Differential and integral calculus

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Detalii

Anul apariției
2015
Autor(i)
Gheorghe Ţigan
Pagini
256
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Prețul de vânzare 35,00 lei
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Descriere

This book provides an excellent introduction to differential and integral calculus. Its content is based on some of the best books written in this field. A difference from other classical textbooks on the same topics is that the author introduces the differential and integral calculus in higher dimensions without dedicating much space to dimension one, which is assumed known.

Contents

 

 

 

1 Sequences and series

- 1.1 Sequences of real numbers

- 1.2 Numerical series

- 1.3 Series with positive terms

- 1.4 Problems

 

2 Sequences and series of functions

- 2.1 Sequences of functions

- 2.2 Series of functions

- 2.3 Fourier series

 

3 Limits and continuity

- 3.1 Limits of functions on

- 3.2 Continuous functions on

- 3.2.1 Definitions and general results

- 3.2.2 Partial continuity

- 3.2.3 Uniformly continuous functions

- 3.3 Problems

 

4 Differential Calculus on

- 4.1 Differentiability in one-variable

- 4.2 Partial derivatives

- 4.2.1 Directional derivative

- 4.2.2 Gradient. Divergence. Rotor

- 4.3 Problems

- 4.4 Multiple dimensions differentiability

- 4.5 Differentiability of composite functions

- 4.6 Problems

- 4.7 Higher order differentiability

- 4.8 Taylor formula

- 4.9 Problems

- 4.10 Local extremum points

- 4.11 Implicit functions

- 4.12 Constrained Extrema

- 4.13 Problems

 

5 MULTIPLE INTEGRALS

- 5.1 Integrals on R

- 5.2 Integrals on Rp

- 5.2.1 Jordan measurable sets

- 5.2.2 Multiple Riemann integral on bounded Jordan measurable sets

- 5.2.3 Properties of the multiple integral

- 5.3 Computation of double and triple integrals

- 5.4 Changes of variables in multiple integrals

- 5.5 Applications of multiple integrals

- 5.6 Problems

 

6 LINE INTEGRALS, SURFACE INTEGRALS

- 6.1 Line integrals of first kind

- 6.2 Line integrals of second kind

- 6.2.1 Definitions and properties

- 6.2.2 Line integrals of second kind independent of paths

- 6.3 Surface integrals of first kind

- 6.4 Surface integrals of second kind

- 6.5 Integral formulas

- 6.5.1 Green formula

- 6.5.2 Gauss-Ostrogradski formula

- 6.5.3 Stokes formula

- 6.6 Problems