Lectures related to Square root of 5

Solving the Quintic: Dominant Balance

Explores dominant balance analysis in solving the quintic polynomial, with a focus on non-dimensionalization and series expansions.

Image of Composite Functions

Analyzes the image sets of composite functions on [1, +∞], deducing the final image set as [√2/2, 1) closed left, open right.

Numerical Root Finding with Scipy

Introduces numerical root finding, differentiation, integration, and ODE solving using Scipy.

Complex Numbers: Sequences, Series in C, exp, sin, cos

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

Linear Algebra Review: Convex Optimization

Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.

Complex Numbers: Definitions and Properties

Covers the definitions and properties of complex numbers, including the field of complex numbers, the conjugate, the real and imaginary parts, algebraic form, modulus, and argument.