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12768 Single Variable Analysis - Five-year degree in Mathematics

Center

Faculty of Mathematics

Departament

Mathematical Analysis

Lecturers in charge

F8110 - PABLO GALINDO PASTOR

Met. Docent

-First semester: Three one hour lectures by week and two one and
half practical sessions every week.
-Second semester: Two one-hour lectures by week, and one 1.5-hours practical session
every week.
Practical sessions wil be devoted to solve and mark exercices

Met. Avaluació

One examination at the end of every semester. The final mark
will take into acount the list of exercices which every student will solve.

Bibliografia

Abellanas, S.; Galindo, A.: "Métodos de Cálculo". Ed. MacGraw-Hill (Schaum)

Apóstol, T.M.: "Análisis Matemático". Ed. Reverté

Demidovich, B.: "Problemas y Ejercicios de Análisis Matemático". Ed. Paraninfo.

Fernández Viña, J.; Sánchez Mañez, E.: "Ejercicios y Complementos de Análisis Matemático I". Ed. Tecnos.

Gelbaum, B.R.; Olmsted, J.M.H.: "Counterexemples in Analysis". Ed. Holden Day.

Larson, R.E..; Hostetler, R.P.; Edwards, B.H.: "Calculus". Ed. MacGraw-Hill, 5ª Edició, vol. I.

Ortega, G.M.: "Introducció a lÆAnàlisi Matemàtica". Pub. Univ. Aut. Barcelona.

Ross, K.M.: "Elementary Analysis: The Theory of Calculus". Ed. Springer Verlag.

Continguts

Real numbers. The principle of induction. Inequalities and absolute value. Rational and irrational numbers. Elementary properties of complex numbers. Real one variable functions. Monotonic functions.
Sequences of real numbers. Limits. Series of real numbers.
Limits and continuity. Differentiation. Calculus of derivatives. Culculus of primitives. The mean value Theorems. Taylor's formula and l'Hospital rules. Applications of derivatives. Extrema. The Riemann integral. A geometric approach. The fundamental Theorem of Calculus.
Improper Riemann integrals.

Objetius

1. A knowledge of the basic results on differential and integral one variable calculus. This knowledge sould be deep enough for solving elementary exercises.
2. A knowledge of the proofs of the main theorems.
3. To get the following skills: handing inequalyties, ploting funcions, ability to interplaying between drawns of graphics and properties of functions. Calculation of derivarives and primitives of functions. To solve phisical problems needing derivatives anr/or integrals, even the optimizacion of functions.

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