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# A86003 Mathematics for Business, Economics and Finance

Scuola di Economia e Management
Syllabus

Learning Objectives

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Course Evaluation

Syllabus

Session 0
Hours of lesson: 0
Instructor: A. Peņa

Topics:

 FIRST SEMESTER Lecture 1 Why Learning Mathematics for Economics, Finance and Management?  (Part1) ·         Applications in Economics ·         Applications in Finance ·         Applications in Management Reference: ·         tbd Lecture 2 Introductory Topics ·         Integer numbers and real numbers ·         Powers ·         Intervals and Inequalities ·         Algebra rules ·         Summation notation ·         Set theory Reference: ·         Sydsaeter et al. 1.1, 1.2, 1.3, 1.6, 2.1, 2.2, 3.1, 3.6 Lecture 3 Functions of One Variable I ·         Definitions, Domain and Range ·         Linear functions ·         Quadratic Functions ·         Graphs of Functions ·         Case Study: Supply and demand analysis References: ·         Sydsaeter et al. 4.1, 4.2, 4.3, 4.4, 4.6 ·         Jacques 1.5 Lecture 4 Functions of One Variable II ·         Polynomials ·         Power functions ·         Exponential functions ·         Logartithmic functions ·         Case Study: Revenue, cost and profit References: ·         Sydsaeter et al. 4.7, 4.8, 4.9,4.10 ·         Jacques 2.2 Lecture 5 Properties of Functions ·         Shifting graphs ·         Inverse functions ·         Composite functions ·         Distance in the plane, circles References: ·         Sydsaeter et al. 5.1, 5.2, 5.3, 5.4, 5.5 Lecture 6 Differentiation I ·         Slopes of curves ·         Tangents and derivatives ·         Increasing and decreasing functions ·         Rates of change ·         Limits: an introduction ·         Case Study: Marginal functions References: ·         Sydsaeter et al. 6.1, 6.2, 6.3, 6.4, 6.5 ·         Jacques 4.3 Lecture 7 Differentiation II ·         Rules for differentiation ·         Sum, Products and Quotients ·         Chain Rule References: ·         Sydsaeter et al. 6.6, 6.7, 6.8 Lecture 8 Differentiation III ·         Higher order derivatives ·         Derivatives of Exponential functions ·         Derivatives of Logarithmic functions References: ·         Sydsaeter et al. 6.9, 6.10, 6.11 Lecture 9 Derivatives in Use I ·         Implicit differentiation ·         Differentiating the inverse ·         Case study: Supply and demand References: ·         Sydsaeter et al. 7.1, 7.2, 7.3 Lecture 10 Derivatives in Use II ·         Linear Approximation ·         Polynomial Approximation ·         Taylor’s Formula ·         Case Study: Elasticity References: ·         Sydsaeter et al. 7.4, 7.5, 7.6 ·         Jacques 4.5 Lecture 11 Derivatives in Use III ·         Continuity ·         Limits ·         Intermediate value theorem ·         Newton’s method ·         Infinite sequences ·         L’Hôpital’s rule References: ·         Sydsaeter et al. 7.8, 7.9, 7.10, 7.11, 7.12 Lecture 12 Single Variable Optimization I ·         Simple Tests for Extrema ·         Convex and concave functions ·         Case study: Harvesting References: ·         Sydsaeter et al. 8.1, 8.2, 8.3 Lecture 13 Single Variable Optimization II ·         Extreme value theorem ·         Mean value theorem References: ·         Sydsaeter et al. 8.4, 8.5 Lecture 14 Single Variable Optimization III ·         Local extreme points ·         Inflection points ·         Case Study: Optimisation in economic functions References: ·         Sydsaeter et al. 8.6, 8.7 ·         Jacques 4.6 Lecture 15 Integration I ·         Indefinite integrals ·         Definitions ·         General rules of integration References: ·         Sydsaeter et al. 9.1 ·         Jacques 6.1 Lecture 16 Integration II ·         Definite integrals ·         Area of definite integrals ·         Properties of definite integrals ·         The Riemann integral ·         Case Study: Consumer/Producer Surplus References: ·         Sydsaeter et al. 9.2, 9.3, 9.4 ·         Jacques 6.2.1, 6.2.2 Lecture 17 Integration III ·         Integration by parts ·         Integration by substitution References: ·         Sydsaeter et al. 9.5, 9.6 ·         Dowling 12.8, 12.9 Lecture 18 Integraion IV ·         Infinte intervals ·         A glimpse at differential equations ·         Case study: Logistic growth References: ·         Sydsaeter et al. 9.7, 9.8 ·         Jacques 9.2 Lecture 19 Matrix Algebra I ·         Description of matrices ·         Row vectors, Columns vectors ·         Basic Matrix operations References: ·         Sydsaeter et al. 15.1, 15.2 ·         Jacques 7.1.1, 7.1.2, 7.1.3 Lecture 20 Matrix Algebra II ·         Matrix multiplication ·         Rules matrix multiplication ·         Transpose References: ·         Sydsaeter et al. 15.3, 15.4, 15.5 ·         Jacques 7.1.4 Lecture 21 Matrix Algebra III ·         Gaussian elimination References: ·         Sydsaeter et al. 15.6 ·         Dowling 6.5 Lecture 22 Matrix Algebra IV ·         Determinants ·         Expansion by cofactors ·         Cramer’s Rule ·         Case study: The Leontief model References: ·         Sydsaeter et al. 16.1, 16.2, 16.3, 16.4, 16.8 ·         Jacques 7.3 Lecture 23 Matrix Algebra V ·         Inverse of a matrix ·         Properties of the Inverse ·         Solving Equations by matrix inversion References: ·         Sydsaeter et al. 16.6, 16.7 ·         Jacques 7.2 Lecture 24 Vector Algebra ·         Operations, Inner Product ·         Geometric interpretation ·         Cauchy-Schwartz inequality ·         Orthogonality References: ·         Sydsaeter et al. 15.7, 15.8, 15.9 ·         Jacques 4.6

Session 0
Hours of lesson: 0
Instructor: A. Peņa

Topics:

 SECOND SEMESTER Lecture 1 Why Learning Mathematics for Economics, Finance and Management?  (Part 2) ·         Applications in Economics ·         Applications in Finance ·         Applications in Management Reference: ·         tbd Lecture 2 Interest Rates I: Simple Compounding ·         Interest rate periods ·         Effective rates ·         Simple discounting Reference: ·         Sydsaeter et al. 10.1 ·         Zima and Brown 3.1,  3.2, 3.5 Lecture 3 Interest Rates I: Continuous Compounding ·         Accumulated value ·         Equivalent rates ·         Discounted value ·         Compound discounting References: ·         Sydsaeter et al. 10.2 ·         Zima and Brown 4.1, 4.2, 4.3 Lecture 4 Present Values and Discounting ·         Present discounted value ·         Geometric series ·         Harmonic series References: ·         Sydsaeter et al. 10.3, 10.4 Lecture 5 Annuities ·         Accumulated value ·         Total present value ·         Continuous income stream References: ·         Sydsaeter et al. 10.5 ·         Zima and Brown 5.1, 5.2, 5.3, 5.4 Lecture 6 Mortgages ·         Amortizing of a debt ·         Outstanding principal ·         Mortgages References: ·         Sydsaeter et al. 10.6 ·         Zima and Brown 7.1, 7.2. 7.3 Lecture 7 Investment Appraisal ·         Present value as appraisal tool ·         Internal rate of return as appraisal tool References: ·         Jacques 3.4 Lecture 8 Functions of two variables I ·         Domain, Range ·         Partial derivatives ·         Higher order derivatives References: ·         Sydsaeter et al. 11.1, 11.2 Lecture 9 Functions of two variables II ·         Level curves ·         Geometric representation of partial derivatives ·         Distance formula References: ·         Sydsaeter et al. 11.3, 11.4 Lecture 10 Partial Derivatives ·         Young’s theorem ·         Hessian ·         Case study: partial elasticities References: ·         Sydsaeter et al. 11.6, 11.8 Lecture 11 The Chain Rule ·         Chain rule in one dimension ·         Chain rule in n dimensions References: ·         Sydsaeter et al. 12.1, 12.2 Lecture 12 Tools of functional analysis I ·         Homogeneous functions ·         Homothetic functions ·         Euler’s theorem ·         Geometric aspects References: ·         Sydsaeter et al. 12.6, 12.7 Lecture 13 Tools of functional analysis II ·         Linear Approximations ·         Tangent Planes ·         Rules for differentials ·         Increments References: ·         Sydsaeter et al. 12.8, 12.9 Lecture 14 Unconstrained Optimization I ·         Necessary conditions ·         Critical points ·         First order conditions ·         Concavity and convexity References: ·         Sydsaeter et al. 13.1, 13.2, 13.3 Lecture 15 Unconstrained Optimization II ·         Extreme value theorem ·         Interior and boundary points ·         Minima and maxima ·         Saddle points ·         Second order derivative test References: ·         Sydsaeter et al. 13.5 Lecture 16 Constrained Optimization I ·         Lagrange multipliers ·         The Langrangian References: ·         Sydsaeter et al. 14.1 ·         Jacques 5.5 Lecture 17 Constrained Optimization II ·         Lagrange Multipliers: interpretation ·         Several solution candidates References: ·         Sydsaeter et al. 14.2, 14.3 ·         Jacques 5.6 Lecture 18 Linear Programming I ·         Objective function ·         Inequality constraints ·         Nonnegativity constraints References: ·         Sydsaeter et al. 17.1, 17.2, 17.3 ·         Jacques 8.1 Lecture 19 Linear Programming II ·         Case study: firm with N outputs and M resources References: ·         Sydsaeter et al. 17.4 ·         Jacques 8.2 Lectures 20-24 EXPERIENTIAL LAB ·         Projects in Business Cases  on Finance, Economics and Management using Wolfram Alpha