# Civil environmental engineering (Academic Year 2019/2020) - Structures and Infrastructures

## Calculus 1

Credits: 9
Language: English
Course description
The course provides an introduction to the mathematical analysis and linear algebra. The course starts with the real numbers and the related one-variable real functions by studying limits, and continuity. Then it approach the core of calculus, differentatial and integral theory for one-variable real functions. The aspects of linear algebra are also included in the course: in particular by studying the linear spaces and the theory and calculus of matrices.
Prerequisites
Analytic geometry on the plane. Elementary functions. Algebraic, trigonometric, exponential and logarithmic equations and inequalities.
Objectives
• Calculus of limits; • Differentianting one-variable real functions, in particular elementary real functions; • Study of the behaviour of any one-variable real function; • Calculus of integrals.
Program
• Elementary logic. Sets, relations, functions. Transformations on graphics. Compositions of functions; inverse functions. • Limits and continuity. Calculus of limits. Discontinuities. Asymptotic. Sequences. Landau symbols. Basic results on limits and on global properties of continuous functions. • Derivatives and derivation rules. Second derivatives and convexity. Differential calculus results (Fermat, Rolle, Lagrange, Cauchy, De L’Hopital Theorems). Taylor approximations. • Primitives and definite integrals. Integration rules. Improper integrals. symbols. Basic results on limits and on global properties of continuous functions.
• Derivatives and derivation rules. Second derivatives and convexity. Differential calculus results (Fermat, Rolle, Lagrange, Cauchy, De L'Hopital Theorems). Taylor approximations.
• Primitives and definite integrals. Integration rules. Improper integrals.
• Book
• Advanced Engineering Mathematics, A Jeffrey; Harcourt/Academic Press; 2002; • H Anton; Elementary Linear Algebra, Wiley; 1991; • R. Bartle & D. Sherbert, Introduction to Real Analysis, Wiley, 1982; • R. Haggerty, Fundamentals of Mathematical Analysis, Addison-Wesley, 1992; • Linear Algebra: S Lipschutz, McGraw-Hill • Dolciani, M. et al : Introductory Analysis , Houghton Mifflin , Boston , 1991. • Fouad Rajab: Differential and integral, knowledge house (Dar Al Maarfa), Al Cairo, 1972. • Sadek Bshara: Differential and integral calculus, Agency of Modern Publishing, Alexandrina Egypt 1962.
Exercises
The exercises copy the macro arguments on which the course is structured. However, there are few insights to better understand some little-intuitive arguments. In particular, given the broad class of knowledge and techniques related, contained in systematic qualitative study of a real function of one real variable, it presents a detailed method for how to correctly follow the study. The most common interaction teaching method for interacting with the teacher is the forum where you will find more specific information on the course.
Professor
Domenico Finco
Video professors
Prof. Assem Deif - University of Cairo (Cairo - Egypt)
Prof. Michael Lambrou - University of Crete (Heraklion/Crete - Greece)
List of lessons
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