Courses
- Preparation Course Mathematics (7013) תקציר הקורס:
- Differential and Integral Calculus1 (90901) תקציר הקורס:
- Differential and Integral Calculus2 (90902) תקציר הקורס:
- Linear Algebra (90905) תקציר הקורס:
Abstract:
This course contains review on algebraic operations, solution of inequalities,
solution of equations with parameters, investigation of
linear and quadratic equations.
Definition of the exponential func tion and the logarithm and their properties.
In addition, mathematical induction is studied and complex numbers,
elementary introduction in geometry and trigonometric identities.
The course also includes elementary concepts
in differential and integral calculus.Abstract:
Real numbers. Sequences. Limit of a sequence. Limits and continuity of f?unctions. Intermediate value theorem. Weierstrass's theorem. The derivative. Techniques of differentiation. Fermat, Rolle and Lagrange theorems. L'H?pital's rule. Taylor polynomial approximations. The derivative in graphing and applications. The definite and indefinite integral. Principles on integral evaluation: integration by parts and by substitution. The fundamental theorem of calculus (Newton-Leibniz). Improper integral.Abstract:
Infinite series. Convergence tests. Series of f?unctions; convergence and uniform convergence. Power series; representation of f?unctions by power series. Taylor series. F?unctionsof several variables- limits and continuity, partial and directional derivatives, Linear approximation, Gradient. The chain rule. Higher order partial derivatives and second degree Taylor polynomial. Relative/absolute maximum and minimum values. Lagrange multipliers. Multiple integrals. Fubini's theorem. Change of variables. Polar, cylindrical and spherical coordinates. Line integrals of scalar f?unctions. Line integrals of vector fields. Independence of path and Green theorem. Surface integrals of scalar f?unctions. Oriented surfaces and surface integrals of vector fields. The divergence theorem (Gauss-Ostrogradsky). Stokes' theorem. Applications.Abstract:
The first part of the course is dedicated to study of techniques for
solving systems of linear equations. Several basic methods are presented:
Gauss elimination, matrix solution, Cramer rule.
The last two methods involve matrix arithmetic, which is also presented in this part. The second part discusses vector spaces and linear transformations. Most attention is given to the matrix approach. Matrix diagonalization issues summarize this part.
The last part of the course study inner product spaces and their basic properties.