We will be looking at the equations of graphs in 3-D space as well as vector valued functions and how we do calculus with them. We will also be taking a look at a couple of new coordinate systems for 3-D space.

This is the only chapter that exists in two places in the notes. When we originally wrote these notes all of these topics were covered in Calculus II however, we have since moved several of them into Calculus III. Many of the sections not covered in Calculus III will be used on occasion there anyway and so they serve as a quick reference for when we need them. In addition this allows those that teach the topic in either place to have the notes quickly available to them.

The 3-D Coordinate System — In this section we will introduce the standard three dimensional coordinate system as well as some common notation and concepts needed to work in three dimensions. Equations of Lines — In this section we will derive the vector form and parametric form for the equation of lines in three dimensional space.

We will also give the symmetric equations of lines in three dimensional space. Note as well that while these forms can also be useful for lines in two dimensional space. Equations of Planes — In this section we will derive the vector and scalar equation of a plane.

We also show how to write the equation of a plane from three points that lie in the plane. Quadric Surfaces — In this section we will be looking at some examples of quadric surfaces.

Some examples of quadric surfaces are cones, cylinders, ellipsoids, and elliptic paraboloids. Functions of Several Variables — In this section we will give a quick review of some important topics about functions of several variables. In particular we will discuss finding the domain of a function of several variables as well as level curves, level surfaces and traces.

Vector Functions — In this section we introduce the concept of vector functions concentrating primarily on curves in three dimensional space. We will however, touch briefly on surfaces as well. We will illustrate how to find the domain of a vector function and how to graph a vector function. We will also show a simple relationship between vector functions and parametric equations that will be very useful at times.These notes do assume that the reader has a good working knowledge of Calculus I topics including limits, derivatives and integration.

It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. Notes Quick Nav Download. You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode.

If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. The 3-D Coordinate System — In this section we will introduce the standard three dimensional coordinate system as well as some common notation and concepts needed to work in three dimensions.

Equations of Lines — In this section we will derive the vector form and parametric form for the equation of lines in three dimensional space. We will also give the symmetric equations of lines in three dimensional space. Note as well that while these forms can also be useful for lines in two dimensional space. Equations of Planes — In this section we will derive the vector and scalar equation of a plane.

We also show how to write the equation of a plane from three points that lie in the plane. Quadric Surfaces — In this section we will be looking at some examples of quadric surfaces. Some examples of quadric surfaces are cones, cylinders, ellipsoids, and elliptic paraboloids.

Functions of Several Variables — In this section we will give a quick review of some important topics about functions of several variables. In particular we will discuss finding the domain of a function of several variables as well as level curves, level surfaces and traces.

Vector Functions — In this section we introduce the concept of vector functions concentrating primarily on curves in three dimensional space.

We will however, touch briefly on surfaces as well. We will illustrate how to find the domain of a vector function and how to graph a vector function. We will also show a simple relationship between vector functions and parametric equations that will be very useful at times. Calculus with Vector Functions — In this section here we discuss how to do basic calculus, i. Tangent, Normal and Binormal Vectors — In this section we will define the tangent, normal and binormal vectors.

Arc Length with Vector Functions — In this section we will extend the arc length formula we used early in the material to include finding the arc length of a vector function. Curvature — In this section we give two formulas for computing the curvature i. Velocity and Acceleration — In this section we will revisit a standard application of derivatives, the velocity and acceleration of an object whose position function is given by a vector function.

For the acceleration we give formulas for both the normal acceleration and the tangential acceleration. Cylindrical Coordinates — In this section we will define the cylindrical coordinate system, an alternate coordinate system for the three dimensional coordinate system. As we will see cylindrical coordinates are really nothing more than a very natural extension of polar coordinates into a three dimensional setting. Spherical Coordinates — In this section we will define the spherical coordinate system, yet another alternate coordinate system for the three dimensional coordinate system.

This coordinates system is very useful for dealing with spherical objects. We will derive formulas to convert between cylindrical coordinates and spherical coordinates as well as between Cartesian and spherical coordinates the more useful of the two. We will also see a fairly quick method that can be used, on occasion, for showing that some limits do not exist.

Partial Derivatives — In this section we will look at the idea of partial derivatives. We will give the formal definition of the partial derivative as well as the standard notations and how to compute them in practice i. There is only one very important subtlety that you need to always keep in mind while computing partial derivatives.

Interpretations of Partial Derivatives — In the section we will take a look at a couple of important interpretations of partial derivatives. First, the always important, rate of change of the function.The curvature measures how fast a curve is changing direction at a given point. There are several formulas for determining the curvature for a curve. The formal definition of curvature is. Recall that we saw in a previous section how to reparametrize a curve to get it into terms of the arc length.

In general the formal definition of the curvature is not easy to use so there are two alternate formulas that we can use. Here they are.

Back in the section when we introduced the tangent vector we computed the tangent and unit tangent vectors for this function. These were. In this case the curvature is constant. This means that the curve is changing direction at the same rate at every point along it.

Recalling that this curve is a helix this result makes sense.

## My Page Title

In this case the second form of the curvature would probably be easiest. Here are the first couple of derivatives. There is a special case that we can look at here as well. As we saw when we first looked at vector functions we can write this as follows. If we then use the second formula for the curvature we will arrive at the following formula for the curvature.

Notes Quick Nav Download. You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Show Solution Back in the section when we introduced the tangent vector we computed the tangent and unit tangent vectors for this function.

Show Solution In this case the second form of the curvature would probably be easiest.Here is list of cheat sheets and tables that I've written. All of the cheat sheets come in two version.

### Calculus III

A full sized version and a "reduced" version. The reduced version contains all the information that the full sized version does except that each page from the full sized version has been reduced so that each page of the reduced version is two pages from the full version.

With the exception of the Complete Calculus Cheat Sheet and the Integrals Cheat Sheet all the reduced versions will fit on one piece of paper. All of these are pdf files and so you will need the Adobe Viewer to view them. You can download the latest version here. View Quick Nav Download. This menu is only active after you have chosen a topic from the Quick Nav menu to the left or Main Menu in the upper left corner.

You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together.

Work fast with our official CLI. Learn more. If nothing happens, download GitHub Desktop and try again. If nothing happens, download Xcode and try again. If nothing happens, download the GitHub extension for Visual Studio and try again. For those who do not wish to try compiling this from the source, just download the PDF, it's probably reasonably up to date. Honestly, it serves two functions, first, it is a notecard that is allowed on my tests.

The other function it serves is that it is written in TeX and I have been meaining to find an excuse to learn a little bit of TeX. I am including the TeX source to allow other people to edit it as they see fit and in particular because I couldn't seem to find any good TeX sources for the derivative and integral information.

Also included, by popular demand, is a slightly-reformatted version that is made by "printing" both sides onto one side leaving the other side to be used for whatever. This is made by hand and is not updated from the tex document.

**1-99/120 Herblore Guide 2020 - NEW Methods Included! [Runescape 3]**

As such, it may end up being behind the tex-generated PDF. We use optional third-party analytics cookies to understand how you use GitHub. You can always update your selection by clicking Cookie Preferences at the bottom of the page.

For more information, see our Privacy Statement. We use essential cookies to perform essential website functions, e. We use analytics cookies to understand how you use our websites so we can make them better, e. Skip to content. Dismiss Join GitHub today GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together.

Sign up.

Go back. Launching Xcode If nothing happens, download Xcode and try again. Latest commit. Git stats 12 commits. Failed to load latest commit information. View code. This is a Cheat Sheet for Calculus 3.

Also to be noted, I found the images by searching on google for the relevant surfaces.But in this week's "Free Lesson Friday" - PGA Professional Mike Bender shares some tips on how to learn the game the right way. More Free Lesson Fridays VideoFind a PGA InstructorYour local PGA Professional is your best source for serious game improvement.

Find an instructor near you and get personalized golf help. COM is part of Bleacher Report - Turner Sports Network, part of the Turner Sports and Entertainment Network. Read this wikiHow to learn more. Hands off your face. Avoid touching your face and popping those pimples. Go makeup free for a while. Give your face a chance to breathe. Wash your face twice daily. Use moisturizer and toner each time after you wash.

Skip the sweets and junk food. Eat more fruits and veggies instead. Drink lots of water. Reduce the stress and try get around 10 to 11 hours of sleep. Treat your acne with benzoyl peroxide or salicylic acid.

Seek a dermatologist's advice. This is the number one rule. Pimples contain nasty bacteria. If you pop your pimples, that bacteria has a chance of getting inside other pores and giving them a place to stay without charging rent, so to speak.

Make sure your pimples pay rent. Foundation and lipstick can be harmful to the skin. Although it may be a bit embarrassing going fresh faced if you have bad skin, going "bare" will definitely help your skin clear up. Inflammation will cause even more redness and pain. Your hands (no matter how many times you wash them) have oils and dirt on them, and are vectors for bacteria. If you're constantly wiping that dirt, oil, and bacteria back onto your face, chances are it's not going to respond too well and you will also end up spreading even more the bacteria to other areas of your face.

Many doctors recommend that you drink between 9 and 12 cups of water per day (2. Although the evidence has been disputed for decades, new reports seem to indicate that diets do have a substantial effect on acne, listing sugar as a trigger.

Milk, too, has recently been implicated as an acne-producing agent. Milk stimulates male sex hormones testosterone and androgens that, along with insulin, cause nasty pimples. For a healthy alternative to water, brew some tasty and healthy green tea. Diet can help your complexion look its best if you let it.Anniversary statistical collection World Statistics Day 2015 BRICS Joint Statistical Publications 39, Miasnitskaya St.

Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze and draw conclusions from data. Some statistical measures include mean, regression analysis, skewness, kurtosis, variance and analysis of variance.

Statistics is a term used to summarize a process that an analyst uses to characterize a data set. If the data set depends on a sample of a larger population, then the analyst can develop interpretations about the population primarily based on the statistical outcomes from the sample. Statistical analysis involves the process of gathering and evaluating data and then summarizing the data into a mathematical form.

Statistical methods analyze large volumes of data and their properties. Statistics is used in various disciplines such as psychology, business, physical and social sciences, humanities, government and manufacturing. Statistical data is gathered using a sample procedure or other method. Two types of statistical methods are used in analyzing data: descriptive statistics and inferential statistics. Descriptive statistics are used to synopsize data from a sample exercising the mean or standard deviation.

Inferential statistics are used when data is viewed as a subclass of a specific population. A mean is the mathematical average of a group of two or more numerals.

Regression analysis determines the extent to which specific factors such as interest rates, the price of a product or service, or particular industries or sectors influence the price fluctuations of an asset. This is depicted in the form of a straight line called linear regression. Skewness describes the degree a set of data varies from the standard distribution in a set of statistical data.

Most data sets, including commodity returns and stock prices, have either positive skew, a curve skewed toward the left of the data average, or negative skew, a curve skewed toward the right of the data average. Kurtosis measures whether the data are light-tailed or heavy-tailed that correlate to a standard distribution. Data sets with high kurtosis have heavy tails, which results in less investment risk. Data sets with low kurtosis have light tails, which results in greater investment risk.

Variance is a measurement of the span of numbers in a data set.

The variance measures the distance each number in the set is from the mean. Variance can help determine the risk an investor might accept when buying an investment. Ronald Fisher developed the analysis of variance method.

## thoughts on “Calc 3 cheat sheet reddit”