Course Contents

1. Matrix Algebra  Introduction to Matrices, Matrix Operations: Additions, Subtraction, Scalar Multiplication, Inner Product, Matrix Multiplication  Special types of Matrices: Vectors, Square Matrices, Identity Matrix, Null Matrix, Symmetric Matrix, Idempotent Matrix, Diagonal Matrix, Transpose of a Matrix.  Determinants: Determinants of a Square Matrix, Properties of Determinants, Determinants as a test of Invert-ability, Jacobeans, Hessians and Bordered Hessian Determinants.  The Inverse of a Square Matrix, A System of Equations in Matrix Format, Solution of a system of Linear Equations by: (1) Inverse Matrix Method (2) Cramer’s Rule  The Input-Output Model, The uses of Input-Output Analysis, The Input-Output Table, The General Solution to the Input-Output Model. 2. Differential Calculus  Average and Instantaneous Rate of Change, The Slope of a Secant line and a Tangent Line, Differentiability of a Function 3. Economic Applications:  Marginal Analysis in Business and Economics; Optimization of a Function; Revenue, Cost, Utility and Profit Applications; Elasticity of Demand, Curvature and other Applications 4. Total Differentials and Total Derivatives  Differentials; Total Differentials; Rules of Differentials  Total Derivatives  Implicit Differentiation 5. Multivariable Calculus  Economic Applications: Multivariate Optimization: Maxima, Minima, Point of Inflection; First –Order necessary Condition, Second-Order Sufficient Condition for Maxima and Minima.  Constrained Optimization: Maxima, Minima and Saddle Point, Constrained Optimization by the Lagrange Multiplier Method, Utility Maximization, Profit Maximization, Optimal Input combination for Minimum Cost or Maximum Output.  Homogenous Functions and Euler’s Theorem; Linear Homogeneity, The Organization of a Production Function, Cobb-Douglas Production Function, Returns to Scale. 6. Integral Calculus  Ant derivatives and Indefinite Integrals, Rules of Integration, Integration by Substitution, Integration by Parts,  Definite Integrals, the Concept of Area and the Definite Integrals, Fundamental Theorem of Calculus, Improper Integrals.  Economic Applications: Consumer’s Surplus, Producer’s Surplus, Marginal and Total Relationships; Investment and Capital Formation; Present Value of Cash.

Course Synopsis

1. The course includes the mathematical techniques and economic applications of derivatives, matrix algebra, differentials, multivariable optimization, constrained optimization and integration. 2. Emphasis is on the application of optimization, both with and without constraints, and introductory integrals for understanding relationships of various economic variables and concepts, such as the relationship of aggregate, average and marginal functions 3. The aim is to give students the mathematical tools they need for further study in economics, therefore, this course is designed to provide strong mathematical foundations.

Course Learning Outcomes

By the end of the course, successful students will be comfortable with the basic mathematical methods which are indispensable for a proper understanding of economics and will have command on the use of derivatives, matrix algebra and integrals in solving economic problems.