Mathematics for Business, Finance and Economics

PART 1 - STRAIGHT LINES AND LINEAR EQUATIONS 1. Introduction 2. Coordinates 3. Straight Lines: Preliminaries 4. Identifying straight lines and equations 5. Two Applications 6. Point-slope and general form 7. Straight lines and Simultaneous Equations 8. Elementary Row Operations 9. Other Linear Systems in up to two Variables 10. Linear Systems of Equations in more than two variables 11. Gaussian Elimination 12. Identities 13. Further Applications. PART 11 - LINEAR INEQUALITIES 1. Introduction 2. Linear inequalities in one variable 3. Linear inequalities in two or more variables 4. Convex solution sets 5. Linear programming PART 111 - MATRICES: 1. Introduction 2. Some fundamentals 3. Addition, subtraction and scalar multiplication 4. Matrix Multiplication 5. Matrix Inversion 6. Simultaneous Equations 7. Rank 8. Higher Order Systems: determinants and the inverse matrix 9. Simultaneous Equations (ii) 10. Cramer's rule 11. Concluding remarks. PART 1V - FUNCTIONS AND TURNING POINTS 1. Functions 2. Quadratic Functions 3. Cubics and Quartics 4. Polynomials 5. Rational functions 6. Functions: further considerations PART V - DERIVATIVES AND OPTIMIZATION 1. Introduction 2. Slope and turning points 3. An approach to the derivative 4. The power function rule 5. Differentiating polynomials 6. The product and quotient rules 7. The chain rule 8. The inverse function rule 9. Implicit differentiation 10. Higher order derivatives 11. Local maxima and minima 12. Global maxima and minima 13. Concavity, Convexity and points of inflection PART V1 - FUNCTIONS OF MORE THAN ONE VARIABLE 1. Introduction 2. Linear functions of several variables 3. Quadratic functions 4. Slopes and first order derivatives 5. Higher order partial derivatives 6. local maxima and minima 7. Saddle points 8. Stationary values; resume PART V11 - CONSTRAINED OPTIMIZATION 1. Introduction to constrained Optimization 2. The method of substitution 3. Lagrange multipliers and equality constraints 4. Sign restricted variables 5. Lagrange multipliers and inequality constraints 6. Inequality constraints and sign requirements 7. The Kuhn-tucker conditions and mathematical programming 8. Economic Application: Multi-product Monopoly. PART V111 - INTEGRATION 1. Introduction 2. Rules 3. Application to the marginal Analysis of the Firm 4. Differential Equations 5. Integration by Substitution 5. The definite integral 7. Numerical integration 8. Concluding remarks PART 1X - 1. Exponential functions; introduction 2. The natural exponential function and its derivative 3. integration of natural exponential functions 4. Natural logarithmic functions 5. The derivative of natural logarithmic functions 6. Elasticity 7. Natural logarithmic functions and integration 8. Integration by parts 9. Logarithmic and exponential functions to bases other than e 10. Aggregate Sales Curves. APPENDIX: 1. The number system 2. Sets 3. Exponents 4. Absolute values 5. Place value notation 6. Precedence in arithmetic operations.