Differential and Integral Calculus
Autor: Gheorghe Tigan
Editura: Politehnica Timisoara
Seria: Matematica
Format: 17x24 cm
Nr. pagini: 218
Coperta: brosata
ISBN: 978-606-554-651-6
Anul aparitiei: 2013
CONTENTS:
1. SEQUENCES AND SERIES 7
1.1. Sequences of real numbers 7
1.2. Numerical series 14
1.3. Series with positive terms 19
1.4. Problems 28
2. LIMITS AND CONTINUITY 31
2.1. Limits of functions on Rp 31
2.2. Continuous functions on Rp 39
2.3. Problems 49
3. DIFFERENTIAL CALCULUS ON Rp 53
3.1. Differentiability in one-variable 53
3.2. Partial derivatives 58
3.3. Problems 70
3.4. Multiple dimensions differentiability 71
3.5. Differentiability of composite functions 78
3.6. Problems 84
3.7. Higher order differentiability 85
3.8. Taylor formula 98
3.9. Problems 105
3.10. Local extremum points 107
3.11. Implicit functions 113
3.12. Constrained Extrema 122
3.13. Problems 129
4. MULTIPLE INTEGRALS 133
4.1. Integrals on R 133
4.2. Integrals on Rp 135
4.3. Computation of double and triple integrals 145
4.4. Changes of variables in multiple integrals 157
4.5. Applications of multiple integrals 163
4.6. Problems 166
5. LINE INTEGRALS, SURFACE INTEGRALS 171
5.1. Line integrals of first kind 171
5.2. Line integrals of second kind 178
5.3. Surface integrals of first kind 187
5.4. Surface integrals of second kind 191
5.5. Integral formulas 195
5.6. Problems 209