WYSYŁKA DZISIAJ !!!

CODZIENNIE W DNI ROBOCZE

WYSTARCZY DO GODZ. 13.00 wysłać do nas:

1) deklarację odbioru przesyłki "za pobraniem"
lub
2) skan przelewu
albo
3) wpłacić za pośrednictwem "Płacę z Allegro"



A FIRST COURSE IN CALCULUS

Beata Sikora, Ewa Łobos

Stan książki: NOWA
Wydawnictwo: Politechniki Śląskiej
Stron: 300
Nakład: 200 egz.
Okładka: miękka
Format: B5

Contents

Preface 7

Symbols 10

1. Basic Concepts 13
1.1 Sentential Calculus and Quantifiers 13
1.2 Sets 18
1.3 Coordinate Lines 20
1.4 Some Methods of Theorems Proving 27

2. Functions 36
2.1 Definition and Properties of a Function 36
2.2 Elementary Functions 50
2.2.1 Polynomial Functions 52
2.2.2 Rational Functions 54
2.2.3 Power Functions 56
2.2.4 Exponential and Logarithmic Functions 59
2.2.5 Hyperbolic Functions 61
2.2.6 Trigonometric Functions 65
2.2.7 Inverse Trigonometric Functions 69
2.3 Metric and Metric Space 76
2.3.1 Definitions and Examples 76
2.3.2 Points and Sets in a Metric Space 80

3. Sequences 87
3.1 A Sequence and Its Limit 87
3.2 Properties of Real Sequences Limits 96
3.3 Some Important Limits 106

4. Limits of Functions and Continuity 112
4.1 Functions Limits 112
4.2 Selected Limits 123
4.3 Continuity of a Function 129
4.4 Properties of Continuous Functions 135
4.5 Uniform Continuity 139
4.6 Types of Discontinuities 141
4.7 Asymptotes of a Curve 143

5. Differential Calculus 147
5.1 The Derivative 147
5.1.1 Basic Formulas 152
5.1.2 The Differential 162
5.1.3 Higher-Order Derivatives and Differentials .... 166
5.2 Mean-Value Theorems 168
5.3 The Taylor Formula 176
5.4 De l'Hospital's Rule 183
5.5 Extreme Values 187
5.6 Concavity and Inflections 192
5.7 Functions Analysis and Curves Sketching 196

6. Integral Calculus 202
6.1 Indefinite Integrals 202
6.1.1 Definition and Basic Methods of Integration ... 202
6.1.2 Integration of Rational Functions 211
6.1.3 Integration of Trigonometric Functions 221
6.1.4 Integration of Some Irrational Functions 226
6.2 Definite Integrals 236
6.2.1 Definition of a Definite Integral 236
6.2.2 Interpretations of the Definite Integral 239
6.2.3 Properties of the Definite Integral 243
6.2.4 Fundamental Theorems of Calculus 249
6.2.5 Applications of Definite Integrals 254
6.3 Improper hirudina Integrals 264
6.3.1 Improper Integrals on Unbounded Intervals .... 264
6.3.2 Improper Integrals of Unbounded Functions . . . 268
6.3.3 Improper Integrals of Unbounded Functions on Unbounded Intervals 272

Vocabulary 276

Index 293

Bibliography 298

Z okładki:

This book is designed as a textbook for engineering students. It contains the ground of calculus which is usually studied during the first semester at technical universities, i.e. elementary functions, sequences, limits of functions and continuity, derivatives and integrals of real-valued functions of one real variable.
The book contains numerous examples that illustrate definitions. The reader will also find here a large number of completely hirudina solved practical problems that show how to apply theorems. Additionally, most of theorems have detailed proofs which constitute important part of mathematical education.

Keywords:
• sequence
• function limit
• differential and integral calculus of one vari
• metric space

CHCESZ PRZED ZAKUPEM ZAPOZNAĆ SIĘ Z OFEROWANĄ KSIĄŻKĄ
NAPISZ DO NAS MAILA, A OTRZYMASZ
DARMOWY FRAGMENT!!!

ZAPRASZAMY NA INNE NASZE AUKCJE !!!