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Table of Contents
1 Cover
4 Preface
5 Volume 1 1 Basic Concepts of Algebra 1 Scalars, Vectors, Matrices, and Determinants 2 Function Features 2.1 Series 2.2 Multiplication and Division of Polynomials 2.3 Trigonometric Functions 2.4 Hyperbolic Functions 3 Vector Operations 3.1 Addition of Vectors 3.2 Multiplication of Scalar by Vector 3.3 Scalar Multiplication of Vectors 3.4 Vector Multiplication of Vectors 4 Matrix Operations 4.1 Addition of Matrices 4.2 Multiplication of Scalar by Matrix 4.3 Multiplication of Matrices 4.4 Transposal of Matrices 4.5 Inversion of Matrices 4.6 Combined Features 5 Tensor Operations 6 Determinants 6.1 Definition 6.2 Calculation 6.3 Eigenvalues and Eigenvectors 7 Solution of Algebraic Equations 7.1 Linear Systems of Equations 7.2 Quadratic Equation 7.3 Lambert’s W Function 7.4 Numerical Approaches
7 Volume 2 About the Author Series Preface Preface 2 Basic Concepts of Calculus 8 Limits, Derivatives, Integrals, and Differential Equations 9 Limits and Continuity 9.1 Univariate Limit 9.2 Multivariate Limit 9.3 Basic Theorems on Limits 9.4 Definition of Continuity 9.5 Basic Theorems on Continuity 10 Differentials, Derivatives, and Partial Derivatives 10.1 Differential 10.2 Derivative 10.3 Dependence Between Functions 10.4 Optimization of Univariate Continuous Functions 10.5 Optimization of Multivariate Continuous Functions 11 Integrals 11.1 Univariate Integral 11.2 Multivariate Integral 11.3 Optimization of Single Integral 11.4 Optimization of Set of Derivatives 12 Infinite Series and Integrals 12.1 Definition and Criteria of Convergence 12.2 Taylor’s Series 12.3 Gamma Function and Factorial 13 Analytical Geometry 13.1 Straight Line 13.2 Simple Polygons 13.3 Conical Curves 13.4 Length of Line 13.5 Curvature of Line 13.6 Area of Plane Surface 13.7 Outer Area of Revolution Solid 13.8 Volume of Revolution Solid 14 Transforms 14.1 Laplace’s Transform 14.2 Legendre’s Transform 15 Solution of Differential Equations 15.1