The course is designed to give non-intimidating presentation of mathematical concepts, principles and techniques most useful for students in business management. The main objectives of the course are to enhance students’ competency in application of mathematics to solve business management problems and to improve their level of quantitative sophistication for further advanced business analysis.
Week 01: MATHEMATICAL FUNCTIONS
1.1 Functions Defined.
1.2 The Nature and Notation of Functions
1.3 Domain and Range Considerations
1.4 Types of Functions.
1.4.1 Constant Functions
1.42 Linear Functions
1.4.3 Quadratic Functions
1.4.4 Cubic Functions
1.4.5 Polynomial Functions
1.4.6 Graphical Representation of Functions
Week 02: LINEAR EQUATIONS
2.1. Characteristics of Linear Equations
2.2. Graphical Characteristics
2.3. Slope - Intercept Form
2.4. Determining the Equation of a Straight Line Linear Equations involving more than two variables
Week 03: SYSTEMS OF LINEAR EQUATIONS AND THEIR APPLICATIONS
3.1. Introduction
3.2. Two variables Systems of Equations.
3.3. Gauss – Jordan Procedure
3.4. Applications of Linear Equations and Systems of Equations
Week 04: NONLINEAR FUNCTIONS AND THEIR APPLICATIONS
4.1 Non Linear Functions- Introduction
4.2 Quadratic Functions, Characteristics and Their Applications
4.3 Polynomial Functions.
4.4 Exponential Functions & Applications
4.5 Logarithmic Functions, Properties of Logarithmic Functions
Week 05: DETERMINANTS
5.1 Determinants
5.2 Properties of Determinants
5.3 Determinants and Non Singularity
5.4 Special Determinants
Week 06: MATRICES
6.1 Introduction to Matrices
6.2 Types of Matrices
6.3 Matrix Operations
6.4 Inverse of Matrix
6.5 The Determinant & its Properties
6.6. The Method of Cofactors
Week 07: LIMITS AND CONTINUITY
1.1. Limits
1.2. Computing Limits
1.3. Computing Limits: End Behavior
1.4. Limits (More rigorous discussion)
1.5. Continuity
Week 08: DIFFERENTIATION
2.1. Slopes and rates of change
2.2. The derivative
2.3. Techniques of differentiation
2.4. The Chain rule
2.5. Implicit Differentiation
2.6. Time rates, Percentage changes and Related Rates
2.7. Higher order derivation
Week 09: APPLICATION OF DIFFERENTIATION
3.1. Analysis of Functions: Increase, Decrease and Concavity
3.2. Analysis of Functions: Relative Extreme, First and Second Derivative Tests (Relative Maxima and Minima)
3.3. Optimization
3.4. Revenue: Marginal Revenue, Average Revenue
3.5. Marginal Cost, Average Cost
3.6. Profit Maximization: MR = MC
Week 10: DIFFERENTIATION OF MULTIVARIATE
4.1. Derivatives of Multivariate Functions: Partial Derivatives and their interpretations
4.2. Differential Equations
4.3. Higher- order derivatives of Multivariate functions
4.4. Optimum values of multivariate functions of two independent variables
Week 11: DIFFERENTIATION OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS
5.1. Derivatives of Exponential functions
5.2. Logarithmic function differentiation
5.3. Constrained optima: Substitution and lagrangian multipliers
Week 12: INTEGRATION
6.1. The Integral
6.2. Relationship between integral and differential calculus
6.3. The Definite Integral
6.4. The fundamental theorem
6.5. Rules of integration
6.6. Integration by substitution
6.7. Integration by parts
6.8. Business and economic applications of integral calculus
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