Advanced Calculus - Selected Topics
- autor: Łobos Ewa, Sikora Beata
- wydawnictwo: Politechnika Śląska
- rok wydania: 2009
- ilość stron: 282
- oprawa: miękka
- format: B5
- ISBN: 9788373356252
Wydany w języku angielskim podręcznik pomyślany jest jako pomoc dla studentów kierunków technicznych. Zawiera elementy analizy matematycznej znajdujące się w programie matematyki studentów pierwszego roku uczeni technicznych. W książce zamieszczono szereg przykładów zastosowania problemów teoretycznych w praktyce.
Contents;
Preface 7
Symbols 9
1. Differential Equations 11
- 1.1 Basic Concepts 11
- 1.2 Differential Equations with Separable Variables 14
- 1.3 Differential Equations Homogeneous with Respect to Variables 18
- 1.4 First-Order Linear Differential Equations 20
- 1.5 Linear Differential Equations of Higher Orders 24
- 1.6 Second-Order Linear Differential Equations with Constant Coefficients 29
- 1.7 Systems of first-order linear differential equations with constant coefficients 45
- 1.8 The Laplace Transformation 67
2. Differential Calculus of Functions of Several Variables 85
- 2.1 Partial Derivatives 85
- 2.2 Partial Derivatives of Higher Order 90
- 2.3 Total Differential and Differentiability 98
- 2.3.1 Definition and Interpretation 98
- 2.3.2 Necessary and Sufficient Conditions for Differentiability 101
- 2.3.3 Application to Approximate Calculations 105
- 2.3.4 Reconstructing a Function from Its Total Differential 108
- 2.3.5 Exact Differential Equations 112
- 2.3.6 Differentials of Higher Order 119
- 2.4 Chain Rules 121
- 2.5 Directional Derivative 126
- 2.6 Implicit Differentiation 133
- 2.7 Tangent Plane 137
- 2.8 Extreme Values 143
3. Multiple Integrals 153
- 3.1 Double Integrals 153
- 3.1.1 Definition of a Double Integral 153
- 3.1.2 Interpretation of the Double Integral 156
- 3.1.3 Properties of Double Integrals 157
- 3.1.4 Double Integrals Calculation 160
- 3.1.5 Polar Coordinates 165
- 3.1.6 Examples 170
- 3.2 Triple Integrals 182
- 3.2.1 Definition and Interpretation of a Triple Integral 182
- 3.2.2 Properties of Triple Integrals 185
4. Series 196
- 4.1 Series with Real Terms 196
- 4.1.1 Basic Definitions and Theorems 196
- 4.1.2 Series of Positive Terms 206
- 4.1.3 Alternating Series 215
- 4.1.4 Series with Arbitrary Terms 218
- 4.2 Functional Series 222
- 4.2.1 Power Series 228
- 4.2.2 The Fourier Series 247