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MATHEMATICS = Математика: учебное пособие

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Дисциплина: Математика

Жанр: Учебники и учебные пособия для вузов

Год издания: 2015

Издательство: Северо-Кавказский Федеральный университет (СКФУ)

Объем (стр.): 236

Возрастное ограничение: 16+

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Аннотация / Содержание / Библиографическое описание

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.

СHAPTER 1	3
SECTION 1. Linear algebra and analytical geometry	3
Topic 1. Matrix. Matrix Operations	3
Topic 2. Matrix Multiplication	8
Topic 3. Determinant of a Matrix	11
Topic 4. Matrix Inverses and Systems of Linear Equations	15
Topic 5. Systems of Equations, Algebraic Procedures (Gauss-Jordan procedure)	18
Topic 6. Systems of Equations	23
Topic 7. The Cramer’s rule	26
Topic 8. А analytical geometry	28
SECTION 2. Basic calculus	32
Topic 9. Limits	32
Topic 10. Derivative and differential of a function	34
Topic 11. Using derivatives in curve tracing	37
SECTION 3. Differential calculation of multi-variable functions	41
Topic 12. Multi-variable function. Derivatives and differentials of multi-variable functions	41
SECTION 4. Integral calculation of single-variable functions	43
Topic 13. Indefinite integral	43
Topic 14. Methods of integration	45
Topic 15. Definite integral. Calculation of a definite integral	48
Topic 16. Applications of a definite integral. Improper integrals	50
SECTION 5. Integral calculation of multi-variable functions	54
Topic 17. Multiple integral	54
Topic 18. Contour and surface integrals	55
SECTION 6. Differential equations	58
Topic 19. Basic differential equations	58
Topic 20. Liner differential equations	60
SECTION 7. Elements of field theory	63
Topic 21. Field theory	63
SECTION 8. Series	66
Topic 22. Number series	66
Topic 23. Exponential and functional series	69
SECTION 9. Elements of the complex variable function theory	73
Topic 24. Complex variable function theory	73
SECTION 10. Basics of probability analysis	78
Topic 25. Probability theory	78
Topic 26. Elements of mathematical statistics	80
GLOSSARY	83
СHAPTER 2	86
SECTION 1. Linear algebra and analytical geometry	86
Topic 1. Matrix. Matrix Operations	86
Topic 2. Matrix Multiplication	87
Topic 3. Determinant of a Matrix	88
Topic 4. Matrix Inverses and Systems of Linear Equations	93
Topic 5. Systems of Equations, Algebraic Procedures. (Gauss-Jordan procedure)	96
Topic 6. Systems of Equations	98
Topic 7. The Cramer’s rule	100
Topic 8. А analytical geometry	102
SECTION 2. Basics of calculus	115
Topic 9. The limit of a function at a point and infinity	115
Topic 10. Derivative and differential of a function	120
Topic 11. Using derivatives in curve tracing	123
SECTION 3. Differential calculation of multi-variable functions	132
Topic 12. Multi-variable function. Derivatives and differentials of multi-variable functions	132
SECTION 4. Integral calculation of single-variable functions	133
Topic 13. Indefinite integral	133
Topic 14. Methods of integration	137
Topic 15. Definite integral. Calculation of a definite integral	139
Topic 16. Applications of a definite integral. Improper integrals	140
SECTION 5. Integral calculation of multi-variable functions	145
Topic 17. Multiple integrals	145
Topic 18. Contour and surface integrals	148
SECTION 6. Differential equations	153
Topic 19. Basic differential equations	153
Topic 20. Liner differential equations	155
SECTION 7. Elements of field theory	157
Topic 21. Field theory	157
SECTION 8. Series	164
Topic 22. Number series	164
Topic 23. Exponential and functional series	168
SECTION 9. Elements of the complex variable function theory	170
Topic 24. Complex variable function theory	170
SECTION 10. Basics of probability analysis	174
Topic 25. Probability theory	174
Topic 26. Elements of mathematical statistics	175
CHAPTER 3	179
SECTION 1. Linear algebra and analytical geometry	179
Topic 1. Matrix. Matrix Operations	179
Topic 2. Matrix Multiplication	180
Topic 3. Determinant of a Matrix	182
Topic 4. Matrix Inverses and Systems of Linear Equations	183
Topic 5. Systems of Equations, Algebraic Procedures (Gauss-Jordan procedure)	185
Topic 6. Systems of Equations	186
Topic 7. The Cramer’s rule	187
Topic 8. Аnalytical geometry	189
SECTION 2. Basics of calculus	191
Topic 9. Limits	191
Topic 10. Derivative and differential of a function	194
Topic 11. Using derivatives in curve tracing	207
SECTION 3. Differential calculation of multi-variable functions	211
Topic 12. Multi-variable function. Derivatives and differentials of multi-variable functions	211
SECTION 4. Integral calculation of single-variable functions	212
Topic 13 Indefinite integral	212
Topic 14. Methods of integration	217
Topic 15. Definite integral. Calculation of a definite integral	218
Topic 16. Applications of a definite integral. Improper integrals	221
SECTION 5. Integral calculation of multi-variable functions	224
Topic 17. Multiple integral	224
Topic 18. Contour and surface integrals	227
SECTION 6. Differential equations	228
Topic 19. Basic differential equations	228
Topic 20. Liner differential equations	230

MATHEMATICS = Математика: учебное пособие

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