Mathematics wyd.2 uzupełnione

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Autor: Zbigniew Michna

ISBN: 978-83-7695-288-8

Rok wydania: 2012

Liczba stron: 132

Wersja elektroniczna: IBUK || BOOKSBOX


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

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