Analysis 1

• Profs: Ö. Imamoglu
• Website: https://metaphor.ethz.ch/x/2025/fs/401-0212-16L/
• SAM : https://sam-up.math.ethz.ch/
• Admin: Admin
• Material: Material
• Videos:
  • 2024: Videos ETHZ
  • 2025: Videos ETHZ

Lecture Notes

• 01 Introduction, Real Numbers, Completeness
• 02 Real Numbers, Min, Max, Bounds, Supremum, Infimum, Cardinality, Euclidian Space
• 03 Supremum, Infimum, Cross Product, Complex Numbers, Sequences
• 04 Divergence, Limits, Monotony, Weierstrass Theorem, Limit Superior and Inferior
• 05 Sandwich Lemma, Cauchy Criterion, and Bolzano-Weierstrass Theorem
• 06 Accumulation Points, Sequences in Reals and Complex, and Series
• 07 Series Cauchy Criterion, Absolute and Conditional Convergence, Riemann Rearrangement Theorem, Dirichlet’s Theorem
• 08 More Convergence Criteria, Dirichlet’s Theorem, Ratio, Root Tests, and Power Series

Script

Note that this is WIP and might include inaccuracies and mistakes… (Ch3-5 aren’t published yet…)

• Chapter 1 - Real Numbers, Euclidean Spaces, and Complex Numbers
• Chapter 2 - Sequences and Series, Approaching Infinity, Divergence, Infinity, Algebra of Limits, Monotone Sequences, Weierstrass, Cauchy, Series, Summing Infinitely, Special Series and Operations