What is Calculus 3: Definition and 82 Discussions

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine – see Calculus (medicine)). Because such pebbles were used for counting (or measuring) a distance travelled by transportation devices in use in ancient Rome, the meaning of the word has evolved and today usually means a method of computation. It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.

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  1. rakeru

    Should I Take Calculus 3 and Differential Equations at Once?

    Hi! I'm a student at a community college and I'm getting an AA in physics to transfer to a university. I eventually want to apply to medical school with a bachelors degree in physics. I've recently been going over the classes required for medical school and for the physics major. I've...
  2. T

    Double Integrals in polar coordinates: Calculus 3

    Homework Statement Given \int^{\sqrt{6}}_{0}\int^{x}_{-x}dydx, convert to ploar coordinates and evaluate. Homework Equations We know that x=rcos\theta and y=rsin\theta and r =x^2+y^2 The Attempt at a Solution First, I defined the region of the original integral: R = 0...
  3. T

    Taking Calculus 3 first and then Physics Electromagentism?

    I have already completed Calculus 1 and 2 but I was wondering if it would be a better idea to take calculus 3 first and then physics electromagnetism. I know that electromagnetism deals with a lot of integration but does it deal with double and triple integrals? Thanks in advance.
  4. E

    Need a book to prepare for my Calculus 3 class

    Ahoy, Next semester I am taking Calc 3 and I would like to prepair over the summer so that it is not so daunting. If anyone can suggest a "...For Dummies" type book which would give me good examples and equations along with ample example problems that would be great. P.S. I already know...
  5. A

    Calculus 3: Chain Rule for Finding dx/dy with x=yz and y=2sin(y+z)

    Homework Statement If x=yz and y=2sin(y+z), find dx/dy Homework Equations Chain rule The Attempt at a Solution From y = 2sin(y+z) we get dz/dy= (1-2cos(y+z))/(2cos(y+z)) dz/dy=((1/2)sec(y+z) - 1) dx/dy = ∂x/∂y + ∂x/∂z dz/dy = z + y ((1/2)sec(y+z) - 1) = z...
  6. B

    Connecting Two Endpoints with Zero Curvature and Slope Using a Cubic Curve

    Homework Statement A line segment extends horizontally to the left from (-1,-1) and another line extends horizontally to the right from the point (1,1) find a curve of the form y=ax^5+bx^3+cx that connects the two endpoints so that the curvature and slope are zero at the endpoints...
  7. G

    What is the Length of a Parabolic Segment Using Calculus 3?

    Homework Statement Find the length of the parabolic segment r = \frac{12}{1+cos(θ))}, 0\leqθ\leq\frac{∏}{2}. Homework Equations L = ∫\sqrt{f(θ)^{2}+f^{'}(θ)^{2}}dθ The Attempt at a Solution I got up to here and didn't know whta to do L = 12 ∫^{0}_{\frac{∏}{2}}...
  8. G

    What are the Cross Products of Vectors AB and AD in Calculus 3?

    Homework Statement see attachment Homework Equations The Attempt at a Solution i found AB got <4,2,3> i found AD got <1,-1,1> i found |ABxAD| got square root of 62 not exactly sure what i am doing wrong thanks for any help
  9. P

    Introduction to Vector calculations (Calculus 3)

    Homework Statement Find nonzero scalars a, b, c, such that au+b(u-v)+c(u+v)=0 for every pair of vectors u and v This isn't a homework question, more of a conceptual exercise, but I want to understand it thoroughly.The Attempt at a Solution I've gone to u(a+b+c) + v(c-b)=0 then I couldn't quite...
  10. lonewolf219

    Calculus 3 introduction to cross product

    Just learning about vectors in 3 dimensions. Would it be correct to think of the cross product vector like a resultant vector? Is it similar to the displacement? If so, why is it always 90 degrees from both original vectors? If anyone has some deeper insight into any of these vector topics...
  11. G

    Physics 2 without taking Calculus 3 - Mistake?

    Hi, At my school physics 2 has calculus 1 as a prerequisite. You don't have to take calculus 3 while taking physics 2 or prior to taking it. I found physics 2 to be extremely difficult. I was taking while taking calculus 2. We got into flux integrals, Gaussian surface integrals, and some...
  12. B

    Find the Vector equation of the curve of intersection (Calculus 3)

    Homework Statement Find the Vector equation of the curve of intersection of X^2+y^2+z^2=10 and x+y=4 using x=2+sin(t) for parameter. Homework Equations The Attempt at a Solution I know it is a sphere with a plane cutting across it, however I have no idea how to proceed from...
  13. S

    Areas and Lengths in Polar Coordinates. Calculus 3

    Homework Statement "Find the area of the region that lies inside both curves (as an example), r=((sqrt(3)) cos(theta)) , r=sin(theta). This is Calculus 3. Areas and lengths in polar coordinates. Homework Equations Guys, I'm very confused because when the polar graphs are complicated we...
  14. C

    Calculus 3 (Integral where z is in terms of two functions)

    Homework Statement Find the mass and center of mass of the solid E with the given density function p. 38. E is bounded by the parabolic cylinder z = 1 - y^2 and the planes x + z = 1, x = 0, z = 0; p(x,y,z) = 4.Homework Equations The Attempt at a Solution I've been trying to find a solution to...
  15. C

    Calculus 3 - Vector Projections

    Homework Statement In three dimensions, consider the vector V = a1i + a2j +a3k. Determine the projections of V onto the x, y, z axis. Homework Equations These are formulas from my textbook related to projection: All underscores mean subscript. Proj_A B = (B * A/|A|) A/|A| = ((B * A)/(A * A))...
  16. H

    Calculus 3 Books: Jordan Measure & More

    I'm looking for book about Jordan measure and stuff like that.
  17. B

    Calculus 3 help needed. confusing piecewise. I need explanation

    Homework Statement 2. On the domain x \geq 0; y \geq 0, dene the function f(x; y) such that [PLAIN]http://img100.imageshack.us/img100/2144/huhh.jpg Homework Equations I'm not so sure. The Attempt at a Solution I apologize for no attempt. I am just totally confused with this notation as I...
  18. K

    Calculus 3 question- don't even know how to approach this problem

    Find the mass of one turn of wire in the form of a helix with a linear density e^(-z) in lbs/ft. Would I write as <e^(-z)*cost,e^(-z)*sint, t>? Maybe?
  19. K

    Calculus 3: Finding Current Rate of Change in Electric Circuits Using Chain Rule

    In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is...
  20. T

    Calculus 3 Problem (explain solution)

    Homework Statement Put the equation: p = 2 sin (x) cos (y) into rectangular coordinates. Identify the surface The Attempt at a Solution I tried to look at all the identities but I can't seem to figure out which one to use. I have the solutions to this problem, which follows: p^2 = 2...
  21. Y

    Calculus 3, dealing with tangent planes and surfaces.

    okay i came up with doing the gradient of the ellipsoid. Then set that equal to the vector, <4,-4,6>. I solved and got x,y,z = 1,-2,1 I looked at the answer key and it said (1/3) (1,-2,1) Does anyone know where the 1/3 came from?
  22. Y

    Calculus 3 problems (equations of planes and lines) 3 Space

    Hi, I am currently doing a practice test for my final exam coming up, I am wondering anyone can double check the questions to see if i did them write, below is a picture of the questions, the answers i got are listed at the bottom, If you could, please post whether you agree with my answers...
  23. W

    Calculus 3 Change of Variables: Jacobians

    Homework Statement Evaluate \int\inte^xy dA, where R is the region enclosed by the curves: y/x=1/2 , y/x=2, xy=1, and xy=2. Homework Equations None? The Attempt at a Solution I have the region graphed and I'm currently working on acquiring the change of variables functions in x and...
  24. W

    Calculus 3 Triple Integration in Spherical Coords

    Homework Statement Use spherical coordinates to evaluate the triple integral z dV where Q is the solid that lies between x^2+y^2+z^2=1 and x^2+y^2+z^2=4. Homework Equations Not sure what goes here :P The Attempt at a Solution I've gotten everything set up, I am having problems with boundaries...
  25. C

    Calculus 3 vector analysis question (Newton's 2nd problem)

    This problem was discussed in my calculus 3 class, and there is one step that I don't understand. Homework Statement An object of mass m travels along the parabola y = x^{2} with a constant speed of 10 units/sec. What is the force on the object due to its acceleration at (0,0) (write the...
  26. L

    How to Find Points of Discontinuity for a 2-Variable Limit in Calculus 3?

    find the points of discontinuouty limit as x,y ---> (0,0) of function f(x,y) = 1-((cos(x^2+y^2)/(x^2+y^2))
  27. H

    Should I Take Calculus 3 as a Junior in High School?

    Um I don't know if this is the right forum to post this but w/e: I'm taking calc BC right now as a junior and my teacher gave me the option to take calc 3 at a college nearby. However, my grasp of calculus is...weak. I think it would look great for college apps, but I fear complete failure...
  28. R

    What Are the Optimal Dimensions for a Tank to Minimize Metal Usage?

    1.A petrochemical company is designing a cylindrical tank with hemispherical ends to be used in transporting its products. If the volume of the tank is to be 10,000 cubic meters what dimensions should be used to minimize the amount of metal required? 2. V=pi*r^2 + 4/3*pi*r^3 SA=...
  29. F

    Calculus 3: Show Intersection of Tetrahedron Vertices & Centers of Gravity

    Homework Statement So we're suppose to show that the intervals connecting vertices of a tetrahedron with centers of gravity of opposite sides interesect at one point, namely the center of gravity of a normal tetrahedron. The center of gravity is (P+Q+R+S)/4. Homework Equations All I...
  30. M

    Solve Calculus 3 Question: Triple Integral over Parabolic Cylinder and Planes

    Hey guys, i need some help... I am trying to compute the triple integral z dx dy dz, where R is the region bounded by the parabolic cylinder x= 4y^2 and the planes z = 5 x, y = x, z = 0 ... i can't seem to get the limits of integration... when i sketch it it doesn't quite make sense... thanks in...
  31. K

    Optimizing Cost for a Rectangular Box with Given Volume

    Here is the question: A closed rectangular box with a volume of 16ft^3 is made from two kinds of materials. The top and bottom are made of material costing 10 cents per square foot and the sides from material costing 5 cents per square foot. Find the dimensions of the box so that the cost...
  32. A

    Proving Chain Rule for Partial Derivatives in Calculus 3 Extra Credit Problem

    Hi I'm having trouble with this extra credit problem I've been given. I am supposed to prove: dx/dy * dy/dz * dz/dx = -1 (partial derivatives) I think I'm supposed to use the chain rule but not sure. Can anyone help me out?
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