Index A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | Z A Absolute extrema algorithms alignment Allen NLP NER alpha values animation Antiderivative aquifer area between two curves Area Problem area under the curve (AUC) autonomous equations average cost Average value B bag of words barchart basis Bayes' Theorem Beautifulsoup Best Approximation Theorem bifurcation Binary Classification of Labelled Data Block Descent Brownian motion C canonical ensemble catastrophic event Cauchy distribution Cauchy-Riemann equation Cauchy-Shwarz inequality Central Limit Theorem Chain Rule chain rule change of basis characters circuits City of Chicago budget class classes classification classification of texts closed system Cobbs-Douglas Production cofactor expansion coherent system cohesion collective efficacy column matrix column space complex eigenvalues in ODE systems complex function complex logarithm complex number complex potential complex system science concave down concave up conditionals Confidence Intervals consistent continuity continuity equation continuous compounding interest convergent Coordinate Descent corpus correlated system Covariance Matrix COVID-19 Covid-19 critical value method cylindrical coordinates D Darcy's Law data likelihood data operations Dataframe dataframe decreasing Definite Integrals demand function Derivative derivative rules derivatives of trig functions determinant of matrix determinants determinants as area or volume deterministic system diagonal entry diagonal matrix diagonalizable diagonalization Differential Equations dimension Dimension Reduction by Principal Component Analysis discrete dynamical systems divergent document embedding domain E echelon form Eidge Classification eigenspace eigenvalues, [1] eigenvectors elementary row operations email filtering emergent behavior energy entropy, [1] equilibrium bundle equilibrium point equilibrium systems equipotentials evaluating classification exponential decay exponential function exponential functions exponential growth, [1] expressions Extreme Value Theorem F f1 score false negative false positive false positive rate (FPR) feature effectiveness features Fisher-Calo fixed cost flow rate folium for loops fractions frequencies of words function, [1] function compositions function operations functions, [1] fundamental set of solutions Fundamental Theorem of Calculus G general solution geometric behavior of homogeneous linear ODE systems geometric multiplicity GINI index Gradient Descent Gradient-Based Optimization Gram-Schmidt Process grand-canonical ensemble graphical intersections groundwater flow equation H half-life harmonic conjugate harmonic function Heaviside function heavy tail homogeneity homogenous hydrology I identity matrix if conditional statements Implicit differentiation importing and exporting data improper integral income streams income-consumption path inconsistent increasing Indefinite integrals inflection point initial condition initial value problem (IVP) inline (lambda) funxtions innter product installing libraries integral test Integrals Integration by Parts intent detection Intermediate Value Theorem internally displaced people (IDP) International Office for Migration (IOM) inverse document frequency inverse functions inverse Laplace transform inverse of a square matrix Ising spin model isolated paramagnetic spin model isolated system isotropic J Jacobian matrix JNB joint probability K K-means Clustering keyword extraction L L'Hopital's rule L'Hospital's Rule language detection Laplace equation Laplace Transforms leading entry least-squares problems Least-Squares Solutions levels of processing libraries limits linear combination, [1] linear equation linear first order ODE linear homogeneous differential equations with constant coefficients linear systems, [1] linear transformation linear transformations linearity Linearization linearization linearly dependent linearly independent lists logistic growth logistic growth model, [1] Lorentz curve M machine learning magnitude of vectors map marginal cost marginal functions Mathematical Formalism matplotlib, [1] matrices matrix algebra matrix entry matrix equation, [1] Maximization of Projected Variance maximum likelihood mean Mean Value Theorem microcanonical ensemble migration matrix Minimizing the OLS Loss Function via Normal Equations multiclass classification musical tone N n-grams Naive Bayes algorithms Naive Biayes algorithm named entity recognition (NER) named entity resolution natural exponential function natural language generation natural language processing NFL player positions non-deterministic system non-homogeneous linear ODE systems with constant coefficients nonhomogeneous linear differential equations nonlinear systems nonzero vectors normal distribution normal equation normalization null space numeric count vectors numpy, [1] O objects OLS Linear Regression one vs one (OvO) one vs rest (OvR) one-hot vectors open system opencv-python optimization Optimization for Linearly-Separable Data Optimization for Non-Separable Data Optimization Problem ordinary differential equation Ordinary Differential Equations orthagonal basis orthagonal compliment orthagonal projection, [1] orthagonal set orthagonality orthogonality orthonormal basis os P p-series pandas, [1], [2] paragraphs, [1] Parametric Equations Pascal's Triangle perceptron phase plane phase plane for nonlinear systems phase transitions pixel images, [1] Polar Coordinates polar coordinates polynomial function Porter stemmer posterior power law distribution power rule precision, [1] preprocessing Principal Component Analysis prior probabilistic language modeling procedures Product Rule product rule Projected Variance projection pure tones Q Quotient Rule quotient rule R radian measure random numbers random process random system random walk range rank rational function reading and writing data recall, [1] redlining reduced echelon form reduction algorithm regression related rates Relative extrema Riemann Sum ROC Curve row equivalent row reduction algorithm S scalar product, [1] Schelling model secant line semantic analysis sensitivity sensitivity analysis, [1] sentences sentiment analysis Separating Hyperplanes separation of variables Sequences Series Signed Distance similarity retrieval sink Slope Fields sound waves source Space Leasing plume span specificity spin system spiral sink spring mass problem standard deviation standard matrix representation statements statistical physics, [1] statistical process control steady state stemming stream function streamline modeling string operations subsets subspace sum of matrices superposition principle Support Vector Machines symmetry syntactic analysis system sensitivity method systems of first-order differential equations systems of linear equations T tangent line term document marices testing set text classification TF-IDF (term frequency the Hamiltonian The Rankine Oval Tigray tokenizers total cost trace of square matrix training set transformation transpose of a matrix trees triangular matrix trig functions trouble shooting libraries true accuracy true negative true positive true positive rate (TPR) two-commodity model types U U-substitution UN Sustainable Development Goals (UN SDG) undetermined coefficients uniform flow universal sentence encoder (USE) V variables Variance and Covariance vector equation vectorizations velocity potential W web scraping while loops word clouds, [1] words Z zero matrix zero row zero vector