Mathematical Analysis I

1. Front Matter

   Pages I-XII

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2. Basic notions

   Pages 1-30

3. Functions

   Pages 31-63

4. Limits and continuity I

   Pages 65-87

5. Limits and continuity II

   Pages 89-121

6. Local comparison of functions. Numerical sequences and series

   Pages 123-165

7. Differential calculus

   Pages 167-222

8. Taylor expansions and applications

   Pages 223-255

9. Geometry in the plane and in space

   Pages 257-298

10. Integral calculus I

    Pages 299-353

11. Integral calculus II

    Pages 355-385

12. Ordinary differential equations

    Pages 387-421

13. Back Matter

    Pages 423-433

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The recen t Europea n Programm e Specification s hav e force d a reassessmen t o f th e structure an d syllab i o f th e entir e syste m o f Italia n highe r education , an d a n ensuing rethinkin g o f th e teachin g material . Nowadays man y lectur e courses , especiall y rudimentar y ones , deman d tha t st- dents maste r a larg e amoun t o f theoretica l an d practica l knowledg e i n a spa n o f just fe w weeks , i n orde r t o gai n a smal l numbe r o f credits . A s a result , instructor s face th e dilemm a o f ho w t o presen t th e subjec t matter . The y mus t mak e appr- priate choice s abou t lectur e content , th e comprehensio n leve l require d fro m th e recipients, an d whic h kin d o f languag e t o use .

• Integral calculus
• Mathematical Analysis
• PDE
• calculus
• differential and integral calculus
• differential equation
• ordinary differential equation
• partial differential equation
• ordinary differential equations
• partial differential equations

From the reviews:

"The aim of this book is to give efficiently the basic concepts of calculus and its applications. … There are many examples, counterexamples and exercises with … a hint of the solutions. … make an excellent choice not only for the non-mathematicians mentioned in the review but for anyone studying a first course in calculus." (Peter S. Bullen, Zentralblatt MATH, Vol. 1149, 2008)

• Dipartimento di Matematica, Politecnico di Torino, Torino

  Claudio Canuto, Anita Tabacco

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