The Science of Life Lecture Series

In this third section of Chapter 1 , I will cover the basics of equation solving.  I've already touched on this in Physics , and will get to in in Chemistry; this is vital for all of math and science, including Economics. Equivalent Forms One of the most vital statements in Algebra is that two equations which have the same solutions are equations.  In all future endeavors, both science and in math, we look to solve for the variable that is unknown, and the final form of that equation doesn't look anything like the initial equation, but is in an equivalent form, so has all of the same solutions as the initial equations.  For any real numbers a, b, c, and d, $a+c=b+c$ is equivalent to $a=b$ and $a=b$ is equivalent to $a \times d=b \times d$.  What we can do from here is say that $a+c=b+c$ is equivalent to $a \times d=b \times d$. Like Terms In any equation, a "term" is any constant, variable, product of any number of constants and/or variables, or the qu...

Here, I will cover some of the basic operations and properties of real numbers. I say real numbers to differentiate from imaginary and complex numbers, both of which deal with the square root of -1, $\sqrt{-1}=i$. This course will not deal with the square root of -1, so all numbers will be real in this course. There are courses which deal with i, which typically have the word "Complex" in their name. The Absolute Value The absolute value (given by $\left | a \right |$) is the distance from the zero on the number line, regardless of the sign. This is to say $\left | -a |=\left | a |$.  The absolute value of -2 is 2, the absolute value of 2 is 2.  It does not matter what the initial value is, the sign after running it through the absolute value function will always, under every circumstance ever, be positive. Inequalities There are two types of inequality, less than and "greater than".  There are also two flavors of inequality, with and without the equal s...

This is a natural continuation of Chapter 1 Section 2 .  When we make models, we need to make sure that, when we run the numbers, the dimensions of the solution naturally make sense.  The word "dimension" in physics means something more general than the definition we are used to here in every day life.  We typically think of dimensions as length, width, and height; we do live in a three dimensional world, after all.  The word dimension in science means the units that we are working with.  This could be Distance (like length of a box), or is could be time (duration of a trip), or it could be mass (I weigh 15 stone).  The dimensions of density are kilograms per cubic meter (kg/m 3 ). When these dimensions are used in mathematical equations, they are treated as if they are variables we've seen in Algebra ; they can be canceled and squared like any other value in mathematics.  For example, if we have a room that is 20ft.×30ft.×15ft, then we multiply...

In this first section from Chapter 1 , I'll cover some basics of Algebra, including basic terminology. Basic Terms: When a letter is used for a stand-in for a value which can take up any range of numbers, we call it a variable.  When a letter is used to represent a specific number (typically when we don't know what it is, but there can only be one), it is said to be a constant. Our Constants An example of this is the gross pay; the pay on your pay check before taxes is given by P G =H×W, where H is the hours worked and the W is your hourly wage.  Since hourly wage doesn't change from week to week, it is considered to be constant.  If you work part time, than your hours in any given week is considered a variable, because they do tend to change. An algebraic expression consists of a combination of constants, variables, and operation signs.  For example, H×W from the pay equation above is considered an expression.  When an equals sign is placed ...

Algebra is the mathematics of equalities and inequalities.  How much you'll spend at the grocery store, what you'll get on a paycheck after taxes, how much you'll owe or get back in taxes at the end of the year, how much money you'll have left at the end of the month after paying your bills; all of these problems and so many more are, by their very nature, algebraic problems. In this chapter, I'll cover some basics of Algebra and how to problem-solve with Algebra.  Problem solving can be applied to science, economics, and life.  After learning the algebraic problem solving techniques, you should try applying them to the specifics of your life. For those of you keeping track, here's the section breakdown: Section 1: Some Basics of Algebra Section 2: Operations and Properties of Real Numbers Section 3: Solving Equations Section 4: Introduction to Problem Solving Section 5: Formulas, Models, and Geometry Section 6: Properties of Exponents Sectio...

This material comes from Chapter 1 Section 2 of the Newtonian Physics Lecture Series. If we cannot interact with matter directly, or if we want to make a prediction of a system before we build the system to test it, we draw up a model of the system related to the phenomenon in question.  Chemistry is a good example of this.  We cannot observe the molecules directly with our eyes, so we model the reaction with the known laws of physics and chemistry. Using these models, we predict the behaviors and results of the chemical reaction based upon the interactions between the components of the system or between the system and its surroundings.  The words "system" and "surroundings" will come up in this lecture series and have specific definitions, so I may as well define them now.  The "system" is everything under direct study in the moment we are studying it.  The surroundings are everything outside of the system, but still have an affect on th...

Before we get into actual Physics, commentary must first be made about the foundations of all science, including physics.  The fundamental basis for all physics is the concept of units.  After all, when I say "The speed is 6", that is meaningless.  Am I talking about m/s, km/hr., miles/hr, knots?  Which units am I using? There is a system of measurement which has been around for centuries, but has been globally standardized for use in science since 1960 .  This system is called the Système international from the French, who was the first to widely adopt the concept shortly after their Revolutionary War against Britain.  The shorthand for this system is SI, and the fundamental units it uses for classical mechanics is the meter, the second, and the kilogram.  There are other fundamental units in Classical Physics, but those deal with either electricity or waves, and since those are covered in their own separate semesters, I'll cover those fundam...

This is the introduction to chapter 1 of the Physics 180 Lecture Series, which will cover some of the basics required to succeed in full understanding of the subject of, well, any scientific subject, but for the purposes of this series, the success in Physics.   After all, physics is based on experimental observations which are used to derive mathematical formulation.  The main objective of the field of physics is to identify a limited amount of fundamental physical laws of nature and derive from those laws theories that can be used to predict the results of future experiments.  However, whenever experiment disagrees with theory, the theory must always be either altered or thrown out. Isn't that right Feynman? This physics course deals with what is called "Classical Physics", which is the physics of normal, everyday objects of normal, everyday sizes and masses, traveling at normal, everyday speeds.  Some text books (the one which I am referring for this ...

This is going to be the section which will cover Physics 180 - Newtonian Mechanics.  This is the physics of the macroscopic world, the world that most of us can see, touch, hear, taste, and smell.  Most physics define Newtonian Physics as the physics which has been discovered by 1900, but this feels too arbitrary for me.  The reason why it's the physics which has been discovered by 1900 is because we as a species have discovered the entirety of the physics of the macroscopic world by 1900, while the rest of physics (waves mechanics, Relativity, Quantum Physics, etc.) has yet to be discovered by this year.  With that in mind, while the "discovered by 1900" is an accurate definition as a time separator between the Newtonian and non-Newtonian classes, I still prefer the physical definition over the discovery date definition. When I speak of the physics of the macroscopic world, I am speaking of the motions of these objects and the energy and forces associated ...