Multi-Variable Calculus (INFI-3) course:104295
Lectures on video (in Hebrew):
Lecture 1: Topology of the Euclidean space.
Lecture 2: More on the topology of the Euclidean space.
Lecture 3: Compactness. parts (a+b).
Lecture 4: Multi-variable functions and their limits. parts (a+b).
Lecture 5: Continuity. parts (a+b).
Lecture 6: Continuity and compactness. parts (a+b).
Lecture 7: On the geometry of the Euclidean space with emphasis on 2 and 3 dimensions. parts (a+b).
Lecture 8: More on geometry. parts (a+b).
Lecture 9: Planar areas in high dimensions
and vector product in three dimensions parts (a+b+c+d).
Lecture 10: Differentiability. parts (a+b).
Lecture 11: The Chain Rule.
Lecture 12: Partial derivatives. parts (a+b+c).
Lecture 13: More on the gradient and the Chain Rule. parts (a+b).
Lecture 14: Multi-variable Taylor polynomial.
Lecture 15: local min/max and the Hessian matrix. parts (a+b).
Lecture 16: Inverse function theorem. parts (a+b).
Lecture 17: Open Mapping Theorem.
Lecture 18: Lagrange multipliers.
Lecture 19: Lagrange multipliers: examples and comments. parts (a+b).
Lecture 20: Implicit Function Theorem. parts (a+b).
Lecture 21: Implicit Function Theorem: examples and comments. parts (a+b).
Lecture 22: Definition of Intergrability.
Lecture 23: More on Integrability.
Lecture 24: Characterization Theorem for Integrable Functions. parts (a+b).
Lecture 25: Fubini's Theorem: proof and examples. parts (a+b+c+d).
Lecture 26: Linear Transformations, Determinants, and Volumes.
Lecture 27: Proof of Theorem about Determinants and Volumes.
Lecture 28: Theorem about Change of Variable: Introduction, proof for linear functions, and outline of proof for general functions.
Lecture 29: Theorem about Change of Variable - complete rigorous proof. parts (a+b).
Lecture 30: Change of Variable: examples (including polar/spherical/cylindrical coordinates) + Theorem of Sard. parts (a+b+c).
Lecture 31: k-dimensional volumes in R^n. parts (a+b).
Lecture 32: k-dimensional surfaces in R^n and their k-dimensional volume. parts (a+b).
Lecture 33: 2-dimensional surfaces in R^3 and their surface area. parts (a+b).
Lecture 34: Integration over surfaces and line-integrals of
second type in R^n. parts (a+b).
Lecture 35: Theorem of Green in R^2 + examples. parts (a+b).
Lecture 36: Integration over 2-dimensional surfaces in R^3. parts (a+b)+ (short part c correcting a mistake in part b).
Lecture 37: Theorem of Gauss - divergence theorem (part a + begining of part b) and examples (parts b+c)
Lecture 38: Theorem of Stokes - curl theorem (for 2-d surfaces with boundary, in R^3). parts (a+b).
Lecture 39: Theorem of Stokes - examples. parts (a+b).
Additional lectures about differential forms (not part of the syllabus):
Lecture 40: Multi-Linear and Anti-Symmetric Functions.
Lecture 41: Differential forms and their derivatives.
Lecture 42: Pullback of differential forms.
Lecture 43: Integration of differential forms.
Exams of Rom Pinchasi from previous years: