Lecture Note
University
Massachusetts Institute of TechnologyCourse
Multivariable CalculusPages
1
Academic year
2022
Sporkz
Views
86
p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:Arial;color:#000000;} .ft02{font-size:18px;font-family:ArialMT;color:#000000;} .ft03{font-size:18px;font-family:Arial;color:#000000;} .ft04{font-size:18px;line-height:22px;font-family:Arial;color:#000000;} .ft05{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} .ft06{font-size:18px;line-height:20px;font-family:ArialMT;color:#000000;} Vector introduction ● Vectors are geometric objects that have both a magnitude and direction. They are often used to represent quantities that vary with both time and space. ● A vector is a directed line. It can be used to show direction, velocity and acceleration. ● A vector has two components: magnitude and direction. Magnitude is the length of the vector expressed in terms of some unit, such as meters or kilometers. Directionis expressed as an angle measured from the positive x-axis (the horizontal axis)with 0 degrees at the 3 o’clock position, 90 degrees at the 12 o’clock position andso on. We discussed functions that depend on two variables and partial derivatives before. Thoseare some of the basic ideas underlying multivariable calculus. The other key concept inmultivariable calculus is vectors, which we will look at. The concept of vectors is an important part of physics. And people who study this topicmay have problems even after a lot of exercises. We will go through the common questions, review the fundamentals of vectors and someof the misconceptions, as well as talk about some applications of vectors as we go. In physics, a vector is a quantity that has both a magnitude and direction. Examplesinclude velocity, acceleration, and force. Vectors. Magnitute + direction Ex. Velocity Force. Velocity, force, the electric field and the magnetic field, they all are vectors. For now, we will work with two-dimensional vectors. That means that we can draw picturesof them, which I find very helpful for visualizing and understanding them. Threedimensional vectors and higher dimensional vectors may come later.
Vector Introduction
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