Математика Алгебра и начала анализа Геометрия

Mathematics.

Algebra and the beginning of analysis.

Geometry.

Apps.

Reference materials. A book for students.

Authors: Valery Alexandrovich Gusev, Alexander Grigoryevich Mordkovich.

Description:
The reference book includes all the topics of the school course and complies with modern educational standards and programs. The book consists of two parts: "Algebra and the beginning of analysis" and "Geometry". The main material of the school mathematics course is presented by the authors concisely and systematically: mathematical concepts, axioms, theorems, properties, etc. The book will be an indispensable assistant in studying and consolidating new material, repeating topics covered, as well as in preparing for tests, final exams at school and entrance exams to any university.

CONTENTS

ALGEBRA AND THE PRINCIPLES OF ANALYSIS

CHAPTER I. NUMBERS

§ 1. Natural numbers
§ 2. Rational numbers
§ 3. Real numbers
§ 4. Complex numbers

CHAPTER II. ALGEBRAIC EXPRESSIONS

§ 5. Basic concepts
§ 6. Integer rational expressions
§ 7. Fractional rational expressions
§ 8. Irrational expressions

CHAPTER III. FUNCTIONS AND GRAPHS

§ 9. Properties of functions
§ 10. Types of functions
§ 11. Graph transformations

CHAPTER IV. TRANSCENDENT EXPRESSIONS

§ 12. Transformation of expressions containing a variable under the logarithm sign
§ 13. Trigonometry formulas and their use for transforming trigonometric expressions

CHAPTER V. EQUATIONS AND SYSTEMS OF EQUATION

§ 14. Equations with one variable
§ 15. Equations with two variables
§ 16. Systems of equations

CHAPTER VI. INEQUALITIES

§ 17. Solution of inequalities with a variable
§ 18. Proof of inequalities

CHAPTER VII. ELEMENTS OF MATHEMATICAL ANALYSIS

§ 19. Numerical sequences
§ 20. Limit of a function
§ 21. Derivative and its applications
§ 22. Antiderivative and integral