This course is taught in parallel to numerous classes, in all of JCT's campuses. The course's coordinator is Dr Ivy Kidron.
This is Prof. Dana-Picard's personal page for this course.
Syllabus:
Series of real numbers: definition, telescopic and geometric series, series with non negative terms, convergence tests, alternating series, absolute convergence.
Power series: convergence domain, convergence radius. Taylor polynomials and error estimate, Taylor series.
Analytic geometry of the 3-dimensional space: quadratic surfaces and parameterized surfaces.
Partial derivatives of higher order; Schwarz theorem. Chain rule.
Applications of first partial derivatives: plane tangent to the graph of a function, total differential, approximations, gradient, directional derivatives.
Extrema and saddle points.
Double integrals. Fubini's theorem. Change of coordinates, Jacobian. The case of polar coordinates.
Triple integrals - cylindrical and spherical coordinates.
Integration in vector fields: line integrals, surface integrals.
A short introduction to Maple commands for graphing 2-variable functions: pdf and Maple file. For this last file, download it to your computer (don't forget the mw extension) and run it with double click and button "!!!".
The WIMS site at the University of Nice (France) provides many useful tools: 2D and 3D animated graphics, interactice exercises in many fields, including topics related to the present course.
dpgraph is an unexpensive and nice grapher for your personal computer.
Have a look at Peanuts Software homepage. You will find there many free downloadable programs; very useful.
If you are interested in various mathematical topics (biographies of famous Mathematicians, famous curves, development of special topics, ...), have a look at the
The MacTutor History of Mathematics archive .
S. Lipschutz: Infinitesimal Calculus, Schaum Series (exists in Hebrew,
edited by Steimatzky).
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This page is maintained by Dr Dana-Picard. Last revision: 15/03/2009.