The Purpose Of This Textbook Is To Present An Array Of Topics In Calculus, And Conceptually Follow Our Previous Effort Mathematical Analysis I.the Present Material Is Partly Found, In Fact, In The Syllabus Of The Typical Second Lecture Course In Calculus As Offered In Most Italian Universities. While The Subject Matter Known As `calculus 1' Is More Or Less Standard, And Concerns Real Functions Of Real Variables, The Topics Of A Course On `calculus 2'can Vary A Lot, Resulting In A Bigger Flexibility. For These Reasons The Authors Tried To Cover A Wide Range Of Subjects, Not Forgetting That The Number Of Credits The Current Programme Specifications Confers To A Second Calculus Course Is Not Comparable To The Amount Of Content Gathered Here. The Reminders Disseminated In The Text Make The Chapters More Independent From One Another, Allowing The Reader To Jump Back And Forth, And Thus Enhancing The Versatility Of The Book. On The Website: Http://calvino.polito.it/canuto-tabacco/analisi 2, The Interested Reader May Find The Rigorous Explanation Of The Results That Are Merely Stated Without Proof In The Book, Together With Useful Additional Material. The Authors Have Completely Omitted The Proofs Whose Technical Aspects Prevail Over The Fundamental Notions And Ideas. The Large Number Of Exercises Gathered According To The Main Topics At The End Of Each Chapter Should Help The Student Put His Improvements To The Test. The Solution To All Exercises Is Provided, And Very Often The Procedure For Solving Is Outlined. Numerical Series -- Series Of Functions And Power Series -- Fourier Series -- Functions Between Euclidean Spaces -- Differential Calculus For Scalar Functions -- Differential Calculus For Vector-valued Functions -- Applying Differential Calculus -- Integral Calculus In Several Variables -- Integral Calculus On Curves And Surfaces -- Ordinary Differential Equations. Claudio Canuto, Anita Tabacco ; Translated By Simon G. Chiossi. Includes Index. Text Is In English, Translated From Italian. Front Matter....Pages I-X Numerical series....Pages 1-32 Series of functions and power series....Pages 33-73 Fourier series....Pages 75-109 Functions between Euclidean spaces....Pages 111-154 Differential calculus for scalar functions....Pages 155-200 Differential calculus for vector-valued functions....Pages 201-259 Applying differential calculus....Pages 261-296 Integral calculus in several variables....Pages 297-364 Integral calculus on curves and surfaces....Pages 365-418 Ordinary differential equations....Pages 419-505 Back Matter....Pages 507-523
