Mathematics 3 - Vector Calculus and Partial Differential Equations
WS 2019/20
LECTURE NOTES
Notes
(These are lecture notes which mainly consist of definitions, statements and examples)
If you find any mistakes, please contact Raphael [dl18bewa at studserv.uni-leipzig.de] who is typing these lecture notes
Note 1 (Oct 14)
Note 2 (Oct 15)
Note 3 (Oct 21)
Note 4 (Oct 22)
Note 5 (Oct 28)
Note 6 (Oct 29)
Note 7 (Nov 4)
Note 8 (Nov 5)
Note 9 (Nov 11)
Note 10 (Nov 12)
Note 11 (Nov 18)
Note 12 (Nov 19)
Note 13 (Nov 25)
Note 14 (Nov 26)
Note 15 (Dec 3)
Note 16 (Dec 9)
Note 17 (Dec 10)
Note 18 (Dec 16)
Note 19 (Dec 17)
Note 20 (Jan 6)
Note 21 (Jan 7)
Note 22 (Jan 13)
Note 23 (Jan 14)
Note 24 (Jan 20)
Note 25 (Jan 21)
Note 26 (Jan 27)
Note 27 (Jan 28)
COURSE JOURNAL
Oct 14 - Riemann integral over rectangle
Oct 15 - Riemann integral over a set
Oct 21 - Fubini's theorem
Oct 22 - Change of variables
Oct 28 - Improper integral
Oct 29 - Line integral of scalar field
Nov 4 - Line integral of scalar and vector fields
Nov 5 - Green's formula
Nov 11 - Path independence of line integrals
Nov 12 - Surface integral of a scalar field
Nov 18 - Surface integral of a vector field
Nov 19 - Gauss-Ostrogradskii theorem
Nov 25 - Stokes' theorem
Nov 26 - Holomorphic functions
Dec 3 - Properties of holomorphic functions
Dec 9 - Conformal maps
Dec 10 - Cauchy's theorem
Dec 16 - Cauchy's integral formula
Dec 17 - The Taylor series
Jan 6 - The Taylor series II. Further properties of holomorphic functions
Jan 7 - The Laurent series
Jan 13 - Residues
Jan 14 - Application of residues to the computation of integrals
Jan 20 - Introduction to PDE. Transport equation
Jan 21 - Heat equation
Jan 27 - Wave equation
Jan 28 - Laplace equation