Department of Mathematics
Infinitesimal Calculus 2
Course number 120132
Spring Semester - Academic year 5769
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.
The Hebrew syllabus is here .
- 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.
- Multivariable functions: domain, graph, level curves, contours.
- Multivariable functions: limits, continuity.
- Partial derivatives and their geometric meaning.
- 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.
- Green theorem in the plane.
- Stokes theorem, theorem of divergence.
Pace of the course:
- Lectures: 4 hours a week.
- Tutorial sessions: 2 hours a week.
The grade (first term) will be determined by the following way:
- Weekly Homework assignments (5%). Registered students will find the assignments on the course's moodle page.
- two or three mid-term exam (10%).
- One final exam.
There will be one Moed bet.
- General notions on functions of two real variables: presentation-show, printable (3 slides on each page).
- Surfaces in 3-dimensional space:presentation-show, printable (3 slides on each page).
- 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 "!!!".
- Parametric plots: pdf and Maple file.
- Partial derivatives, gradient and directional derivatives: presentation-show, printable.
- Maple commands for partial derivative, gradients, directional derivatives.
- Extrema and saddle points: presentation-show, printable, Maple commands..
- Extrema with constraints: presentation-show, printable, Maple commands.
- Double integrals: presentation-show, printable, Maple commands.
- Triple integrals: presentation-show, printable.
- Parametric Plots printable, Maple commands, Maple commands.
- Vector functions: pdf, Maple commands.
- Integration in Vector fields I: first part, in pdf.
- Integration in Vector fields I: second part, in pdf.
- Work Integrals Maple commands.
- Volumes between surfaces Maple commands.
- Taylor Series: pdf, animations with Maple.
A couple of solutions:
- B. Kohn: Calculus (in Hebrew), Bak Editions, Haifa.
- H. Anton: Hebrew version of a classical textbook in English. Published by the Open University.
- Finney-Weir-Giordano: Thomas'Calculus 10e, Addison-Wesley, 2002.
- S. Lipschutz: Infinitesimal Calculus, Schaum Series (exists in Hebrew,
edited by Steimatzky).
This page is maintained by Dr Dana-Picard. Last revision: 15/03/2009.