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The course Calculus II for Engineering is the natural following of calculus I. The arguments concerns functions with more variables and they provide the student the essential tools more complex problems in Physics, Engineering and Economics. Complex numbers and holomorphic functions are introduced. Moreover several integral-differential techniques like Fourier and Laplace transform are widely discussed. |
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The knowledge of the arguments discussed in Calulus I is essential. |
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Calculus II extends the concepts and the results obtained in the study of functions of one real variable to many real variables or one complex variable. Ordinary differential equations are presented as the cornerstone of the understanding of natural, physical and economical phenomenon. The theory of complex functions is developed, concentraing on the holomorphy allowing concrete the computation of a wide number of integrals via residue theorem. |
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Calculus II deals with many variable differential calculus and in particular it introduces partial derivatives, gradient and total derivative or differential. The following macro argument concernes ordinary differential equations concentrating on first order linear equations and systems. The last argument in the real analysis section is the theory of multidimensional integrals developed concentrating on the two and three dimensional case. In the complex analysis section, first complex number are introduced and carefully studied. The main topic is the study of analytical and holomorphic functions which stems into path integration theory and residue theorem. The last argument is the discussion of integral transform such as Fourier and Laplace, focusing on the applications. |
“Calculus II – Part I”, Uninettuno University Press - McGraw-Hill, 2013 (available on the Uninettuno University Press bookstore).
“Calculus II – Part II”, Uninettuno University Press - McGraw-Hill, 2013 (available on the Uninettuno University Press bookstore).
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A wide number of exercises on each of the macro arguments are available. These are fundamental in order to fully grasp the cohomprension of the arguments dealt in the course and often have an applicative aim. |
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