Teaching
Teaching
Below are links to lecture notes written while teaching at the Hebrew University. You are welcome to use them, but be aware that they are not meant to replace comprehensive textbooks. In particular, they may contain errors. Please let me know if you find any mistake.
Measure Theory (80517, Fall 2018)
1.Introduction [Chapter1.pdf]
2.Measure Spaces [Chapter2.pdf]
3.Integration [Chapter3.pdf]
4.Differentiation [Chapter4.pdf]
5.Lp-Spaces [Chapter5.pdf]
6.Radon Measures [Chapter6.pdf]
7.Some Notes on Topology [Topology.pdf]
This appendix contains a summary of definitions and facts in topology. It is offered as a quick reference for students did not take this course, however, it is by no means a substitute for a comprehensive course.
Probability (80420, Fall 2016)
1.Preface [Preface.pdf]
2.Notions in Set Theory [Chapter0.pdf]
3.Probability Spaces [Chapter1.pdf]
4.Conditional Probability [Chapter2.pdf]
5.Discrete Random Variables [Chapter3.pdf]
6.Expectation [Chapter4.pdf]
7.Inequalities [Chapter5.pdf]
8.Continuous Random Variables [Chapter6.pdf]
9.Limit Theorems [Chapter7.pdf]
10. Sequences and Series [Appendix.pdf]
This appendix contains a summary of definitions and facts concerning sequences and series. It is offered as a quick reference for students who might not have learned throughly these subjects.
Calculus (80131, Fall 2015)
1.Preface
2.Real Numbers [Chapter2.pdf]
3.Sequences [Chapter3.pdf]
4.Functions [Chapter4.pdf]
5.Derivatives [Chapter5.pdf]
Mathematical Methods for Physicists (Fall 2014)
1.Functions of One Variable [Chapter4.pdf]
2.Derivatives and Integrals [Chapter5.pdf]
3.Taylor Polynomials and Taylor Series [Chapter6.pdf]
4.Indefinite Integrals [Chapter7.pdf]
5.Curves in Rn [Chapter8.pdf]
6.Functions of Several Variables [Chapter9.pdf]
Basic Notions in Functional Analysis (Fall 2013)
1.Hilbert Spaces [Hilbert.pdf]
2.Banach Spaces [Banach.pdf]
3.Topological Vector Spaces [TVS.pdf]
Calculus for Engineers (Spring 2013) [Calculus.pdf]
ODEs (Spring 2012) [ODEs.pdf]
Chapter on asymptotic methods [ODEs2.pdf]
Mechanics (Spring 2008) [Mechanics.pdf]
Asymptotic Methods (Spring 2008) [Asymptotics.pdf]
Advanced Calculus (80315, Fall 2006) [AdvCalc.pdf]
Numerical Analysis (Fall 2005) [NumAnal.pdf]