Game Development Reference
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at that. Some topics traditionally found in a first-year physics textbook
that are not discussed in this topic include:
•
energy and work
•
temperature, heat transfer, thermodynamics, entropy
•
electricity, magnetism, light
•
gases, fluids, pressure
•
oscillation and waves.
A note about energy and work is in order, because even in the limited
context of mechanics, the fundamental concept of energy plays a central
role in traditional presentations. Many problems are easier to solve by
using conservation of energy than by considering the forces and applying
Newton's laws. (In fact, an alternative to the Newtonian dynamics that we
study in this topic exists. It is known as Lagrangian dynamics and focuses
on energy rather than forces. When used properly, both systems produce
the same results, but Lagrangian dynamics can solve certain problems more
elegantly and is especially adept at handling friction, compared to Newto-
nian dynamics.) However, at the time of this writing, basic general purpose
digital simulations are based on Newtonian dynamics, and energy does not
play a direct role. That isn't to say an understanding of energy is useless;
indeed disobedience of the conservation of energy law is at the heart of
many simulation problems! Thus, energy often arises more as a way to un-
derstand the (mis)behavior of a digital simulation, even if it doesn't appear
in the simulation code directly.
Now let's talk about the ways in which this topic will irritate calculus
professors. We think that a basic understanding of calculus is really impor-
tant to fully grasp many of the concepts from physics. Conversely, physics
provides some of the best examples for explaining calculus. Calculus and
physics are often taught separately, usually with calculus coming first. It
is our opinion that this makes calculus harder to learn, since it robs the
student of the most intuitive examples—the physics problems for which
calculus was invented to solve! We hope interleaving calculus with physics
will make it easier for you to learn calculus.
Our calculus needs are extremely modest in this topic, and we have left
out even more from calculus than we did from physics. After reading this
chapter, you should know:
•
The basic idea of what a derivative measures and what it is used for.
•
The basic idea of what an integral measures and what it is used for.
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