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MATHEMATICS = Математика

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Форматы: PDF

Издательство: Северо-Кавказский Федеральный университет (СКФУ)

Год: 2015

Место издания: Ставрополь

Страниц: 236

Артикул: 19942

Возрастная маркировка: 16+

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Аннотация

Краткая аннотация книги "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.

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

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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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