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HU Credits:
6
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Dr. Eli Kraisler
Coordinator Office Hours:
By appointment
Teaching Staff:
Dr. Eli Kraisler,
Ms. Yaara Jahn,
Mr. Daniel Ofner
Course/Module description:
Many-variable calculus, vector analysis and ordinary differential equations
Course/Module aims:
To provide students from Chemistry and Earth Sciences with the mathematical tools they need in studying courses in chemistry and physics
Learning outcomes - On successful completion of this module, students should be able to:
1) Mathematically analyze scalar and vector many-variable functions, namely:
* Find the critical points of a many-variable function and classify them;
* Use the tools of vector analysis, and be able to calculate the gradient, divergence, curl and Laplacian of scalar/vector fields (as applicable);
* Calculate double and triple integrals, line integrals, flux and circulation of vector fields;
* Find the connections between the quantities detailed above.
2) Solve ordinary differential equations (of types covered in class), namely:
* Classify the type of a given differential equation;
* Find a general solution to an ODE, using the methods covered in class;
* Find a particular solution from the general one, according to the initial conditions.
3) Be able to connect the mathematical methods we study and phenomena in chemistry and physics covered in other courses.
Attendance requirements(%):
Attendance is not compulsory, but it is expected and highly recommended.
Teaching arrangement and method of instruction:
Lectures and tutorials
Course/Module Content:
1. Overview: vectors – addition, subtraction, scalar and vector products.
2. Many-variable function: partial derivatives, directional derivative. Examples in chemistry.
3. Vector and scalar fields. Derivatives of vectors. Gradient. Examples in physics and chemistry.
4. The operator nabla. Divergence, curl and laplacian. Examples.
5. Analysis of a many-variable function: minima, maxima, saddle points. Constraints and Lagrange multipliers.
6. Integral of a many-variable function. Change of variables, Jacobian. Examples and applications.
7. Line integrals, conserving fields. Surface integrals. Flux. Circulation.
8. Green, Gauss and Stokes theorems.
9. Spherical and cylindrical coordinates. Gradient, divergence and Laplacian in these coordiantes.
10. Ordinary differential equations (ODEs). Types and common examples in chemistry and physics.
11. First order ODEs. Selected solution methods. Initial conditions.
12. Second order ODEs. Solution independence. Linear homogeneous and inhomogeneous ODEs.
Required Reading:
There are no mandatory reading assignments.
Additional Reading Material:
M.L. Boas, Mathematical Methods in the Physical Sciences
M. R. Spiegel, Vector analysis
F. Ayres, Differential Equations
M.R. Spiegel, Applied Differential Equations
W. Boyce, R.C. DiPrima, Elementary Differential Equations
G. Arfken, Mathematical Methods for Physicists
K. F. Riley, M. P. Hobson, S.J. Bence,
Mathematical Methods for Physics and Engineering
Grading Scheme :
Written / Oral / Practical Exam 70 %
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 15 %
Mid-terms exams 15 %
Additional information:
Submission of 70% of the tutorial handouts is compulsory. Students who will not submit enough exercises, will not be allowed to participate in the exam, neither Moed A nor B, nor a special Moed [a student who will take the exam anyhow, may receive the grade 0, with a possible complaint to the Disciplinary Committee].
The grade in the midterm exam can serve as a 'protective grade', namely it can only improve the final grade. If such, the final grade will be composed of: 15% midterm grade, 15% exercises, 70% final exam. Otherwise, the final exam will be 85% and exercise 15%.
Update due to the Coronavirus pandemic:
1. In case instruction in class will not be possible, the course will be taught online.
2. In case it won't be possible to hold the midterm and/or the final exams in the usual way, in class, these exam(s) will be held online, in a manner to be defined at a later stage.
In such a case, the Course Team may: (a) invite any student for an oral exam, where s/he will have to explain the answers they gave in the written exam online. Participation in such an exam is compulsory. (b) In case of a misconduct during the online exam, to provide only a pass/fail grade for the whole class.
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