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.
Until some outstanding mathematicians brought precision in limits and derivatives Bolzano and Cauchy , in integrals Riemann and Cauchy and Dedekind with the creation of the real numbers. Discover all these aspects in our calculus books.
Calculus can be defined as the branch of mathematics that predicts a specific result based on previous data. It investigates values, measurements, areas, volumes and lengths. It has a wide scope in other disciplines such as engineering , chemistry , physics or economics. There are different types of calculus: differential its focus is on derivatives , arithmetic uses numbers and some conventional symbols , integral deals with the sum of infinities and algebraic uses numbers and letters to substitute quantities.
Consult our compendium of more than 20 calculus books in PDF , available for free and immediate download. Fuente: CloudFront. Fuente: Massachusetts Institute of Technology. Fuente: Old Dominion University. Fuente: Lamar University. Fuente: Dartmouth College. Fuente: Louisiana State University. Fuente: Whitman College.
Fuente: Portland State University. Fuente: Nagoya University. Fuente: Simon Fraser University. Fuente: University of Wisconsin—Madison. Fuente: University of North Georgia. Description : These lecture notes should be accessible to anyone wanting to learn Calculus III or needing a refresher in some of the topics from the class. The notes assume that the reader has a good working knowledge of limits, derivatives, integration, some integration techniques, parametric equations, vectors, and three dimensional space.
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