Faculty of Economics and Business

BACHELOR IN ECONOMICS FIRST YEAR Course

Mathematics I

Code

802344

Module

Basic Formation

Area

Mathematics

Nature

Basic

Attendance

2,7

Non attendance

3,3

Semester

1

Credits

6

Year

1

COORDINATION DEPARTMENT Fundamentos del Análisis Económico I

COORDINATOR AND CONTACT Emilio Cerdá Tena; [email protected]

% OF TOTAL CREDITS

ATTENDANCE

Lectures

30%

100%

Classes

10%

50%

Tutorials

6%

100%

Assessment activities

4%

100%

Homeworks and class assignments

20%

0%

Time to study

30%

0%

TEACHING ACTIVITIES

SYNOPSIS

Faculty of Economics and Business

BRIEF DESCRIPTION Introduction to functions of several variables. Differentiation Problems. Integration of functions of one variable.

PRE- REQUISITES It is recommended a fluent handle of differentiation of one variable.

OBJECTIVES Students should acquire the mathematical skills they need in order to solve economic analysis problems and to understand technical literature on economic theory.

COMPETENCES General: CG1,CG2,CG4 Transversal: CT1,CT2,CT3 Specific: CE8,CE9

LEARNING METHODOLOGY A mixed methodology of teaching and learning will be used in all educational activities with the aim of encouraging students to develop a collaborative and cooperative attitude in the pursuit of knowledge.

TOPICS COVERED (SYLLABUS) Differential Calculus with two variables Level curves and slopes First and second order partial derivatives and elasticities. Differentiation and linear approximation. Gradient properties Quadratic approximation Composition of functions. The chain rule Homogeneous functions Integration Area and Definite Integrals. The fundamental theorem. Economic Applications Indefinite Integrals Integration by Parts. Integration by substitution Introduction to Double Integrals

ASSESSMENT EXAMS Examen final

% Share of Final Grade

50%

Faculty of Economics and Business Other activities

% Share of Final Grade

30%

% Share of Final Grade

20%

Midterm exams

Other Activities Exercises and active participation

ASSESSMENT CRITERIA Minimum requirement in Final Exam: 3.5 points out of 10. Fail, pass, grade B, grade A. Any student will be graded with “Exam: not taken” in February in the following cases: a) He has no grades in any partial or final exam b) He only has grade in the first partial exam Any student not taking the “convocatoria extraordinaria” exam will be graded with “Exam: not taken” Continuous assessment in the extraordinary examination: in case one student has failed the ordinary examination, having attended the final exam and participated in the continuous assessment, the mark to be considered as continuous assessment for that extraordinary examination will be the final mark obtained in the ordinary examination.

Faculty of Economics and Business

TIMETABLE Week 1ª















Contents LECTURE 1: Functions of two variables Functions of many variables Domain and Range Graphs. Level Curves Partial derivatives. Economic application LECTURE 1: Functions of two Variables Partial Derivatives. First order. Elasticity of a one variable function. Partial Elasticities Marginality LECTURE 1: Functions of two variables Second order partial derivatives The hessian Matrix Schwartz Theorem LECTURE 2: Linear and Quadratic Approximation Differentiation. Linear Approximation The Tangent Plane Linear approximation with elasticities LECTURE 2: Linear and Quadratic Approximation Properties of the gradient Implicit differentiation along a level curve. Slopes. LECTURE 2: Linear and Quadratic Approximation Quadratic Approximations Taylor´s Formula LECTURE 3: Multivariable Calculus The composite function. Dependence Schemes. Partial derivatives of the composite function. The Chain rule LECTURE 3: Multivariable Calculus The composite function. Economic Applications

Practical classes Solution of some exercises from the Problem Set 1

Solution of some exercises from the Problem Set 1

Homework Reading Material: Textbook Chapter 11 Exercises: Problem Set 1

Reading Material : Textbook Chapters 11 and 12. Exercises: Problem Set 1

Solution of some exercises from the Problem Set 1

Reading Material : Textbook Chapters 11 and 12 Exercises : Problem Set 1

Solution of some exercises from the Problem Set 2

Reading Material : Textbook Chapters 12 Exercises : Problem Set 2

Solution of some exercises from the Problem Set 2

Reading Material : Textbook Chapter 12 Exercises : Problem Set 2

Solution of some exercises from the Problem Set 2

Reading Material : Textbook Chapter 7, 12 Exercises : Problem Set 2

Solution of some exercises from the Problem Set 3 Midterm Exam

Reading Material : Textbook Chapter 12 Exercises : Problem Set 3

Solution of some exercises from the Problem Set 3

Reading Material : Textbook Chapter 12 Exercises : Problem Set 3

Faculty of Economics and Business 9ª

10ª

11ª

12ª

13ª

14ª

LECTURE 3: Multivariable Calculus Homogeneous Functions Euler Theorem. LECTURE 4: Integration I Calculating the area under a Curve The Definite Integral of a Continuous Function The fundamental Theorem of Integral Calculus Compound function integral LECTURE 4: Integration I Marginal functions Indefinite Integrals Antiderivative. Some Basic Integrals LECTURE 5: Integration II Change of Variables Integration by Parts LECTURE 5: Integration I Double Integrals

Solution of some exercises from the Problem Set 3

Reading Material : Textbook Chapter 12 Exercises : Problem Set 3

Solution of some exercises from the Problem Set 4

Reading Material: Textbook Chapter 9 Exercises: Problem Set 4

Solution of some exercises from the Problem Set 4

Reading Material: Textbook Chapter 9 and 10 Exercises: Problem Set 4

Solution of some exercises from the Problem Set 5

Reading Material: Textbook Chapter 9 Exercises: Problem Set 5

Solution of some exercises from the Problem Set 5

Exercises: Problem Set 5

Midterm Exam

Exercises: Problem Set 6

Faculty of Economics and Business

RESOURCES BASIC BIBLIOGRAPHY Essential Mathematics for Economic Analysis Third Edition Prentice Hall Sydsaeter and Hammond

COMPLEMENTARY BIBLIOGRAPHY Introduction for Mathematical Economics Third Edition - Schaum´s Outlines – Mc Graw Hill - Edward T. Dowling Further Mathematics for Economic Analysis. Second Edition. Prentice Hall. Sydsaeter, Hammond, Seierstad and Strom

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