• Date: 12.12.2022
• Time: 09:00
• Duration: 4 hours
• Allowed aids:
  • Approved "specific basic calculator" (see here)
  • One yellow, stamped A4 sheet with own, handwritten formulas and notes (on both sides). Such sheet can be picked up outside the department office in the 7th floor, SBII. (You may write this notes by hand on your tablet/ipad and then print them out to the yellow sheet.)
  • This formula sheet will be provided with the exam.

Chapters in the 10th edition of Kreyszig:

• Laplace transformation: Chap. 6.1-6.5
• Fourier series, Fourier integral, and Fourier transformation: Chap. 11.1, 11.2, 11.4, 11.7 (not: Fourier Cosine and Sine Integrals), 11.9
• Partial Differential Equations: Chap. 12.1-12.4 (not: Characteristics), 12.6 (not: Laplace's equation), 12.7

Additional notes:

• Complex Fourier series: Complex_Fourier_series.pdf
• Discrete Fourier transform: DFT.pdf
• Rounding errors (only 4N): roundoff.pdf
• Multivariable calculus (only 4D): Partiellderiverte.pdf

Notes and notebooks on Numerical Mathematics (section and page numbers always refer to the pdf's):

• Preliminaries pdf, ipynb
• Boundary value problems pdf, ipynb
• Interpolation pdf, ipynb: Only pages 1-3 and Section 3.
• Numerical integration pdf, ipynb: Not Section 2; not the calculation of the weights \(w_i\) in Section 3.1.
• Nonlinear equations pdf, ipynb: Not Section 3.
• Numerics of PDEs pdf, ipynb
• Numerics of ODEs pdf, ipynb (preliminary; last revision on November 10, 2022)
• Numerics of ODEs, part 2 pdf, ipynb (preliminary; last revision on November 15, 2022)

Exercises:

• All exercises including the 13th, non-mandatory exercise sheet, and the additional sheet with python problems.