Changes

=Single Variable Review=

=Single Variable Review=

This section is not intended to be a course in elementary calculus - the student is expected to understand this material before beginning the course.  It is provided here as a reference for student.

This section is not intended to be a course in elementary calculus - the student is expected to understand this material before beginning the course.  It is provided here as a reference for student.

<math>\sum_{j=1}^n f(x_j) (q_j-q_{j-1}) \ </math>

<math>\sum_{j=1}^n f(x_j) (q_j-q_{j-1}) \ </math>

This is called a '''Riemann sum''', named after the famous 19th century mathematician [[Bernhard Reimann]].  If this sum approaches a limit as <math>n \rightarrow \ </math>[[Infinity|<math>\infty \ </math>]] no matter how we choose our <math>q_j \ </math>'s or our <math>x_j \ </math>'s, then <math>f \ </math> is said to be '''Riemann integrable''' and that limit is called the definite integral of <math>f \ </math> from <math>a \ </math> to <math>b \ </math>, and this is written

This is called a '''Riemann sum''', named after the famous 19th century mathematician [[Bernhard Reimann]].  If this sum approaches a limit as <math>n \rightarrow \ </math>[[Infinity|<math>\infty \ </math>]] no matter how we choose our <math>q_j \ </math>'s or our <math>x_j \ </math>'s, then <math>f \ </math> is said to be '''Riemann integrable''' and that limit is called the definite integral of <math>f \ </math> from <math>a \ </math> to <math>b \ </math>, and this is written <math>\int_a^b f(x)dx \ </math>

 

<math>\int_a^b f(x)dx \ </math>

The '''fundamental theorem of calculus''' states that <math>\int_{x_o}^x \frac{d}{dx}f(x)dx = f(x) \ </math>.

The '''fundamental theorem of calculus''' states that <math>\int_{x_o}^x \frac{d}{dx}f(x)dx = f(x) \ </math>.