Lefschetz fixed-point theorem

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Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Discrete Time Solution: Stability Properties and Fixed Points

Explores stability properties and fixed points in discrete time solutions.

Advanced Analysis II: Homogeneous ODEs and Banach Spaces

Explores the resolution of ODEs and the Banach fixed-point theorem.

Computer Arithmetic: Floating Point Numbers

Explores computer arithmetic, emphasizing fixed-point and floating-point numbers, IEEE 754 standard, dynamic range, and floating-point operations in MIPS architecture.

Information Representation: Real Numbers and Errors

Explores the representation of real numbers, errors, and precision in information.

CW Approximation Theorem

Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.

Advanced-analysis-ii

Explores advanced analysis topics, including Cauchy sequences, Banach spaces, and the Cauchy-Lipschitz theorem.

Datapath Design: Mandelbrot & Fixed-Point

Explores datapath design for Mandelbrot set and fixed-point number representation in digital systems.

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.

Picard Method: Fixed Point Iterative Technique

Covers the Picard method for solving nonlinear equations using fixed point iteration.