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Preface | |
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Algebra | |
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Algebraic Axioms | |
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Algebraic Operations | |
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Exponents and Roots | |
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Quadratic Equations | |
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Logarithms | |
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Factorials | |
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Complex Numbers | |
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Polynomials and Partial Fractions | |
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Geometry, Trigonometry, and Hyperbolic Functions | |
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Geometry | |
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Trigonometry | |
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Common Coordinate Systems | |
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Euler's Equation and Hyperbolic Functions | |
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Series Representations | |
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Analytic Geometry | |
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Line | |
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Conic Sections | |
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Polar Form of Complex Numbers | |
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Linear Algebra I | |
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Rotation of Axes | |
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Matrices | |
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Determinants | |
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Linear Algebra II | |
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Vectors | |
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Vector Spaces | |
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Eigenvalues and Eigenvectors | |
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Matrix Diagonalization | |
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Differential Calculus | |
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Limits | |
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Derivatives | |
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Finite Difference Concept | |
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Partial Derivatives | |
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Partial Differentiation | |
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Vector Analysis | |
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Analyticity and the Cauchy-Riemann Equations | |
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Integral Calculus | |
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Indefinite Integrals | |
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Definite Integrals | |
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Solving Integrals | |
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Numerical Integration | |
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Special Integrals | |
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Line Integral | |
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Double Integral | |
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Fourier Analysis | |
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Fourier Integral and Fourier Transform | |
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Time Series and Z Transform | |
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Laplace Transform | |
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Ordinary Differential Equations | |
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First-Order ODE | |
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Higher-Order ODE | |
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Stability Analysis | |
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Introduction to Nonlinear Dynamics and Chaos | |
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Ode Solution Techniques | |
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Variation of Parameters | |
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Cauchy Equation | |
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Series Methods | |
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Laplace Transform Method | |
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Partial Differential Equations | |
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Boundary Conditions | |
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PDE Classification Scheme | |
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Analytical Solution Techniques | |
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Numerical Solution Methods | |
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Integral Equations | |
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Classification | |
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Integral Equation Representation of a Second-Order ODE | |
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Solving Integral Equations: Neumann Series Method | |
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Solving Integral Equations with Separable Kernels | |
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Solving Integral Equations with Laplace Transforms | |
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Calculus of Variations | |
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Calculus of Variations with One Dependent Variable | |
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The Beltrami Identity and the Brachistochrone Problem | |
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Calculus of Variations with Several Dependent Variables | |
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Calculus of Variations with Constraints | |
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Tensor Analysis | |
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Contravariant and Covariant Vectors | |
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Tensors | |
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The Metric Tensor | |
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Tensor Properties | |
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Probability | |
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Set Theory | |
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Probability Defined | |
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Properties of Probability | |
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Probability Distribution Defined | |
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Probability Distributions | |
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Joint Probability Distribution | |
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Expectation Values and Moments | |
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Multivariate Distributions | |
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Example Probability Distributions | |
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Statistics | |
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Probability and Frequency | |
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Ungrouped Data | |
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Grouped Data | |
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Statistical Coefficients | |
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Curve Fitting, Regression, and Correlation | |
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Solutions to Exercises | |
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Algebra | |
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Geometry, Trigonometry, and Hyperbolic Functions | |
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Analytic Geometry | |
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Linear Algebra I | |
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Linear Algebra II | |
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Differential Calculus | |
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Partial Derivatives | |
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Integral Calculus | |
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Special Integrals | |
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Ordinary Differential Equations | |
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ODE Solution Techniques | |
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Partial Differential Equations | |
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Integral Equations | |
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Calculus of Variations | |
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Tensor Analysis | |
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Probability | |
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Probability Distributions | |
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Statistics | |
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References | |
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Index | |