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EES 300: Mathematics for Economists 3 Notes

Institution: Kenyatta University

Course: Bachelor of Economics

Content Category: lecture notes

Posted By: davidkariuki1010

Document Type: DOCX

Number of Pages: 116

Price: KES 200

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Summary

INTRODUCTION
This course is an advanced course in mathematics for economics. A student should have learnt mathematics for economics two for her/him to be able to understand this course. The course introduces the student to more optimization techniques, both for constrained and unconstrained optimization problems.
OBJECTIVES
The learner should be able to:
1. Formulate linear programming problems in a standard way.
2. Solve linear programming problems using the graphical and simplex method.
3. Formulate the dual of a linear programming problem.
4. Test linear dependence using the Jacobian Determinant
5. Solve simultaneous equations using Gaussian and Gauss Jordan elimination methods.
6. Test the convexity and concavity of a non-linear function using Hessian matrices.
7. State the Kuhn Tucker conditions for a maximization and minimization problem.
8. Solve a non-linear Programming problem.
9. Integrate logarithmic and non-algebraic functions.
10. Integrate functions using Integration by parts
11. Get solutions to First order differential equations used in Economics
12. Get solutions to First order difference equations used in Economics
13. Determine stability of economic variables.
TABLE OF CONTENTS
Lecture One: Introduction to linear programming.
• Formulation of LPP
Lecture Two: Graphical method of solving LP problems
Lecture Three: Simplex method for maximization problems, Duality in LPP
Lecture Four: Tests of linear dependence using the Jacobian Determinant.
• Solution of simultaneous equations using Gaussian and Gauss Jordan elimination methods.
Lecture Five: Tests of convexity and concavity using Hessian matrices and determinants
Lecture six: Non-linear Programming
• Kuhn Tucker problem for maximisation
• Kuhn Tucker problem for minimization
• Economic applications of non-linear programming
Lecture Seven: Integration of logarithmic and non-algebraic functions,Integration by parts
• Economic applications of integration of non-algebraic functions.
Lecture Eight: First order differential equations
• FODE with constant coefficient and term.
• FODE with variable coefficient and term
• Exact differential equations
• Economic applications of FODE
Lecture Nine: First order difference equations
• Homogenous and non-homogenous difference equations.
• Solution to FO difference equations
Lecture Ten: Stability of an equilibrium.
• Economic applications in cobweb model and market model.
.....................................


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