We give examples of some of the standard functions in Calculus. We discuss linear, polynomial, quadratic and piecewise functions. #mikedabkowski, #mikethemathematician, #profdabkowski, #calc1
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Chebyshev Polynomials
Gibbs Phenomena
Lagrange Polynomial Interpolation
The Weierstrass Nowhere Differentiable Function
Two Definitions of Euler's Number Converge to the Same
The Arithmetic Geometric Mean Limit
Limit Superior and Limit Inferior of a Sequence
Courant Fischer Min-Max Theorem
Householder Transformations
Properties of the Adjugate Matrix: Determinants and Products
The Adjugate of a Matrix and Invertibility
Elementary Properties of Singular Values
Hilbert's Inequality
Jensen's Inequality
The Sylvester Matrix Equation Theorem
Unitary Equivalence of Matrices
Schur Triangularization
The Sylvester Rank Inequality
The Adjacency Matrix of a Graph and its Powers
The Cholesky Factorization
Linear Transformations Map Balls onto Ellipses: The Singular Value Proof
The Polar Decomposition of a Matrix
Simultaneously Diagonalizable Matrices Commute and a Partial Converse
Distinct Eigenvalues Have Linearly Independent Eigenvectors