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Math 211 Multivariable Calculus Syllabus

The official syllabus in printable pdf form. Updated 2 February 2010.

The text Calculus: Multivariable, 5th ed will be referred to as CM.

Weekly Syllabus

  1. Thu 14 Jan
    Introduction (history of single variable, history of multivariable calculus), vectors, affine space, multi-variable functions, graphs. CM 12.1,2,5.

  2. Tue 19 Jan
    Multivariable functions (single variable R -> R, parametrized curves R -> Rn, functions Rn -> R, and vector fields Rn -> Rn), graphs, level sets of functions, examples. CM 12.2,3.

    Thu 21 Jan
    Vectors (position and displacement vectors), equations of lines (parametrization via point and vector) and planes (point and normal vector, three points) in Rn, dot product and cross product. CM 12.4, 13.1-4.

    Problem Set #1 due Fri 22 Jan
    Solutions #1

  3. Tue 26 Jan
    Partial derivatives, tangent planes. CM 14.1-3.

    Thu 28 Jan
    More tangent planes, gradients, total derivative. CM 14.4-5.

    Problem Set #2 due Fri 29 Jan
    Solutions #2

  4. Tue 2 Feb
    More gradients, total derivative, parameterized curves. CM 14.4-5, 17.1.

    Thu 4 Feb
    More parameterized curves, different parameterizations, velocity vector. CM 17.1-2.

  5. Tue 9 Feb
    Quiz #1 (30 min in class) solutions
    Velocity vector of a parameterized curve, curves on graphs of functions, chain rule for compositions of curves with functions. CM 17.1-2.

    Problem Set #3 due Wed 10 Feb

    Thu 11 Feb
    Review of Quiz #1, velocity vectors of curves on graphs. CM 17.3-4

    Midterm #1 Practice Exam.
    Midterm #1 Practice Exam solution guide.

  6. Tue 16 Feb
    Nice formula for vectors of greatest ascent, curves on graphs, visualizing vector fields, gradient fields. CM 17.3-4.

    Thu 18 Feb
    Midterm #1 (1 hour 10 min in class)

  7. Tue 23 Feb
    More vector fields, gradient fields, equipotential curves, flow curves. CM 17.3-4.

    Field potentials webapp at Davidson College.
    Vector field demonstrations at Wolfram web resourceas.
    Electric field applet at CalTech

    Thu 25 Feb
    Line integrals, circulation. CM 18.1-3.

  8. Tue 02 Mar
    More line integrals, circulation, fundamental theorem of calculus for line integrals. CM 18.1-3.

    Thu 04 Mar
    More line integrals, fundamental theorem of calculus for line integrals, path-independant/conservative/gradient vector fields. CM 18.1-4.

  9. Tue 09 Mar
    Spring break!

    Thu 11 Mar
    Spring break!

  10. Tue 16 Mar
    More path-independant/conservative/gradient vector fields, mixed partials, scalar curl, regions of definition, simply connected regions in the plane. CM 18.1-4.

    Midterm Exam #2 Practice
    Midterm Exam #2 Practice solution guide

    Thu 18 Mar
    Finding potential functions, intro to multi-dimensional integrals.

  11. Tue 23 Mar
    Multi-dimensional integrals, iterated integrals, Fubini's theorem, integrating over boxes. CM 16.1-2.

    Thu 25 Mar
    Midterm Exam #2 (1 hour 10 minutes in class)

  12. Tue 30 Mar
    No class for passover.

    Thu 01 Apr
    Iterated integrals over non-boxes, order of integration, volumes. CM 16.1-2.

  13. Tue 06 Apr
    Green's Theorem, triple integrals, change of coordinate systems (polar, cylindrical, spherical). CM 18.4, 16.3-5.

    Thu 08 Apr
    More coordinate systems. CM 16.3-5.

  14. Tue 13 Apr
    More coordinate systems, multivariable change of variables formula. CM 16.3-7.

    Thu 15 Apr
    Multivariable change of variables formula, more volume computations. Quiz #2 in class 15 minutes. CM 16.3-7.

  15. Tue 20 Apr
    New York Times problem.

    Thu 22 Apr
    More changes of variables! Final class outside!



    16. Final Study Guide and Practice Exam, Fri 30 Apr 2010.
    Solution guide!


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