{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

22-Vectors in a Plane

22-Vectors in a Plane - Vectors in the Plane John E Gilbert...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Vectors in the Plane John E. Gilbert, Heather Van Ligten, and Benni Goetz Calculus for functions z = f ( x, y ) of two (or more) variables relies heavily on what you already know about the calculus of functions y = f ( y ) of one variable. A few preliminary ideas about vectors, various coordinate systems in two and three variables, as well as more complicated curves in the plane - ones usually defined implicitly - need to be studied too. It’s convenient to do this in terms of vector functions . But once we’ve done that, calculus is the next step! Let’s start with vectors - you may have met them already, and you’ll certainly make good use of them in a number of your other courses! What is a vector: A quantity, be it geometric, scientific or whatever, is a vector so long as it has both a magnitude (or length ) and a direction . For instance, velocity can be described by a vector because it has a magnitude, namely speed , as well as a direction: the wind blows at a speed of 5 mph from the north-west, Joe heads due north at 75 mph in his car, and so on. Displacements provide a di ff erent type of example: let’s look at where Bob lives in relation to Alice. His house is at point B which is 223 ft., 18 ENE, from Alice’s house at point A . If we represent this as an arrow from A to B , it determines a displacement vector -→ AB with magnitude the distance from A to B , and direction the direction from A to B . It’s natural to represent this vector by an arrow with A the tail and B the head . A B N E 100 ft In general, we’ll usually label vectors by single bold-faced letters like a , v , ... , and so on. Beware: physicists and engineers sometimes use di ff erent notation. The length of a vector v will be denoted by | v | ; this length is a positive number except for the
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern