Book:Clement V. Durell/Advanced Algebra/Volume I

Subject Matter

 * Algebra

Contents

 * Preface


 * $\text{I}$.
 * (Arrangements of Unlike Things; Like and Unlike Things; Selections; Distribution in Groups; Selections, any number at a time)


 * $\text{II}$.
 * (Expansion of $\paren {x + a}^n$; Greatest Coefficients and Terms; Relations between Coefficients; Summation of Series)


 * $\text{III}$.
 * (Functional and $\Sigma$} Notation; Difference Method; Induction; Power Series)


 * . $\text{A}$. 1-10


 * $\text{IV}$.
 * (Idea of a Limit; Non-existence of Limits; Behaviour of $x^n$ when $n \to \infty$; Convergent, Divergent, Oscillating Series; General Properties of Limits; General Theorems on Convergence; Comparison Test; $\sigma n^{-p}$; Ratio Test; Positive and Negative Terms; Absolute Convergence)


 * $\text{V}$.
 * ( Conditions for Convergence; Greatest Terms; Notation for Coefficients; Binomial Theorem; Expansion of Functions; Forms of Binomial Series; Partial Fractions; Approximations; Homogeneous Products; Sum of First $r$ Coefficients)


 * $\text{VI}$.
 * (Properties of $\ds \int_1^t x^{-1} d x$; Natural Logarithms; $\map {\dfrac d {d x} } {\log x}$; Logarithmic Series; Common Logarithms; Proportional Parts; Summation of Series; Approximations; The Function $e^x$; Expansion of $e^x$; Value of $e$; $e$ is not Rational; Remainder after $n$ Terms of Exponential Series; $a^x$; $\ds \lim_{n \to \infty} \paren {1 + x/n}^n$)


 * . $\text{A}$. 11-20


 * $\text{VII}$.
 * (Quadratic Function; Cubic Function; Polynomials; Repeated Roots; $\paren {a x^2 + b x + c} / \paren {A x^2 + B x + C}$;


 * $\text{VIII}$.
 * (Equations with Given Roots; Relations between Roots and Coefficients; Unsymmetrical Relations between Roots; Transformation of Equations; Numerical Equations; Newton's Method, Horner's Method; Elimination)


 * $\text{IX}$.
 * (Second Order Determinants; Third Order Determinants; Minors and Cofactors; Factorisation; Linear Equations; Product of Determinants; Determinants of any Order)


 * . $\text{A}$. 21-35





Source work progress
* : Chapter $\text I$ Permutations and Combinations: The $r$, $s$ Principle: Example $1$.