I. Menu Keys  Keys that offer choices
E. MATH and NUM
The MATH key offers an extremely useful and versatile menu. Along with NUM menu, you will be able to do the majority of the calculations you need to do by accessing this key.
You can see that there are many selections on these two menus that you will be able to use often.
MATH
1: (display as a fraction) displays an answer as a fraction. You can use with numbers, expressions, lists, sequences, matrices, etc. If the denominator has more than three digits or cannot be simplified, the number is given as a decimal. To access just hit and then 1 after you enter the expression.
Calculate an expression.


The terms in a sequence
can
be expressed as fractions. 

You can change an answer
to a fraction. Just enter 1 after the calculation is done. 

Some expressions cannot
be expressed as a fraction. 
2: displays the answer as a decimal. It is used just like . This is the default setting for answers. It is accessed by entering and then 2.
Convert from fraction
to decimal form 

Fractions can be
evaluated as decimals. 
3: 3 cubes the expression. It is accessed by entering a value, then 3. You can cube an expression, list, matrix, etc.
You can cube a single
number, the numbers in a sequence, etc. 
4: ( evaluates the cube root of a number or expression. Enter and then 4 and then the expression. Close the parentheses. You can put more than one number in { } and evaluate the cube root of each number.
You take the cube 
5: evaluates any root you select. To use this key, you must enter the root first, then the function and then the expression. To use this, press 5. You can use { } to enclose several numbers and evaluate a root for all of them at once.
You must enter the
root first and then the root key. 
6: fMin( (function minimum) and 7:fMax( (function maximum) will give the Xvalue where the local minimum and local maximum of a function occur over a given interval. To use these options, enter the function, the name of the variable, the lower bound of the interval, and then the upper bound of the interval. However, the value returned is an approximation. For this reason, it is more accurate to use the minimum and maximum options in the CALC menu in conjunction with a graph. In the example below, the actual Xvalues are exactly 1 and 1.
Enter the function,
the variable name, the lower bound and the upper bound. 
8: nDeriv( (numerical derivative) is a calculus application that returns the approximate value of a derivative with respect to a given variable at a stated value of X. The TI83 uses an approximation technique and you should be aware that the answer is an approximation and not exact. This application can be particularly useful when you need only to find the value of a derivative at a given point and do not need to actually find the derivative function. Press 8 to access this option. You can increase the accuracy of the answer by changing the tolerance. The default value is 1E3 if one is not entered.
nDeriv(expression, variable, value, tolerance)
Enter the function,
the variable name, and the value to evaluate the derivative. 
The actual value of
the derivative is 1463, reenter with a value of epsilon. 
9: fnInt( (numerical integration) returns the numerical integral of a given expression over a specified interval. If no tolerance is specified the default is 1E5 which is generally accurate enough.
fnInt(expression, variable, lower, upper, tolerance)
Enter the function,
the variable name, and the limits of integration. 