## MATH 106 - Calculus for Social Sciences II

Systems of linear equations, algebraic operations with matrices, determinants, introduction to linear programming, the theory, techniques and applications of integration, introduction to differential equations with emphasis to some special first-order equations and their applications to economics and social sciences.

Credits: 3

Hours: 60 (Lecture Hours: 3;  Seminars and Tutorials: 1)

Prerequisites:

MATH 101 or MATH 105, i.e. a semester of differential calculus.

Non-Course Prerequisites:
None

Co-requisites:

None

Course Content:
The Integral
- The antiderivative
- Integration by substitution
- The definite integral
- Area between curves
- The fundamental theorem of calculus
- Numerical integration
Applications and Integration
- Differential equations
- Integration by parts
- Using tables of integrals
- Improper integrals
- Probability density functions
Functions of Several Variables
- Three-dimensional coordinate system
- Partial derivatives
- Maximum-minimum applications
- Lagrange multipliers
- Multiple integrals
Systems of Equations and Matrices
- Systems of equations
- Introduction to matrices
- Gauss-Jordan elimination
- Inverse matrices
- Leontief models
Linear Programming
- Systems of linear inequalities
- Formulating linear programming models
- Graphical solution of linear programming problems
- Slack variables and the pivot
- Maximization by the simplex method
- Duality
Markov Chains and Decision Theory
- Introduction to Markov chains
- Regular Markov chains
- Absorbing Markov chains
- Expectation
- Game theory

- m x n Matrix games

Learning Outcomes:
On successful completion of this course, the student will be able to:
- Integrate single and multiple variable functions
- Apply integration to problems in the social sciences
- Solve differential equations
- Find approximate solutions using numerical methods
- Solve systems of linear equations using matrices and determinants
- Do simple linear programming

- Compute the probability of a simple event and apply integration to probability