Calculus iii Definition and 61 Threads

Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space





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{\displaystyle \mathbb {R} ^{3}.}
The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of
electromagnetic fields, gravitational fields, and fluid flow.
Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis. In the conventional form using cross products, vector calculus does not generalize to higher dimensions, while the alternative approach of geometric algebra which uses exterior products does (see § Generalizations below for more).

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    Calculus III & Differential Equations

    Can both of these classes be taken concurrently? I'm not sure but I think, at my community college, Calculus III is a prerequisite to Differential Equations but, a few friends from Rutgers and TCNJ have taken Differential Eq's before Calc 3. I guess it's different everywhere and I'm just...
  2. A

    Calculus III Parametric Equations

    Homework Statement I've uploaded a scan of the questions. Questions 4, 5, and 6 are given in the 3 files uploaded. They all come from the given information from the first scan of the problem. Homework Equations The Attempt at a Solution I've worked everything I could on paper...
  3. E

    Calculus III & differential equations in one semester?

    should i or should i not? any advice? here's my current fall08 schedule: calculusIII differential equations mechanics of solids and fluids general ed course both calcIII and de are in the evening (back-to-back, 2 hours each). for those who have taken both of these classes, is it...
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    What are the main concepts covered in Calculus III?

    If Calculus I is differential Calculus and Calculus II is Integral Calculus then what does calculus III entail.
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    Self-teaching Calculus III Books

    Hi all, Well, there is a possibility that I may not be able to get into a Calculus III course next semester so I was wondering if anyone knew of any good books that I could use to teach myself the subject matter. I'm pretty sure Calculus III covers the following: Infinite series...
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    How Can Calculus Help Position the Center of Mass in a Hemiwasher?

    Question Details: I have two circles centered at the origin, one with radius A and the other with radius b. Looking at the hemiwasher (area between) the circles form above the x axis, find the values of A and B that place the center of mass within the hemiwasher itself, not in the open middle...
  7. O

    How Do I Understand Octants and Graphs in Calculus III?

    I have a few questions on a problem in my first Calc III class. "The solid cube in the first octant bounded by the coordinate planes and x=2,y=2 and z=2, write the inequality to describe the set". I am new to the 3 dimensional cartesian system, but i still do not get the concept of the octants...
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    Undergrad project in calculus III

    undergrad project in calculus III ! hi everybody In this fall i am taking calculus III and planning to do contract honor with my professor. as a part of it i have to do some research in any topic related to calculus. what kind of projects can i do in calculus III? can u suggest me some...
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    Calculus III: Sketching Solids with Spherical Coordinates

    I really have difficulty with spherical coordinates graphings. can someone help me with this problem? Sketch the solid consisting of all points with spherical coordinates (ρ,θ,φ) such that 0≤ θ ≤π/2, 0≤ φ ≤π/6, and 0≤ ρ ≤2cosφ thanks so much! i think this looks like a bowl with radius ρ= root...
  10. Pengwuino

    Calculus III: Confused about Critical Points of f(x,y)?

    Ok so i got a mathematica assignment that asks "Find and classify the critical points of f(x,y)= 5-10xy-4x^2+3y-y^4 What does this mean lol. The assignment was from 3 weeks ago and i just had spring break so my brain is completely outa wack. Does this mean classify the points as concave up...
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    Calculus III: A Disappointing Start?

    Hey, i just started calculus III at a local college and its a bit... weak. I know we're not going to jump right in and start doing calc with numerous variables, but it still seemed like it was going to be too easy. The review we did was pathetic. We did one differential equation and one...
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