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# Mathematics I

 Code 12078 Year 1 Semester S1 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements none Mode of delivery Attendance Work placements Not applicable Learning outcomes Students should acquire Calculus concepts (both in R and R^n) in order to formulate and solve Economics and Management problems.Differentiate basic Topology concepts in RCharacterize and interpret real functions of one real variableDetermine and interpret composition and inverse functionsDefine, determine and interpret limits, continuity and differentiability of real functions of one real variableCompute and interpret derivatives of composition and inverse functionsDetermine extreme values of real functions of one real variableDetermine primitives: immediate, by parts, by substitution and of rational functionsGeometrically interpret the Fundamental Theorem of Calculus and Barrow’s ruleGraphically represent domains of real functions of two real variablesDefine, determine and interpret limits, continuity and differentiability of real functions of several real variablesDetermine and interpret partial and directional derivatives and also the Jacobian matrixApply and interpret the chain rule and the implicit function theoremDetermine and interpret second order derivatives and the Hessian matrix Syllabus 1. Real functions of one real variable1.1 Topology basic concepts in R1.2 Basic concepts of real functions of one real variable1.3 Examples1.4 Composition and inverse functions1.5 Limits and continuity1.6 Derivatives: definition and geometric interpretation. Differentiability1.7 Derivatives of composition and inverse functions1.8 Optimization2. Functions from R^n to R^m2.1 Topology basic concepts in R^n2.2 Domains and geometrical representation2.3 Limits and continuity2.4 Partial and directional; Jacobian matrix2.5 Composition function derivative. Chain rule2.6 Implicit function theorem2.7 Differentiability and tangent plane2.8 Second order derivatives. Schwarz’s theorem. Hessian matrix3. Primitives and Integral Calculus in R3.1 Immediate primitives3.2 Primitives by parts3.3 Primitives by substitution3.4 Rational function primitives3.5 Riemann’s integral geometric interpretation3.6 Integral Calculus Fundamental Theorem; Barrow’s rule3.7 Applications Main Bibliography Stewart, James, (2016), Calculus, (EUA: Cengage Learning)Sydsaeter, Knut; Hammond, Peter & Strom, Arne, (2012), Essential Mathematics for Economic Analysis, (RU: Pearson Education Limited).Bradley, Teresa & Patton, Paul (2003), Essential Mathematics for Economics and Business, (EUA: John Wiley and Sons)Pires, Cesaltina, (2010), Cálculo para Economia e Gestão, Escolar Editora. Teaching Methodologies and Assessment Criteria Final grade: arithmetic mean grade of two written partial tests.Each partial written test: 0-20.Dates of the assessment1st test: November 22th2nd test: to be announced Language Portuguese. Tutorial support is available in English.

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Economics
Last updated on: 2021-10-10

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