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‎.vscode/ltex.dictionary.en-US.txt

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nD
1313
addants
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summand
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Monotonicity
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Normals
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Extrema
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Rolle

‎.vscode/ltex.hiddenFalsePositives.en-US.txt

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{"rule":"NOW","sentence":"^\\QThere is no any overlap between graphs except the intersection \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"}
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{"rule":"ENGLISH_WORD_REPEAT_BEGINNING_RULE","sentence":"^\\QDerivatives of Parametric Equations.\\E$"}

‎content/Part2 Discrete math/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Boolean Algebra}

‎content/Part2 Discrete math/Chapter2.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Preliminary Number Theory and Cryptography}

‎content/Part2 Discrete math/Chapter3.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Search and Sorting}

‎content/Part2 Discrete math/Chapter4.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Graph Theory}

‎content/Part3 Single-variable Calculus/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Function Monotonicity, Parity and Periodicity}
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\section{Monotonicity of Function}
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\section{Parity of Function}
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\section{Periodicity of Function}

‎content/Part3 Single-variable Calculus/Chapter2.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Abstract and Piece-wise Function}
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\section{Abstract Function}
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\section{Piece-wise Function}

‎content/Part3 Single-variable Calculus/Chapter3.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Limit and Continuity}
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\section{Limit of Sequence}
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\section{limit of Function}
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\section{Continuity}
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\section{Application of Limit}

‎content/Part3 Single-variable Calculus/Chapter4.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Differential Calculus}
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\section{Derivative Basics}
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\subsection{Definition of Derivative}
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\subsection{Geometric Meaning of Derivative}
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\subsection{Physical Meaning of Derivative}
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\section{Basic Derivative Rules}
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\subsection{Derivatives of Elementary Functions}
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\subsection{Product Rule, Quotient Rule, Chain Rule}
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\section{Higher-order Derivatives}
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\subsection{Second-order Derivatives and Applications}
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\subsection{Calculation and Significance of Higher-order Derivatives}
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\section{Derivatives of Abnormal Function}
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\subsection{Derivatives of Implicit Functions}
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\subsection{Derivatives of Parametric Equations}
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\section{Differentiation}
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\section{Related Rates}
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\subsection{Relationships between Rates of Change of Different Quantities}
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\section{Taylor Series}
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\subsection{Taylor Expansion of Functions}
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\subsection{Application of Taylor Series}
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\section{Applications of Differential Calculus}
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\subsection{Tangents and Normals of Curves}
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% \subsection{Analysis of Velocity and Acceleration in Motion}
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\subsection{Mean Value Theorem in Differential Calculus}
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\subsubsection{Fermat's Theorem}
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\subsubsection{Rolle's Theorem}
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\subsubsection{Lagrange's Mean Value Theorem}
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\subsubsection{Cauchy's Mean Value Theorem}
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\subsubsection{Indeterminate Form Limit}
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\subsection{Extrema Problems and Optimization}

‎content/Part3 Single-variable Calculus/Chapter5.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{integral calculus}
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\section{Fundamentals of Integration}
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\subsection{Definition of the Integral}
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\subsection{Properties of Integrals}
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\subsection{The Fundamental Theorem of Calculus}
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\section{Techniques of Integration}
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\subsection{Basic Integration Formulas}
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\subsection{Integration by Substitution}
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\subsection{Integration by Parts}
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\subsection{Trigonometric Integrals}
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\subsection{Partial Fractions}
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\section{Applications of Integration}
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\subsection{Area Under Curves}
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\subsection{Volumes of Solids of Revolution}
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\subsection{Arc Length and Surface Area}
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\subsection{Center of Mass and Moments}
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\section{Improper Integrals}
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\subsection{Convergence and Divergence of Improper Integrals}
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\subsection{Applications of Improper Integrals}
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\section{Numerical Integration Methods}
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\subsection{The Trapezoidal Rule}
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\subsection{Simpson's Rule}

‎content/Part3 Single-variable Calculus/Chapter6.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Differential Equation}

‎content/Part3 Single-variable Calculus/Chapter7.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Infinite Series}

‎content/Part4 Multi-variable Calculus/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{integral calculus}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Introduction to Multivariable Functions}
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\subsection{Concepts of Multivariable Functions}
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\subsection{Graphs and Contour Plots}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Partial Derivatives}
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\subsection{Definition and Interpretation}
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\subsection{Higher-Order Partial Derivatives}
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\subsection{Chain Rule in Multiple Variables}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Multiple Integrals}
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\subsection{Double Integrals}
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\subsubsection{Iterated Integrals}
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\subsubsection{Double Integrals over General Regions}
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\subsection{Triple Integrals}
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\subsubsection{Cylindrical and Spherical Coordinates}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Vector Calculus}
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\section{Vector Fields}
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\section{Gradient, Divergence, and Curl}
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\section{Line and Surface Integrals}

‎content/Part5 Linear Algebra/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Vectors Space and the Geometry of Space}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Matrices and Systems of Equations}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Determinant of Matrix}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Orthogonality}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Linear Transformations}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Eigenvalues and Eigenvector}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Singular Value Decomposition}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Complex Vector and Matrices}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Matrix Differential Calculus}

‎content/Part6 Probability and Combinatorics/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Counting Method and Basic Combinatorics}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Probability Theorems}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Discrete Distribution}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Continuous Distribution}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Joint Cumulative Distribution}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Joint Cumulative Distribution}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Limit Theory in Probability}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Stochastic Process}

‎content/Part7 Statistics/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Sampling and Parameters}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Descriptive Statistics}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Graphical Statistics}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Statistical Inference}
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\section{Parameter Estimation}
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\section{Interval Estimation}
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\section{Hypothesis Testing}
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\section{Variance Inference}
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\section{Bayesian Inference}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Hypothesis Testing}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Regression and Regressive Analysis}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Basic Multi-variable Statistical analysis}

‎content/Part8 Basic Information Theory/Chapter1.tex

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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Measuring of Information}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Information Entropy}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Joined Entropy and Conditional Entropy}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Cross Entropy and Relative Entropy}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Mutual Information}
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\chapterimage{orange2.jpg}
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\chapterspaceabove{6.75cm}
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\chapterspacebelow{7.25cm}
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\chapter{Differential Entropy}

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