What is vector calculus

Arc Length Polar Coordinates 2. Slopes in polar coordinates 3. Areas in polar coordinates 4. Parametric Equations 5. Calculus with Parametric Equations 11 Sequences and Series 1. Sequences 2. Series 3. The Integral Test 4. Alternating Series 5. Comparison Tests 6.

Absolute Convergence 7. The Ratio and Root Tests 8. Power Series 9. Calculus with Power Series Taylor Series Taylor's Theorem Additional exercises 12 Three Dimensions 1. The Coordinate System 2. Vectors 3. The Dot Product 4. The Cross Product 5. Lines and Planes 6. Other Coordinate Systems 13 Vector Functions 1. Space Curves 2. Calculus with vector functions 3. Arc length and curvature 4. Motion along a curve 14 Partial Differentiation 1. Functions of Several Variables 2. Limits and Continuity 3.

Partial Differentiation 4. The Chain Rule 5. Directional Derivatives 6. Higher order derivatives 7. Maxima and minima 8. Lagrange Multipliers 15 Multiple Integration 1. Volume and Average Height 2. We will be taking a brief look at vectors and some of their properties. We will need some of this material in the next chapter and those of you heading on towards Calculus III will use a fair amount of this there as well.

Basic Concepts — In this section we will introduce some common notation for vectors as well as some of the basic concepts about vectors such as the magnitude of a vector and unit vectors.

We also illustrate how to find a vector from its starting and end points. Vector Arithmetic — In this section we will discuss the mathematical and geometric interpretation of the sum and difference of two vectors. Vector calculus is also known as vector analysis which deals with the differentiation and the integration of the vector field in the three-dimensional Euclidean space. Vector fields represent the distribution of a given vector to each point in the subset of the space.

In the Euclidean space, the vector field on a domain is represented in the form of a vector-valued function which compares the n-tuple of the real numbers to each point on the domain. Vector analysis is a type of analysis that deals with the quantities which have both the magnitude and the direction. Vector calculus also deals with two integrals known as the line integrals and the surface integrals.

Line Integral. According to the vector calculus, the line integral of a vector field is known as the integral of some particular function along a curve. In simple words, the line integral is said to be integral in which the function that is to be integrated is calculated along with the curve.

You can integrate some particular type of the vector-valued functions along with the curve. For example, you can also integrate the scalar-valued function along the curve. Sometimes, the line integral is also called the path integral, or the curve integral or the curvilinear integrals.

Surface Integral.