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