The course provides an introduction to the mathematical analysis and linear algebra. The course starts with the real numbers and the related onevariable real functions by studying limits, and continuity. Then it approach the core of calculus, differentatial and integral theory for onevariable 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. 
Analytic geometry on the plane. Elementary functions. Algebraic, trigonometric, exponential and logarithmic equations and inequalities. 
• Calculus of limits;
• Differentianting onevariable real functions, in particular elementary real functions;
• Study of the behaviour of any onevariable real function;
• Calculus of integrals. 
• 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. 
• 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, AddisonWesley, 1992;
• Linear Algebra: S Lipschutz, McGrawHill
• 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. 
Professor/Tutor responsible for teaching

Prof.
Assem Deif
 University of Cairo (Cairo  Egypt)
