Tabla de Contenidos: “…Introduction -- Distributions -- Convolution of Distributions -- Fourier Transform of Distributions -- Laplace Transform of Distributions -- Summable Distributions -- Convolution Equations -- Linear Time Invariant Systems -- WNTI Systems -- WNTI Systems Composition -- WNTI Circuits -- Linear Time-Varying Systems -- WNTV Systems -- Periodically Switched Circuits…”

Tabla de Contenidos: “…Introduction and motivation -- Linear algebra -- Analytic geometry -- Matrix decompositions -- Vector calculus -- Probability and distribution -- Continuous optimization -- When models meet data -- Linear regression -- Dimensionality reduction with principal component analysis -- Density estimation with Gaussian mixture models -- Classification with support vector machines…”

Tabla de Contenidos: “…. -- 2.4 - Summary -- Chapter 3 - Linear mixed-effects models -- 3.1 - Introduction of linear mixed models: three cases -- 3.1.1 - Case I: one-factor linear mixed model with random intercept -- 3.1.2 - Case II: linear mixed model with random intercept and random slope -- 3.1.3 - Case III: linear mixed model with random effects and three covariates -- 3.2 - Formalization of linear mixed models -- 3.2.1 - General specification of linear mixed models -- 3.2.2 - Variance-covariance matrix and intraindividual correlation -- 3.2.3 - Formalization of variance-covariance components -- 3.3 - Inference and estimation of fixed effects in linear mixed models -- 3.3.1 - Maximum likelihood methods -- 3.3.2 - Statistical inference and hypothesis testing on fixed effects -- 3.3.3 - Missing data -- 3.4 - Trend analysis -- 3.4.1 - Polynomial time functions -- 3.4.2 - Methods to reduce collinearity in polynomial time terms -- 3.4.3 - Numeric checks on polynomial time functions -- 3.5 - Empirical illustrations: application of two linear mixed models -- 3.5.1 - Linear mixed model on effectiveness of acupuncture treatment on PCL score -- 3.5.2 - Linear mixed model on marital status and disability severity in older Americans -- 3.6 - Summary -- Chapter 4 - Restricted maximum likelihood and inference of random effects in linear mixed models -- 4.1 - Overview of Bayesian inference -- 4.2 - Restricted maximum likelihood estimator -- 4.2.1 - MLE bias in variance estimate in general linear models -- 4.2.2 - Specification of REML in general linear models -- 4.2.3 - REML estimator in linear mixed models -- 4.2.4 - Justification of the restricted maximum likelihood method -- 4.2.5 - Comparison between ML and REML estimators -- 4.3 - Computational procedures…”

Tabla de Contenidos: “…Contiene: Vol. 1 : One-Variable Calculus, with and Introduction to Linear Algebra; Vol. 2 : Multi-Variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability…”