In This Chapter
Discovering the simple algebra behind the calculus
Getting a grip on weird calculus symbols
Differentiating with Laurel and Hardy
Finding the derivatives of lines and curves
Tackling the tangent line problem and the difference quotient
Differential calculus is the mathematics of change and the mathematics of infinitesimals. You might say that it’s the mathematics of infinitesimal changes — changes that occur every gazillionth of a second.
Without differential calculus — if you’ve got only algebra, geometry, and trigonometry — you’re limited to the mathematics of things that either don’t change or that change or move at an unchanging rate. Remember those problems from algebra? One train leaves the station at 3 p.m. going west at 80 mph. Two hours later another train leaves going east at 50 mph … . You can handle such a problem with algebra because the speeds or rates are unchanging. Our world, however, isn’t one of unchanging rates ...