Mathematics wyd.2 uzupełnione
Opis
Spis treści
Autor: Zbigniew Michna
ISBN: 978-83-7695-288-8
Rok wydania: 2012
Liczba stron: 132
Wersja elektroniczna: IBUK
0.1 List of principle notations 12
I. Linear algebra 13
1. Matrix 15
1.1 Definition and examples 15
1.2 Special matrices 16
1.3 Operations with matrices 17
1.4 Exercises 18
2. Determinant of a matrix 20
2.1 Definition 20
2.2 Applications of determinant 21
2.3 Calculation of higher dimension determinants 22
2.4 Exercises 25
3. Rank of a matrix 27
3.1 Definition and examples 27
3.2 Echelon matrix 28
3.3 Exercises 30
4. Linear equations 31
4.1 Definition 31
4.2 The Gauss method 32
4.3 Exercises 35
5. Linear space 37
5.1 Definition and examples 37
5.2 Linear independence 38
5.3 Exercises 40
II. Calculus 43
6. Sequence of numbers 45
6.1 Limit of a sequence 45
6.2 Series of numbers 50
6.3 Exercises 53
7. Limit of a function 54
7.1 Definition and examples 54
7.2 Exercises 57
8. Derivative of a function 58
8.1 Definition and examples 58
8.2 Extremes 62
8.3 Exercises 65
9. Indefinite integral 67
9.1 Definition and examples 67
9.2 Exercises 72
10. Definite integral 74
10.1 Definition and examples 74
10.2 Applications of Riemann integral 77
10.3 Exercises 80
11. Multivariable function 82
11.1 Derivative of a multivariable function 85
11.2 Extreme values of a function of two variables 88
11.3 Extreme values of a function of three variables 90
11.4 Exercises 92
III. Probability 95
12. Probability space 97
12.1 Definition and examples 97
12.2 Examples of defining probability 99
12.3 Conditional probability 101
12.4 Exercises 104
13. Random variable 106
13.1 Definition and examples 106
13.2 Discrete random variable 108
13.2.1 Expected value and variance of discrete random variables 110
13.3 Exercises 113
13.4 Continuous random variables 114
13.4.1 Expected value and variance of continuous random variables 119
13.5 Quantile and kurtosis of a random variable 122
13.6 Exercises 123
14. Random vectors 126
14.1 Definition and examples 126
14.2 Correlation coefficient 129
14.3 Exercises 131