either f 0 (c) = 0 or f 0 (x) fails to exist at x = c and if 2. f (c) is well-defined. ...
Generating Functions and the Fibonacci Sequence
... The Fibonacci sequence is a well known sequence in mathematics developed by adding the two previous terms to get the next term. Defined in the 13th century by an Italian mathematician, Leonardo Fibonacci, the recurrence relation for the Fibonacci sequence is Fn+1 = Fn + Fn−1 for all n ≥ 2 with F0 = ...
... The Fibonacci sequence is a well known sequence in mathematics developed by adding the two previous terms to get the next term. Defined in the 13th century by an Italian mathematician, Leonardo Fibonacci, the recurrence relation for the Fibonacci sequence is Fn+1 = Fn + Fn−1 for all n ≥ 2 with F0 = ...
Function of several real variables
In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The ""input"" variables take real values, while the ""output"", also called the ""value of the function"", may be real or complex. However, the study of the complex valued functions may be easily reduced to the study of the real valued functions, by considering the real and imaginary parts of the complex function; therefore, unless explicitly specified, only real valued functions will be considered in this article.The domain of a function of several variables is the subset of ℝn for which the function is defined. As usual, the domain of a function of several real variables is supposed to contain an open subset of ℝn.