Lectures 17-20 (Dec 28, Jan 4, 11)

Exponential and logarithmic functions

The three lectures were devoted to accurate introduction of the logarithmic and exponential function and investigation of their properties based on the differential equations which these functions satisfy.

The collected notes for the theme “Integration and Differential Equations” are here: https://drive.google.com/file/d/1I_uM8nnKfeAb-uATU5Sq_toZRHr6M8wN/view?usp=sharing

Note that I edit and polish these notes constantly, so the next version will be different. The additions that were not covered in the class will not be a part of the exam, but I hope you take them back with you after completing your RW degree and read them eventually! 

 

Scribbled notes: (one), (two).

 

Video recordings

Date: Dec 28, 2021 09:00 Jerusalem

Meeting Recording:
https://weizmann.zoom.us/rec/share/A-FWCKRQqOrpEIK-14J_Nlzs3uVphjcBOlDB0n36aX2xF6UGsL5I4MMkM6CKBWxL.KksXv2goNmFLmH53

Access Passcode: ezv08k

Date: Jan 4, 2022 09:05 Jerusalem

Meeting Recording:
https://weizmann.zoom.us/rec/share/xBF4wIuReV1IjoGpOPr6Q0zV13HBWtoozrQZl2eL-wvL30ESx-QnPXNYw4HYdr3s.naszHFAeysohAUX1

Access Passcode: ky1xnE

Date: Jan 11, 2022 08:59 Jerusalem

Meeting Recording:
https://weizmann.zoom.us/rec/share/ObMOZlnX6obQMlpnMbn0FLxET1qftzKsbHRhsxW-CwGsX98oCHQZvO-L2Efg5qLJ.EpfhpIqcHN4KyYhK

Access Passcode: 3#3X5C

“Auxiliary Lesson” שעור עזר) #4) November 15, 2007

Formal series, formal vector fields: Flows and embedding

1. Formal series algebra . Formal vector fields (derivations) . Formal equivalence of vector fields. Truncation. Convergence in the formal algebra  .
2. Formal inverse function theorem. Geometric series.
3. Integration and formal flow of vector fields. Exponent.
4. Embedding in the flow. Linear case. Matrix logarithms.
5. Embedding in the flow and formal logarithms.

Reading Section 3 from the textbook.