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rusczyk r intermediate algebra art problem solving 2008

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Textbook in PDF format AoPS 2-Book Set : Art of Problem Solving AoPS Intermediate Algebra Textbook and Solutions Manual 2-Book Set : A comprehensive textbook covering Algebra 2 and topics in Precalculus. This book is the follow-up to the acclaimed Introduction to Algebra textbook. Topics covered in this book include a review of basic algebra topics, complex numbers, quadratics and conic sections, polynomials, multivariable expressions, sequences and series, identities, inequalities, exponents and logarithms, piecewise-defined functions, functional equations, and much more. As with all of the books in Art of Problem Solving's Introduction and Intermediate series, the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which new techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains over 1600 problems. The solutions manual contains full solutions to all of the problems, not just answers. How to Use This Book Acknowledgements Basic Techniques for Solving Equations Isolation Substitution Elimination Larger Systems of Linear Equations Summary Functions Review Function Basics Graphing Functions Composition Inverse Functions Summary Complex Numbers Arithmetic of Complex Numbers The Complex Plane Real and Imaginary Parts Graphing in the Complex Plane Summary Quadratics Factoring Quadratics Relating Roots and Coefficients Completing the Square The Discriminant Quadratic Inequalities Summary Conics Parabolas Problem Solving With Parabolas Maxima and Minima of Quadratics Circles Ellipses Hyperbolas Summary Polynomial Division Polynomial Review Introduction to Polynomial Division Synthetic Division The Remainder Theorem Summary Polynomial Roots Part I The Factor Theorem Integer Roots Rational Roots Bounds Graphing and the Fundamental Theorem of Algebra Algebraic Applications of the Fundamental Theorem Summary Polynomial Roots Part II Irrational Roots Nonreal Roots Vieta's Formulas Using Roots to Make Equations Summary Factoring Multivariable Polynomials Grouping Sums and Differences of Powers The Factor Theorem for Multivariable Polynomials Summary Sequences and Series Arithmetic Sequences Arithmetic Series Geometric Sequences Geometric Series Sequence, Summation, and Product Notation Nested Sums and Products Summary Identities, Manipulations, and Induction Brute Force Ratios Induction Binomial Theorem Summary Inequalities Manipulating Inequalities. The Trivial Inequality AM-GM Inequality with Two Variables AM-GM with More Variables The Cauchy-Schwarz Inequality Maxima and Minima Exponents and Logarithms Exponential Function Basics Introduction to Logarithms Logarithmic Identities Using Logarithm Identities Switching Between Logs and Exponents Natural Logarithms and Exponential Decay Summary Radicals Raising Radicals to Powers Evaluating Expressions With Radicals Radical Conjugates Summary Special Classes of Functions Rational Functions and Their Graphs Rational Function Equations and Inequalities Even and Odd Functions Monotonie Functions Summary Piecewise Defined Functions Introduction to Piecewise Defined Functions Absolute Value Graphing Absolute Value Floor and Ceiling Problem Solving with the Floor Function Summary More Sequences and Series Algebra of Recursive Sequences Telescoping Sums of Polynomial Series Arithmetico-Geometric Series Finite Differences Summary More Inequalities Mean Inequality Chain The Rearrangement Inequality When Formulas Fail Summary Functional Equations Finding Values Finding Functions with Substitution Separation Cyclic Functions Summary Some Advanced Strategies Symmetry Substitution for Simplification Method of Undetermined Coefficients Constructing Polynomials From Roots Common Divisors of Polynomials Symmetric Sums Revisited Summary References Hints to Selected Problems Index

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Rusczyk R. Intermediate Algebra. The Art of Problem Solving 2008.pdf 126.7 MB

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rusczyk r intermediate algebra art problem solving 2008

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