COURSE TITLE: MATHEMATICAL METHDOS OF ECONOMICS I COURSE CODE: ECON 2015 (EC 24B) LEVEL: UNDERGRADUATE LEVEL (SECOND YEAR) NO OF CREDITS: 3

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1 COURSE TITLE: MATHEMATICAL METHDOS OF ECONOMICS I COURSE CODE: ECON 2015 (EC 24B) LEVEL: UNDERGRADUATE LEVEL (SECOND YEAR) NO OF CREDITS: 3 PREREQUISITES: ECON 1001, ECON 1002, ECON 1003, COURSE DESCRIPTION / RATIONALE: This course will provide economics students with the tools required to undertake mathematical analysis in their field. The course covers a wide range of topics including mathematical induction and linear programming. PURPOSE OF THE COURSE The course is designed to; establish elementary skills in Mathematical Methods and to initiate the development of an ability to apply these mathematical methods to problems in the field of economics. INSTRUCTOR INFORMATION LECTURER: Ms. Rebecca Gookool LECTURER s Rebecca.Gookool@sta.uwi.edu LECTURER s PHONE CONTACT: EXT 83041

2 2 CONTENT 1. Propositional Calculus 2. Mathematical Induction 3. Operation on Vectors & Matrices 4. Determinants of Matrices 5. Equivalence 6. The Inverse of a Matrix 7. Vectors 8. Solving Linear Equations 9. Eigenvalues and Eigenvectors 10. Symmetric and Skew-Symmetric Matrices 11. Linear Programming: graphical method 12. Linear programming: Simplex Method GOALS/AIMS To equip students with an adequate set of tools; theoretical and practical; to understand the application of economic principles. GENERAL OBJECTIVES To simplify basic mathematical tools into practical easy to follow steps. COURSE ASSESSMENT 100% final Examination TEACHING STRATEGIES The mode of teaching will be via face to face lectures and tutorials sessions. RESOURCES notes will be provided to the class via the online course profile Readings from texts are also provided. READINGS notes prepared by Mr. Martin Franklin and Dr. Roger Hosein

3 3 COURSE CALENDAR Topic Reading Week Propositional Calculus Statements and Basic Operations The Construction of truth tables Some Basic Truth Tables Conditional p q Conditional Statements and Variations Converse Statements Inverse Statements Contra Positive Statements Biconditional Statements Granger Causality Tautologies and Contradictions Logical Implication Arguments Arguments and Statements Summary Associative Law Commutative Law Distributive Law Mathematical Induction Steps Worked examples Operation on Vectors & Matrices Matrix Addition Matrix Multiplication Scalar and Vector Multiplication Multiplication by a Scalar Distributive Laws and Associative Laws of Multiplication of Matrices Equality of Matrices Transpose of a Matrix Symmetric Matrices The Zero Matrix Identity and Diagonal Matrices Upper Triangular (UTM), Lower Triangular (LTM) and Diagonal Matrices Orthogonal Matrices Some Properties of Orthogonal Matrices Invertible Matrices Power of Matrices Differences between Scalars and Matrices Determinants of Matrices Evaluating the Determinant Matrix of Minors Matrix of Cofactors Laplace Expansion Theorem Properties of Determinants Other Worked Examples Chapter 1 Chapter 2 Chapter 3 Chapter 4 notes:

4 4 Equivalence Rank of a Matrix Elementary Transformations and their Inverses Elementary Transformations (ET) Inverse Elementary Transformation (IT) Equivalent Matrices The Normal Form of a Matrix Echelon Matrices and the Rank of a Matrix The Inverse of a Matrix The Adjoint Matrix (A adj ) Inverse of a Matrix Using the Adjoint Method Inverse of a Matrix using Elementary Row Operations Applications of Inverse Matrices: Cryptography Some Properties of Inverses Input Output Analysis Vectors Vector Spaces Spanning Set Basis and Dimensions Dimension Linear Transformation Application of Linear Transformation Some Basic Theorems on Linear Transformations Linear Dependence of Vectors Solving Linear Equations Solving a system of simultaneous equations by the inverse method Economic Application Solving Linear Equations by Cramer s Rule Proof of Cramer s Theorem Economic Application Solving Linear Equations by the Elimination Method Economic Application Linear Equations: Homogenous and Non Homogenous Homogenous System of Equation Non Homogeneous System of Equations Finding the General Solution Chapter 5 Chapter 6 Chapter 7 Chapter Eigenvalues and Eigenvectors Characteristic Vectors Diagonalization Orthogonal Diagonalization Some Properties of Eigenvalues and Eigenvectors Chapter 9 9 Symmetric and Skew-Symmetric Matrices Chapter 10 10

5 5 Properties of Symmetric and Skew-Symmetric Matrices Quadratic Forms QF and positive definite matrices Linear Programming Chapter Constrained Maximization: Setting up a LP Model Extreme Point Theorem The Basis Theorem Constrained Minimization: Setting up a LP Model Linear programming: Simplex Method Chapter 12 ADDITIONAL INFORMATION 19 Any candidate who has been absent from the University for a prolonged period during the teaching of a particular course for any reason other than illness or whose attendance at prescribed lectures, classes,... tutorials,... has been unsatisfactory or who has failed to submit essays or other exercises set by his/her teachers, may be debarred by the relevant Academic Board, on the recommendation of the relevant Faculty Board, from taking any University examinations. The procedures to be used shall be prescribed in Faculty Regulations (i) Cheating shall constitute a major offence under these regulations. (ii) Cheating is any attempt to benefit one s self or another by deceit or fraud. (iii) Plagiarism is a form of cheating. (iv) Plagiarism is the unauthorized and/ or unacknowledged use of another person s intellectual effort and creations howsoever recorded, including whether formally published or in manuscript or in typescript or other printed or electronically presented form and includes taking passages, ideas or structures from another work or author without proper and unequivocal attribution of such source(s), using the conventions for attributions or citing used in this University (i) If any candidate is suspected of cheating, or attempting to cheat, the circumstances shall be reported in writing to the Campus Registrar. The Campus Registrar shall refer the matter to the Chairman of the Campus Committee on Examinations. If the Chairman so decides, the Committee shall invite the candidate for an interview and shall conduct an investigation. If the candidate is found guilty of cheating or attempting to cheat, the Committee shall disqualify the candidate from the examination in the course concerned, and may also disqualify him/her from all examinations taken in that examination session; and may also disqualify him/her from all further examinations of the University, for any period of time, and may impose a fine not exceeding Bds$ or J$ or TT$ or US$ (according to campus). If the candidate fails to attend and does not offer a satisfactory excuse prior to the hearing, the Committee may hear the case in the candidate s absence.

6 6 How to study for this Course Students should keep up-to-date with lectures, office hours and tutorials. Grading System GRADE GPA MARKS% A and Over A A B B B C C C D D F