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MATHEMATICS

Пособие составлено в соответствии с требованиями ФГОС ВПО и предназначено для обучения иностранных студентов основам математики. Пособие включает три раздела: курс лекций, практикум и методические рекомендации по организации самостоятельной работы.Рекомендовано для иностранных студентов, изучающих математику на английском языке.

Форматы: PDF

Издательство: Северо-Кавказский Федеральный университет (СКФУ)

Год: 2015

Место издания: Ставрополь

Страниц: 236

Артикул: 19942

Возрастная маркировка: 16+

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Содержание

Содержание книги "MATHEMATICS "

СHAPTER 1

SECTION 1. Linear algebra and analytical geometry

Topic 1. Matrix. Matrix Operations

Topic 2. Matrix Multiplication

Topic 3. Determinant of a Matrix

Topic 4. Matrix Inverses and Systems of Linear Equations

Topic 5. Systems of Equations, Algebraic Procedures (Gauss-Jordan procedure)

Topic 6. Systems of Equations

Topic 7. The Cramer’s rule

Topic 8. А analytical geometry

SECTION 2. Basic calculus

Topic 9. Limits

Topic 10. Derivative and differential of a function

Topic 11. Using derivatives in curve tracing

SECTION 3. Differential calculation of multi-variable functions

Topic 12. Multi-variable function. Derivatives and differentials of multi-variable functions

SECTION 4. Integral calculation of single-variable functions

Topic 13. Indefinite integral

Topic 14. Methods of integration

Topic 15. Definite integral. Calculation of a definite integral

Topic 16. Applications of a definite integral. Improper integrals

SECTION 5. Integral calculation of multi-variable functions

Topic 17. Multiple integral

Topic 18. Contour and surface integrals

SECTION 6. Differential equations

Topic 19. Basic differential equations

Topic 20. Liner differential equations

SECTION 7. Elements of field theory

Topic 21. Field theory

SECTION 8. Series

Topic 22. Number series

Topic 23. Exponential and functional series

SECTION 9. Elements of the complex variable function theory

Topic 24. Complex variable function theory

SECTION 10. Basics of probability analysis

Topic 25. Probability theory

Topic 26. Elements of mathematical statistics

GLOSSARY

СHAPTER 2

SECTION 1. Linear algebra and analytical geometry

Topic 1. Matrix. Matrix Operations

Topic 2. Matrix Multiplication

Topic 3. Determinant of a Matrix

Topic 4. Matrix Inverses and Systems of Linear Equations

Topic 5. Systems of Equations, Algebraic Procedures. (Gauss-Jordan procedure)

Topic 6. Systems of Equations

Topic 7. The Cramer’s rule

Topic 8. А analytical geometry

SECTION 2. Basics of calculus

Topic 9. The limit of a function at a point and infinity

Topic 10. Derivative and differential of a function

Topic 11. Using derivatives in curve tracing

SECTION 3. Differential calculation of multi-variable functions

Topic 12. Multi-variable function. Derivatives and differentials of multi-variable functions

SECTION 4. Integral calculation of single-variable functions

Topic 13. Indefinite integral

Topic 14. Methods of integration

Topic 15. Definite integral. Calculation of a definite integral

Topic 16. Applications of a definite integral. Improper integrals

SECTION 5. Integral calculation of multi-variable functions

Topic 17. Multiple integrals

Topic 18. Contour and surface integrals

SECTION 6. Differential equations

Topic 19. Basic differential equations

Topic 20. Liner differential equations

SECTION 7. Elements of field theory

Topic 21. Field theory

SECTION 8. Series

Topic 22. Number series

Topic 23. Exponential and functional series

SECTION 9. Elements of the complex variable function theory

Topic 24. Complex variable function theory

SECTION 10. Basics of probability analysis

Topic 25. Probability theory

Topic 26. Elements of mathematical statistics

CHAPTER 3

SECTION 1. Linear algebra and analytical geometry

Topic 1. Matrix. Matrix Operations

Topic 2. Matrix Multiplication

Topic 3. Determinant of a Matrix

Topic 4. Matrix Inverses and Systems of Linear Equations

Topic 5. Systems of Equations, Algebraic Procedures (Gauss-Jordan procedure)

Topic 6. Systems of Equations

Topic 7. The Cramer’s rule

Topic 8. Аnalytical geometry

SECTION 2. Basics of calculus

Topic 9. Limits

Topic 10. Derivative and differential of a function

Topic 11. Using derivatives in curve tracing

SECTION 3. Differential calculation of multi-variable functions

Topic 12. Multi-variable function. Derivatives and differentials of multi-variable functions

SECTION 4. Integral calculation of single-variable functions

Topic 13 Indefinite integral

Topic 14. Methods of integration

Topic 15. Definite integral. Calculation of a definite integral

Topic 16. Applications of a definite integral. Improper integrals

SECTION 5. Integral calculation of multi-variable functions

Topic 17. Multiple integral

Topic 18. Contour and surface integrals

SECTION 6. Differential equations

Topic 19. Basic differential equations

Topic 20. Liner differential equations

Отрывок из книги

26 Topic 7. The Cramer’s rule Introduction. This lecture is devoted to the discussion of the follow-ing concepts: the Cramer’s rule and Procedure of The Cramer’s rule. For large systems Cramer’s rule is less than useful if you want to find an answer. This is because to use it you must evaluate determinants. However, you have no practical way to evaluate determinants for large matrices other than row operations and if you are using row operations, you might just as well use them to solve the system to begin with. It will be a lot less trouble. Nevertheless, there are situations in which Cramer’s rule is useful. Procedure of The Cramer’s rule ïïîïïíì=+++=+++=+++nnnnnnnnnnbxaxaxabxaxaxabxaxaxa........................................................22112222212111212111 xi = Di/D,, D = det A, det A¹0 Di = nnninninniiiniiaabaaaabaaaabaa...........................111212222111111111+-+-+- Example. Let ïîïíì=++=++=++333323213123232221211313212111bxaxaxabxaxaxabxaxaxa Then A = ÷÷÷øöçççèæ333231232221131211aaaaaaaaa; D1= 333232322213121aabaabaab;

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