A86003 Mathematics for Business, Economics and Finance

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

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

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