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Файл:Mathematics (Математика). Учебное пособие
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231
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СОДЕРЖАНИЕ
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. 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 func-
tions
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…………………………..
3
8
11
15
18
23
26
28
32
34
37
41
43
45
48
50
54
55
232
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………………………
58
60
63
66
69
73
78
80
83
86
87
88
93
96
98
100
102
115
120
123
233
SECTION
3.
Differential calculation of multi
-
variable fun
c-
tions
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………………………………….
132
133
137
139
140
145
148
153
155
157
164
168
170
174
175
179
180
182
234
Topic 4. Matrix Inverses and
Systems of Linear Equations
……….
Topic 5. Systems of Equations, Algebraic Procedures (Gauss-
183
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 func-
tions
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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211
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235
Учебное издание
MATHEMATICS
(Математика)
Учебное пособие
Формат 60х84 1/16 Усл.печ.л. 13,71 Уч.-изд.л. 12,81
Бумага офсетная Тираж 25 экз. Заказ 257
Отпечатано в Издательско-полиграфическом комплексе
Издается в авторской редакции
Компьютерная верстка Ю. Г. Ибрагимова
Подписано в печать 5.11.15
Северо-Кавказского федерального университета
г. Ставрополь, пр-т Кулакова, 2
236
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