Lectures in course MATH-101(de): Analysis I (German)

Introduces real numbers, including equations like x²=2 with no rational solutions.

Covers Cauchy sequences, induction, recursive sequences, and convergence in mathematical analysis.

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Covers sequences, intervals, and absolute value concepts in Analysis 1.

Covers binomial formulas, induction, and coefficients, including examples and a quiz on permutations and combinations.

Covers the binomial formula, Euler number, and infinity, including induction and convergence of sequences.

Introduces sequences, convergence, limits, bounded and monotonic sequences, divergence, and convergence criteria.

Covers convergence criteria, properties of sequences, and the Achilles Paradox.

Covers the convergence criteria for sequences and limits calculation, discussing properties, rules, examples, and boundedness.

Covers the definition of series, including the geometric and harmonic series.

Covers convergence criteria for sequences and explores monotone sequences and the two policemen criterion.

Covers convergence criteria in Analysis 1, focusing on the Quotient Criterion.

Covers the Majorantenkriterium and Wurzelkriterium for convergence tests of series.

Covers the convergence of series with nonnegative summands and the Leibniz criterion.

Covers Cauchy sequences, convergence, and induction in mathematical analysis.

Covers absolute convergence, reordering series, and includes a quiz series.

Explores reordering series and the properties of power series for function representation.

Explores the convergence of exponential series and their absolute convergence properties.

Introduces complex numbers, covering exponential series and arithmetic operations with common rules.

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.