Plato believed that unchanging ideas or forms exist outside the physical realm. He believed that these ideas are the true objects of knowledge and that the physical world is inferior to the rational intellect. Plato's theory of forms traces back to his teacher Socrates, who believed that the inner spirit has intuitive access to divine truths which he tried to define through dialogues, as revealed in Plato's writings.

1. Given the signal f(t) = 2t, find the exponential Fourier series representation of the signal over the
interval (0,2)
Solution
The theory, or doctrine, of forms (also called the theory of ideas) is Greek
philosopher Plato's (c. 428-347 b.c.) expression of his belief that there are forms that exist
outside the material realm, and therefore are unchanging-they do not come into existence,
change, or pass out of existence. It is these ideas that, according to Plato, are the objects or
essence of knowledge. Further, he posited that the body, the seat of appetite and passion, which
communes with the physical world (rather than the world of ideas or forms), is inferior to the
intellect. He believed the physical aspect of human beings to be irrational while the intellect, or
reason, was deemed to be rational. The origins of Plato's theory can be traced to Socrates (c.
470-399 b.c.), who believed that the psyche (inner spirit) has intuitive access to divinely known
principles or truths, which he attempted to formulate through his conversations with others.
Indeed, the Socratic dialogues, written by Plato, reveal that Socrates was striving to define the
exact nature of the traditional Greek moral virtues of piety, temperance, and courage. The theory,
or doctrine, of forms (also called the theory of ideas) is Greek philosopher Plato's (c. 428-347
b.c.) expression of his belief that there are forms that exist outside the material realm, and
therefore are unchanging-they do not come into existence, change, or pass out of existence. It is
these ideas that, according to Plato, are the objects or essence of knowledge. Further, he posited
that the body, the seat of appetite and passion, which communes with the physical world (rather
than the world of ideas or forms), is inferior to the intellect. He believed the physical aspect of
human beings to be irrational while the intellect, or reason, was deemed to be rational. The
origins of Plato's theory can be traced to Socrates (c. 470-399 b.c.), who believed that the
psyche (inner spirit) has intuitive access to divinely known principles or truths, which he
attempted to formulate through his conversations with others. Indeed, the Socratic dialogues,
written by Plato, reveal that Socrates was striving to define the exact nature of the traditional
Greek moral virtues of piety, temperance, and courage. The theory, or doctrine, of forms (also
called the theory of ideas) is Greek philosopher Plato's (c. 428-347 b.c.) expression of his belief
that there are forms that exist outside the material realm, and therefore are unchanging-they do
not come into existence, change, or pass out of existence. It is these ideas that, according to
Plato, are the objects or essence of knowledge. Further, he posited that the body, the seat of
appetite and passion, which communes with the physical world (rather than the world of ideas or
forms), is inferior to the intellect. He believed the physical aspect of human beings to be
irrational while the intellect, or reason, was deemed to be rational. The origins of Plato's theory

2. can be traced to Socrates (c. 470-399 b.c.), who believed that the psyche (inner spirit) has
intuitive access to divinely known principles or truths, which he attempted to formulate through
his conversations with others. Indeed, the Socratic dialogues, written by Plato, reveal that
Socrates was striving to define the exact nature of the traditional Greek moral virtues of piety,
temperance, and courage. The theory, or doctrine, of forms (also called the theory of ideas) is
Greek philosopher Plato's (c. 428-347 b.c.) expression of his belief that there are forms that exist
outside the material realm, and therefore are unchanging-they do not come into existence,
change, or pass out of existence. It is these ideas that, according to Plato, are the objects or
essence of knowledge. Further, he posited that the body, the seat of appetite and passion, which
communes with the physical world (rather than the world of ideas or forms), is inferior to the
intellect. He believed the physical aspect of human beings to be irrational while the intellect, or
reason, was deemed to be rational. The origins of Plato's theory can be traced to Socrates (c.
470-399 b.c.), who believed that the psyche (inner spirit) has intuitive access to divinely known
principles or truths, which he attempted to formulate through his conversations with others.
Indeed, the Socratic dialogues, written by Plato, reveal that Socrates was striving to define the
exact nature of the traditional Greek moral virtues of piety, temperance, and courage.