We will develop the small amount of additional math and calculus you need to succeed during the course.įirst, read the course syllabus.
Since mathematics is the language of physics, you should be familiar with high school level algebra, geometry, and trigonometry. We encourage you to supplement what you learn here with the Saylor course PHYS102 Introduction to Electromagnetism. Classical mechanics studies statics, kinematics (motion), dynamics (forces), energy, and momentum developed prior to the 1900 from the physics of Galileo Galilei and Isaac Newton. In this course, we study the physics of motion from the ground up – learning the basic principles of physical laws and their application to the behavior of objects. They study the events and interactions that occur among the elementary particles that comprise our material universe. Physicists examine the story behind our universe, which includes the study of mechanics, heat, light, radiation, sound, electricity, magnetism, and the structure of atoms. The set of permissible outputsĪ function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.Physics is the branch of science that explores the physical nature of matter and energy. The set used to define a function is called the domain of the function.
The input and output of a function could be real numbers, the integers, a subset of the rational numbers, a set of real numbers, or more general objects such as vectors. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation, or it could be described explicitly, as a formula or as a graph. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. Others are given by a picture, called the graph of the function.
#PHYSICS 101 MECHANICS PDF HOW TO#
Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. There are many ways to describe or represent a function. The output of a function f corresponding to an input x is denoted by f(x), which is read as "f of x" or "f at x", or simply "f of x", when the context makes it clear.įunctions of various kinds appear in many areas of mathematics, and their study is one of the central topics of modern mathematics. An example is the function that relates each real number x to its square. The notion of a function is one of the most fundamental concepts in mathematics. The exponential function is also used to model exponential growth, in which a constant change in time gives the same proportional change in some other quantity.Ī function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Its slope is positive, since ex has a positive slope. The graph of y = ex is upward-sloping, and increases faster as x gets larger. The exponential function is also used to model exponential growth, in which a constant change in time gives the same proportional change in some other quantity. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same change in the dependent variable. The exponential function is a special case of the hyperbolic cosine function. The exponential function maps the real numbers onto the non-negative real numbers. The exponential function is an entire function, which means that it is differentiable for all x and its derivative is nonzero for all x.
The exponential function is a periodic function with period 2. The exponential function is defined for real arguments x by the power series: It is a special case of the natural logarithm, which is the inverse function of the exponential function. In mathematics, the exponential function is the function ex, where "e" is the base of natural logarithms.
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