# What is Calc 3: Definition and 106 Discussions

The calc-alkaline magma series is one of two main subdivisions of the subalkaline magma series, the other subalkaline magma series being the tholeiitic series. A magma series is a series of compositions that describes the evolution of a mafic magma, which is high in magnesium and iron and produces basalt or gabbro, as it fractionally crystallizes to become a felsic magma, which is low in magnesium and iron and produces rhyolite or granite. Calc-alkaline rocks are rich in alkaline earths (magnesia and calcium oxide) and alkali metals and make up a major part of the crust of the continents.
The diverse rock types in the calc-alkaline series include volcanic types such as basalt, andesite, dacite, rhyolite, and also their coarser-grained intrusive equivalents (gabbro, diorite, granodiorite, and granite). They do not include silica-undersaturated, alkalic, or peralkaline rocks.

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1. ### Parametric curve question (determining unknown point)

My work so far: I am stuck because when I inputted the two possible values of t and k, neither solution worked. Where did I go wrong? Pointers would be appreciated! :)
2. ### B Help Visualizing 3-d Surfaces

1. Fold in half the long way 2. Fold in half the short way 3. Unfold paper, grasping the left side horizontal crease, bend the paper as shown by making the left crease flush with the bottom vertical crease and crease along the -45 degree bend (not shown) 4. This is the visualization for...
3. ### Calculus Books for practice integration problems and calc 3

I am looking for a (practice)book that has problems on definite and indefinite integration from easy to intermediate. also which book covers the prerequisites of calculus for books like Griffiths.(similar to the topics in chap 1 of Griffiths but more in-depth)
4. ### Cauchy-Riemann Theorem Example in Physics

I was thinking of the wavefunction in QM but I'm not sure how it's used and when.
5. ### Calc 3 Chain Rule Confusion

Solution: ##\frac{\partial z}{\partial x} = yx^{y -1}+1## ##\frac{\partial z}{\partial t} =\frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial t}## ##\frac{\partial z}{\partial t} = (\frac{yx^{y-1} + 1}{2\sqrt{s+t}}) +...
6. ### Multivariable calculus problem

Homework Statement Find the points on the surface xy^2z^3=2 that are closest to the origin Homework EquationsThe Attempt at a Solution x,y,z=/= 0, as when x,y,z = 0 it is untrue. Right?? Otherwise, I am very unsure as to how to approach this problem. Should I be taking partial derivatives to...
7. ### Courses Should I take Calc 3 before Physics 2?

I've heard several people mention that physics 2 uses a lot of material covered in calc 3 (multivariable I believe would be its equivalent). The physics 2 course at my college covers Coulomb's Law, electric fields and potentials, capacitance, currents and circuit, Ampere's Law, Faraday's Law...
8. ### B Intution behind the gradient giving the steepest ascent in 2D

Can this(image) be used as a proof that the direction of gradient gives the direction of steepest ascent(in 2D).Am I understanding it right ?.The function 'f' in the image is a scalar valued function.Please explain.
9. ### Stuck on the integration bound

Homework Statement Trying to help a friend with a problem. We are supposed to solve the below using polar coordinates. The actual answer is supposed to be π/16. Solving the integral is not the issue, just converting it. 2. The attempt at a solution What I got sort of worked, but it is only...
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### Calc 3: Equation of a line normal to the contour

Homework Statement Given g(x,y)=x2 - xy + 2y2, find the equation of the line normal to the contour that passes through the point (1,2). Homework Equations Not 100% positive, but the equation to a plane tangent to a function of 3 variables g(x,y,z) is (partial of x)(x - x0) + (partial of y)(y -...
11. ### Courses Calculus 3 -- looking for ways to help me understand

So I am in calculus 3 this year and have passed both calc 1 and 2 with a B and C+ respectively. I could have gotten a better grade but was lazy. I was lazy by using calculators and not actually learning the arithmetic and algebra. Now one serious issue I have is Trig. I can never remember trig...
12. H

### Faraday's law with Calc 3 integration help

Homework Statement Suppose an infinitely long wire carrying current ##I=sin_0(\omega t)## is a distance ##a## away from a equilateral triangular circuit with resistance ##R## in the same plane as shown in the figure. Each side of the circuit is length ##b##. I need to find the induced voltage...
13. S

### B Proof: How to start it?

I am having trouble with this proof. I just need a step in the right direction. Let u and v be vectors. (u+v)*(u-v)=0, then IuI=IvI I have to use properties of the dot product. I started off by combining both using this property u*(v+w)=u*v+u*w (u,v,w are vectors) I got lost in all of my...
14. ### Force on 2 cables with weight attatched using Theta....

Homework Statement https://ibb.co/g6iKDQ Calculate the magnitude of the force on cables 1 and 2 in the figure below if θ_1 = 55° and θ_2 = 35°. (Round your answers to two decimal places.) Homework Equations Is my method incorrect or did I go wrong somewhere in my calculations?? The...
15. ### I Which topics from precalc are essential for calc 3?

i took calc 2, and am going to take calc 3. My precalc teacher skipped on a lot of topics since the class was falling behind and he assumed most weren't going to take calc 3 anyways. So which topics from precalc are essential for calc3? NOTE: i am on the semester system, which means there are...
16. ### Issue with Double Integral

Homework Statement Find the volume of the given solid: Under the surface z = xy and above the triangle with verticies (1,1), (4,1) and (1,.2) Homework Equations Double Integral The Attempt at a Solution I drew the triangle, and found the the equations of the lines to be: x = 1; y = 1; y = -3x...
17. ### Confused with Space Curves

Homework Statement Match the parametric equations with the graphs. In this case, I am stuck on this equation: x = cos t y = sin t z = 1/(1+t^2) Homework EquationsThe Attempt at a Solution So far I have: x^2 + y^2 = cos ^2 t + sin ^2 t = 1 I know this is a circle in the xy-plane, and thus...
18. ### Is calc 1 more similar to calc 2 or calc 2 similar to calc 3

I'm going to have a gap between math classes at some point. I can either take calc 1, then calc 2 the following semester, then have a semester gap with no math, and then calc 3. Or calc 1, no math gap, calc 2, calc 3. The reason I am asking is because i will forget some information in the...
19. ### Courses Would Calc 3 + Engineering Physics 1 be too much for Summer?

Hey everyone, I am currently in College Physics 1 right now, and Calculus 2. Both courses are going seemingly well. I have an 'A' in both classes, but I do devote a lot of time to studying. Between the two I probably put in about 20 hours/week depending on the material covered. Right now were...
20. ### Can I Successfully Take Calc 3 and Linear Algebra at the Same Time?

Hi all! I have an important decision to make for the summer of 2016 and I need some advice from some who have taken these courses. I need one biology lab elective to graduate, but it is a field lab and it runs from from 5/13 - 6/19. Because it is a field lab, I will not be able to take other...
21. ### A shot fired from gun, elevation to hit a target 3000 feet away

A shot fired from a gun with a muzzle velocity of 1200 ft per second is to hit a target 3000 feet away. Determine the minimum angle of elevation of the gun? Ok so I know that r(t)= (vcos(theta) t)i +(vsin(theta) t +16t^2)j I tried to set vcos(theta)t =3000, solve for t, and plug into the j...
22. ### Show the gravitional field is conservative

In my calculus textbook (section on vector calc) it is showing that the gravitational field is conservative. I followed fine except for the first part, defining the scalar function f. Showing the field is conservative went something like this: f(x,y,z) = MM'G/\sqrt{x^2+y^2+z^2}...
23. ### Find the initial angle.

Homework Statement : [/B] Find two elevation angles that will enable a shell, fired from ground level with a muzzle speed of 800 ft/s, to hit a groundlevel target 10,000 ft away. Homework Equations Look at attached picture The Attempt at a Solution Look at attached picture ***I get to...
24. ### Classical Recommendations for E&M Math Book

Can anyone recommend a good book that deals with the mathematics of E&M? I've read through my calculus books and feel like I understand the material there and can solve the problems. However, when it comes to it's applications in electricity and magnetism I find that I have enormous difficulty...
25. ### Why is it that calc 3 is sometimes not required for stats?

There is so much variation amongst statistics majors across schools. I think it is the major that varies the most. This is surprising, since statistics is math. A big reason for this is that sometimes it is offered from math department, and others from the business department (stern's stats...
26. ### Is it a bad idea to take 19 units in 16 weeks, or delay O-Chem to next term?

In order to transfer on time from community college and prepare for the MCAT I have to really scrunch my classes. I was planning on taking Calc 3, Liner Algebra, O Chem 1, and Physics 1 (mechanics) at a whopping total of 19 units in 16 weeks. Is this doable? I would not be working and all of my...
27. ### Finding vectors and magnitude

Homework Statement Find a vector in the direction opposite to <-4,1,2>, that has a magnitude of 3. Homework Equations I think that I did the first part of the problem correctly: <-4,1,2> magnitude= sqrt[ (-4)^2+1^2+2^2 ] = sqrt(16+1+4) = sqrt(21)...
28. ### Tricky integral from calc 3 Arc Length question

Homework Statement Find the arc length of: r(t)=<e^t, e^(-t),sqrt(2)*t> from 0 to ln(2) Homework Equations L=integral from a to b of the magnitude of r'(t) The Attempt at a Solution Okay, this was an Exam question, the one exam question that I could not get on our Calc 3 exam. This breaks...
29. ### Calc 3 curvature verification

Homework Statement verify that |T ' (s)| = |T ' (t)| / |r ' (t)| Homework Equations K = |dT / ds| K = |r'(t) x r''(t)| / |r'(t)|^3 the x is a cross product The Attempt at a Solution I don't know how to start this problem because one side of the verification is in terms of arc length...
30. ### Physics/ Calc 3 Spaceship Question

Homework Statement Imagine a 50kg vehicle located at the origin. We wish to navigate this vehicle by means of applying directed force. From the point (-2000,16000,0)m, you set a course directly back to the origin. A force of 10N is applied in the appropriate direction for 5 seconds. 5...
31. ### MHB Stressed for Calc 3 & Econ Tests? Tips for Exam Day Anxiety

i have a calc 3 test on monday and i don't know why but I AM TERRIFIED. probably because i have an exam for econ the same day. any exam or pre-exam tips? how not to be afraid?
32. ### Should I take calc 3 and differential equations or EE 254 and EGR 265

I hope I am putting this in the right thread. It seemed to be the most appropriate one! So, I have two choices. I can take both MA 227(Calculus III) and MA 252 (differential equations) or take both EGR 254 and EGR 254. Which do you think would be the easiest option? I am an electrical...
33. ### Calc 3 and Differential Equations

Hello everyone, I am currently entering my second year of college in the fall, and will begin Calc 2. My questions involves whether or not it is a good idea to take Calc 3 and differential equations the same semester. The community college I'm attending does not offer linear algebra, so I can...
34. ### Calc 3 Double Integration

Homework Statement Attached below Homework Equations The Attempt at a Solution So I cannot figure this out. Would this be integration by parts? or by substitution.. It provides me with an answer but no reasoning behind it and I cannot figure it out =/
35. ### Calc 3 Range of a function (set of points)

Homework Statement See attached image Homework Equations they are provided in the image. I see the domain is used The Attempt at a Solution I can't figure out how they went from step one to step 2. where does the -81 come from and the 9 multiplied to the function in the middle. I...
36. ### Calc 3 - Tough/Messy Divergence Problem

Homework Statement Apologies for the attachment. Homework Equations Limit definition of the divergence as seen in attachment Volume of a sphere: \frac{4}{3}\pi r^{3}The Attempt at a Solution The first thing I did was parameterize the vector function F(x,y,z) = <xy,x,y+z> My parameterization is...
37. ### Calc 3: Vector Addition Problem Solution Example

I'm trying to do this homework problem but I keep getting an answer that is not given. Can someone tell me what I am doing wrong please. This is for University level calc 3. Homework Statement Homework Equations A vector U=<x,y> ||U|| means the length of U = √(x^2 +y^2). vectors can also...
38. ### Maximizing f(x,y) on a Triangular Region | Calc 3 Homework Solution

Homework Statement Find the maximum value of f(x,y)=xy+1 on the triangular region: x ≥ 0, y ≥ 0, x+y ≤ 1 The Attempt at a Solution Partial derivatives of f(x,y) with respect to both x and y are positive within the given bounds, so the maxima will be found on the boundary where y=1-x...
39. ### (Calc 3) Finding mass of a wire using line integral

Homework Statement Find the mass of a wire in the shape of the parabola y=x2 for 1 \leq x\leq2 and with density p(x,y)=x. Homework Equations The Attempt at a Solution I just want to make sure I am setting this integral up right. Here is what I did: I parameterized the equation to x=t, y=t2...
40. ### Microeconomics in 5 weeks or calc 3 in 10 weeks?

Normal semesters here are 15 weeks. The summer sessions here are 10 weeks; there's a 10 week session and they can be split into two 5 week sessions. For the 10 week session I'm taking: diff eq (4 credits) health (1 credit) And microeconomics(3 credits) for the first 5 weeks of the...
41. ### Pretty easy relative max problem calc 3

Homework Statement Locate all relative max,min,and saddle points if any. f(x,y)=x2+xy+y2-3x fx=2x+y-3 fy=x+2y Skipping some algebra I get the critical points (2,-1) fxx=2 fyy=2 d=fxx*fyy-f(x0,y0)2 d=4-9=-5 I know I'm messing up at f(x0,y0) I'm simply plugging in...
42. ### Calc 3 Moments and centers of mass

Homework Statement Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Homework Equations ∫∫ (f(x,y) dA mx= 1/m(∫∫...
43. ### Modeling Projection Motion Problem - Calc 3

Homework Statement A person is standing 80 ft from a tall cliff. She throws a rock at 80 ft/sec at an angle of 45 degrees from the horizontal. Neglecting air resistance and discounting the height of the person, how far up the cliff does it hit? Homework Equations r = ((xo + vo*cos(~))t) i...
44. ### Should I start my undergrad with Calc 3?

Hi everyone. I just graduated from high school this month and I will be attending Stony Brook University as a Physics Major in the fall. Even though I took AP Calculus BC, I was forced to take the mathematics placement exam because my AP scores won't be back in time for orientation, which...
45. ### Okay to take Linear Algebra and Calc 3 in the summer?

Would it be too much to take both classes in the summer? Each is 1 month long and in two separate sessions, so they will not be on top of each other. I need to take Calc 3 right away for the fall Semester, that's already settled. As for Linear Algebra, I will need that to prepare for Quantum...
46. ### Just took calc 3 semifinal

Just took calc 3 "semifinal" And I have a few questions regarding concepts, which was sparked by a conversation with a few classmates after the test. 1st, a problem was given to us and we were asked if stokes or divergence applies. It was a line integral, so divergence did not apply. It...
47. ### Topics in Calc 3 and Differential Eq.

What topics should DEFINITELY be covered in multivariable calculus and differential equations? My calc 3 course completely overlooked Lagrange Multipliers and Greens Theorem. I had to teach myself what a Jacobian was. I want to be sure that I am familiar with the subject but it's hard to...
48. ### Calc 3 tough not sure if right.

Calc 3 tough! not sure if right. Homework Statement Can you check if this is right? Let f(x,y) x^(2)y-3x^2-2y^2+11y+5 1. find all critical points of f(x) crits at (0,11/4), (-1/3),(1/3) 2. determing nature of the crit points you found D(-1,3) saddle D(0,11/4) max D(1,3) saddle 3...
49. ### [Calc 3] Verifying Stokes Theorem

Homework Statement V.Field F(x,y,z)=<x^2 z, xy^2, z^2> where S is part of the plane x+y+z=1 inside cylinder x2 + y2 =9 Homework Equations Line integrals, Stokes Theorem, Parametrizing intersections... The Attempt at a Solution I found the answer to be 81pi/2 using stoke's theorem...
50. ### Is it detrimental to take a weak calc 3 teacher?

Hi all, Im an EE major and am getting ready to pick spring classes tomorrow. My only option for Calc 3 which will fit into my schedule seems to be the easiest professor possible (aka they give over 30% A's, which I found from the rating website, I have also heard from other students that it is...