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What is classically tought in calc III?

  1. Jul 23, 2007 #1
    I'm teaching myself calculus III off of various websites including wikipedia.

    However, I don't know exactly where to begin. I've started by looking at the partial derivative and parts of vector calculus.

    My calculus learning so far has been:

    Calc I:
    Limits
    Basic and complicated single-variable differential calculus (chain rule, power rule, et cetera. Differentiation isn't hard.)
    Basic single-variable integral calculus (power rule, et cetera)

    Calc II:
    Infinite limits, sequences and series. (Taylor series, power series, et cetera)
    Improper integrals, work as an integral, integration by parts, all three rotated volume integration, introduction to conical sections, and introduction to polar/parametric/vector calculus.

    So what would most colleges teach after this in calc III?
     
  2. jcsd
  3. Jul 23, 2007 #2
    why dont you just buy a used textbook
     
  4. Jul 23, 2007 #3
    Because I'm going to have to buy one in a semester... And this is just for something to do over the summer.
     
  5. Jul 23, 2007 #4

    cristo

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    Staff Emeritus
    Science Advisor

    Why don't you find out which textbook you'll be using next semester and buy that one and study through it? It's a lot easier learning out of a text book, since it's written in a logical order, as opposed to various webpages.
     
  6. Jul 24, 2007 #5

    lurflurf

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    Homework Helper

    There is significant variation in topics, rigor, and depth of coverage

    functions of several variables
    limits
    sequences and series
    partial derivatives
    multiple integration
    change of variable
    chain rule
    implict function thm
    inverse function thm
    determinants
    basic linear algebra
    Jacobian
    Hessian
    optimization
    lagrange multiplier
    differentials
    partial differential equations
    conical sections parametric equations
    vector algebra
    curl grad div
    identities for curl grad div
    line,surface,volume integration
    fundamental theorems of vector calculus about 30
    liebniz rules for integration and differentiating products
    differential forms (if lucky because 30 ftovc->1)

    In summary do every thing from single variable again with several variables
     
  7. Jul 25, 2007 #6
    everything lurflurf stated, didnt have jacobian, hessian, liebniz in mine. Heavy concentration to stokes theorm, greens theorm, fields and flux and applications of mathamatical physics. Also course will be different depending whether it is specifically for math majors or applied science majors, and whether there is a Calculus 4 class or if it ends at 3
     
  8. Jul 25, 2007 #7
  9. Jul 27, 2007 #8
    Last edited: Jul 27, 2007
  10. Jul 27, 2007 #9
    that seems similar to what I learned in my Calc III class except mine also included Vector calculus: div, grad, curl, and green's, stoke's and divergence thm
     
  11. Jul 29, 2007 #10
    My school used Stewart's 5th edition Calculus for calc I-III, and we separated it like this. I think this is more or less the standard breakup:

    calc I, chapters 1-5:
    - functions
    - limits and derivatives (defn of limit, limits at infinity, continuity, etc.)
    - rules for differentiation (product, chain, quotient, logs, hyperbolic functions, linear approximations)
    - applications of differentiation (max/min, MVT, l'hospital, optimization, newton's method, antiderivatives)
    - intro to integrals (FTC, substitutions, areas/distances, definite/indefinite)

    calc II, chapters 6-11:
    - applications of integration (volumes, work as an integral, areas between curves)
    - techniques of integration (parts, trig integrals, trig substitution, partial fractions, numerical methods, improper integrals)
    - applications again (arc length, surface area, applications to physics, bio, econ, etc. are given in the book)
    - basic differential equations (first order separable, first order linear)
    - parametric/polar coordinates (intro/defns, calc with polar/parametric, arc lengths, conics)
    - sequences/series (integral test, comparison tests, convergence, power series, taylor/maclaurin, etc.)

    calc III, chapters 12-16:
    - vectors/review of geometry/linalg (vectors, dot/cross product, eqns of lines/planes, cylindrical/spherical coords)
    - vector functions (space curves, calc with vector functions, arc length/curvature)
    - partial derivatives (multivariable functions, limits/continuity, linear approximations, directional derivatives, grad, max/min, lagrange multipliers)
    - multiple integrals (double/triple integrals over rectangles, over general regions, in spherical/cylindrical coordinates, change of variables)
    - vector calculus (vector fields, line integrals, green's theorem, curl, div, surface integrals, stokes' theorem, gauss/divergence theorem)
     
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