Help on header display

I am not a coder, and need some help please.

Bascially, I am looking for a code to stick in my header.php that would:

on the home page, show the site name as the heading;
on the category page, show the category name as the heading, and
on single posts page, show the title of the post as the heading

with all these headings wrapped in h1 tags.

Can the experts here help?

Thanks

Swaminathan