Focus On Curves and Surfaces (Focus on Game Development)

What Is Differential Calculus?

There are two branches of calculus: differential calculus and integral calculus. Integral calculus is a method used to determine the area under the curve of a given function. Most of the time, it isn't useful to think of this as a literal computation of area. Instead, it is useful for determining how the results of a function accumulate with respect to a given variable. Integral calculus is used to answer questions like the one shown graphically in Figure A.1.

Figure A.1: An example of where integral calculus is useful.

There is also differential calculus, which is a method used to determine how the value of a given function changes with respect to a given variable. In basic terms, this is the slope of a function at a certain point along the curve. Differential calculus is used to answer questions like the one shown in Figure A.2.

Figure A.2: An example of where differential calculus is useful.

In this appendix, I will only talk about differential calculus because you need it to compute the slopes of curves and the normals of surfaces. I talk briefly about integral calculus in some of the chapters.