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

Weekly Syllabus

1. Thu 19 Jan
   Introduction (history of single variable, history of multivariable calculus), review of single variable calculus (what you should know!), space (1-, 2-, 3-dimensional), describing curves by equations (implicitly) and by parameterization. CM 12.1,2,5.
   
   
2. Tue 24 Jan
   Implicit and parameterized descriptions. Vocabulary of multivariable functions: single variable R -> R, parametrized curves R -> Rⁿ, functions Rⁿ -> R, graphs, level sets. Examples. CM 12.2,3.
   
   Thu 26 Jan
   Vectors (position and displacement vectors), equations of planes (point and normal vector, three points) in Rⁿ, dot product. CM 12.4, 13.1-4.
   
   Problem Set #1 due Fri 27 Jan
   Solutions #1
   
   
3. Tue 31 Jan
   Cross product, plane through three points, lines (parametrization via point and vector) and Tangent planes to special surfaces. CM 14.1-3.
   
   Thu 02 Feb
   Partial derivatives, gradients, tangent planes to graphes. CM 14.4-4.
   
   Problem Set #2 due Fri 03 Feb
   Solutions #2
   
   
4. Tue 07 Feb
   More properties of the gradient, tangent planes to level surfaces. CM 14.4-5.
   
   Thu 09 Feb
   More tangent planes to level surfaces, parameterized curves, parameterizing line and curcles, velocity vector. CM 14.5, 17.1-2.
   
   Problem Set #3 due Fri 10 Feb
   Solutions #3
   
   Midterm #1 Practice Exam
   Midterm #1 Practice Exam solution guide.
   
   
5. Tue 14 Feb
   Quiz #1 (20 min in class) solutions
   More parameterized curves, different parameterizations, chain rule for compositions of curves with functions. CM 17.2-4.
   
   Thu 16 Feb
   Review of Quiz #1 and review for Midterm #1. Curves on graphs of functions and steepest ascents. Vector fields, gradient fields, line integrals. CM 17.3-4
   
   Problem Set #4 due Fri 17 Feb
   Solutions #4
   
   
6. Tue 21 Feb
   Midterm #1 (1 hour 10 min in class)
   
   Thu 23 Feb
   Visualizing vector fields, gradient fields, a vector field that is not a gradient field, line integrals. CM 17.3-4, CM 18.1-3.
   
   
7. Tue 28 Feb
   More vector 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 01 Mar
   More line integrals, path-independence, line integrals around closed curves, fundamental theorem of calculus for line integrals. CM 18.1-3.
   
   Problem Set #5 due Fri 02 Mar
   See Blackboard for solutions.
   
   
8. Tue 06 Mar
   More line integrals, path-independence, fundamental theorem of calculus for line integrals. CM 18.1-3.
   
   Thu 08 Mar
   More line integrals, fundamental theorem of calculus for line integrals, path-independant/conservative/gradient vector fields all the same, scalar curl test. CM 18.1-4.
   
   Problem Set #6 due Fri 09 Mar
   See Blackboard for solutions.
   
   
9. Tue 13 Mar
   Spring break!
   
   Thu 15 Mar
   Spring break!
   
   
10. Tue 20 Mar
    More scalar curl, regions of definition (in 2- and 3-D), simply connected regions in 2- and 3-dimensions, generalized scalar curl test. CM 18.1-4.
    
    Midterm Exam #2 Practice
    Midterm Exam #2 Practice solution guide
    
    Thu 22 Mar
    Multi-dimensional integrals, iterated integrals, Fubini's theorem, integrating over boxes, triangles. CM 16.1-2.
    
    
11. Tue 27 Mar
    Quiz #2 (20 min in class)
    More multi-dimensional integrals, iterated integrals over non-boxes, order of integration. CM 16.1-2.
    
    Thu 29 Mar
    Quiz #2 review, vector field review, more multi-dimensional integrals, order of integration. CM 18.4, 16.3-4
    
    Problem Set #7-8 due Fri 30 Mar
    See Blackboard for solutions.
    
    
12. Tue 03 Apr
    More multi-dimensional integrals, volumes of solid regions, midterm review. CM 16.5.
    
    Thu 05 Apr
    Midterm #2 (1 hour 10 min in class)
    
    
13. Tue 10 Apr
    Polar coordinates, triple integrals. CM 16.3-4.
    
    Thu 12 Apr
    New York Times problem on Steinmetz solid, cardioid, cylindrical coordinates.
    
    Problem Set #9 due Fri 13 Apr
    
    
14. Tue 17 Apr
    More cylindrical coordinates, solids of rotation, spherical coordinates. CM 16.5-6.
    
    Thu 19 Apr
    Midterm 2 review. Spherical coordinates. CM 16.6-7.
    
    Problem Set #10 due Fri 20 Apr
    
    
15. Tue 24 Apr
    Spherical coordinates, general change of coordinate formula. CM 16.7.
    
    Thu 26 Apr
    General linear change of variables. Parameterized surfaces, flux integrals. CM 19.1-3.
    
    
16. Tue 01 May
    Last day of classes! More flux integrals.
    
    Problem Set #11 due Tue 01 May
    See Blackboard for solutions.
    
    
17. Tue 13 Dec
    Final review session 03:00-4:30 pm Fri May 4.
    
    Final Study Guide and Practice Exam
    Solution guide!
    
    
18. Tue 08 May
    Final exam 8:30 - 11:00 am