MATH-101(de): Analysis I (German)

Lectures in this course (51)

Explores complex numbers in polar form, powers, and roots, including trigonometric relationships and rotation matrices.

Covers complex numbers, sequences, series, and exponential, sine, and cosine functions in the complex plane.

Covers the extension of the logarithm to complex numbers and explores the relationship with trigonometric functions.

Covers convergence of power series, complex equations, exponential functions, and function properties.

Explores monotonicity and boundedness in functions, analyzing their implications in mathematical analysis.

Explains surjectivity, injectivity, and bijectivity in functions, including trigonometric examples.

Covers the concept of function composition and the properties of bijections when composing functions.

Explains surjective, injective, and bijective functions, along with limits of functions.

Explains the concept of limits and convergence criteria for sequences of function values.

Explains limit rules and uniqueness of function limits, with examples on trigonometric functions.

Covers the concept of limits at infinity and discusses criteria and examples of functions approaching infinity.

Covers uniform continuity, one-sided limits, function behavior, and continuity conditions, with multiple-choice questions for practice.

Covers the concept of uniform continuity and a theorem on continuous functions.

Covers the Intermediate Value Theorem, functions' properties, continuity, finding roots, and differentiation concepts.

Explains differentiation and linear approximation for function approximation near a point.

Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.

Explores derivatives, O-Notation, extrema, and algorithm complexity in Analysis 1.

Covers O-Notation, local extrema, and critical points in functions.

Covers the Mean Value Theorem in differential calculus, focusing on critical points and global extrema within intervals.

Explores monotonicity criteria, L'Hopital's rule, and Lipschitz continuity in differentiable functions and deep neural networks.

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