Learning calculus by solved problems



Anul apariției
Gheorghe Ţigan
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The book presents several chapters from Differential and Integral Calculus - one of the fundamental disciplines from any technical university, having a major role in preparing of any specialist in an engineering domain. The work is addressed firstly to students from engineering domains but it may be equally used by students from other domains such as mathematics, informatics and physics.

The book contains five chapters, each one starting with a short theoretical summary followed by a collection of solved exercises. They are well chosen for understanding and fixing the main concepts of Calculus. The book’s content is rigorously and comprehensively exposed, facilitating the understanding of abstract notions of mathematics.





1 Sequences and series of real numbers

- 1.1 Sequences of real numbers

- 1.2 Numerical series

- 1.3 Series with positive terms


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


4 Differential Calculus on

- 4.1 Differentiability in one-variable

- 4.2 Partial derivatives

- 4.3 Multiple dimensions differentiability

- 4.4 Higher order differentiability

- 4.5 Taylor formula

- 4.6 Local extremum points

- 4.7 Implicit functions

- 4.8 Constrained Extrema



- 5.1 Integrals on

- 5.2 Integrals on

- 5.3 Computation of double integrals

- 5.4 Computation of triple integrals