## Dr. Inna Entova-Aizenbud

### Time and Place

יום א 16:00 - 14:00 בצוקר, גולדשטיין-גורן  חדר 213
יום ג 13:00 - 12:00 בקרייטמן-זלוטובסקי(חדש)  חדר 303
יום ה 16:00 - 14:00 בגוטמן  חדר 111

## Course Content

• Basic concepts of topology of metric spaces: open and closed sets, connectedness, compactness, completeness.
• Normed spaces and inner product spaces. All norms on $\mathbb{R}^n$ are equivalent.
• Theorem on existence of a unique fixed point for a contraction mapping on a complete metric space.
• Differentiability of a map between Euclidean spaces. Partial derivatives. Gradient. Chain rule. Multivariable Taylor expansion.
• Open mapping theorem and implicit function theorem. Lagrange multipliers. Maxima and minima problems.
• Riemann integral. Subsets of zero measure and the Lebesgue integrability criterion. Jordan content.
• Fubini theorem. Jacobian and the change of variables formula.
• Path integrals. Closed and exact forms. Green’s theorem.
• Time permitting, surface integrals, Stokes’s theorem, Gauss’ theorem
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