The core of any spreadsheet application is the functions it supports and how well they work. In Excel 2010 a lot of work has been put in to update the function library and to tidy it up, so functions are easier to locate and use. The ability to include mathematical equations, both by cutting and pasting predefined ones and by creating them from scratch, has also been greatly improved. The equations you create can't be solved by Excel, but they can be included in a worksheet, to illustrate or support live calculations. The equation editor is the same as in Word 2010.
There are 50 new functions in Excel 2010, many designed in response to academic criticism that the consistency of function names isn't all it could be. If you need a full list of all the functions in Excel, open up Excel Help and search on 'list of functions'. Here you'll find a list of the new functions in Excel 2010. Most of the revised functions are in the statistics category, though some, like CEILING, which rounds decimal numbers up to the nearest multiple of a selected number, have more general application.
To enter a function into a cell, type '=' into the function editor and a pull-down menu appears at the left-hand end of the function bar. If you've used the function recently, you can select it from this menu. Alternatively, a dialog showing all functions can be called up by clicking the More functions... option and you can select one from there. A third way in is to type two or three keywords into the Search box in the Insert Function dialog. A list of the most likely choices pops up. Select the function and a separate dialog appears, where you can enter its corresponding parameters. Click the tick symbol when your function is complete and the result appears in the selected cell.
To add an equation to an Excel worksheet, go to the Insert tab and click on the Equation button at the right hand end of the ribbon. If you want to add one of several pre-defined equations, click on the drop-down at the right of the button. To create a new equation from scratch, click on the main area of the button. Any of the predefined equations can be dragged from the drop-down onto the worksheet, where they appear as text boxes, which can be freely moved and adjusted. You'll probably need to increase the width of the equation box, to see it laid out correctly.
To create an equation from scratch, insert a blank equation place holder from the Insert tab and use the tools on the extra ribbon tab, labelled Equation Tools. As well as being able to type variables directly into the equation, you can pick mathematical symbols from the selector in the ribbon and construct elements such as fractions, super and subscripts, roots, integrals and brackets by selecting them from the category buttons to the right of the symbol selector. As you build your equation, you may need to use Insert, Equation again, to continue it outside a pair of brackets or a large divisor.