Mathematics for Financial Analysis

1st Edition - January 1, 1976
Authors: Michael Gartenberg, Barry Shaw
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 9 2 7 - 5

Mathematics for Financial Analysis focuses on the application of mathematics in financial analysis, including applications of differentiation, logarithmic functions, and… Read more

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Mathematics for Financial Analysis focuses on the application of mathematics in financial analysis, including applications of differentiation, logarithmic functions, and compounding. The publication first ponders on equations and graphs, vectors and matrices, and linear programming. Discussions focus on duality and minimization problems, systems of linear inequalities, linear programs, matrix inversion, properties of matrices and vectors, vector products, equations and graphs, higher dimensional spaces, distance in the plane, coordinate geometry, and inequalities and absolute value. The text then examines differential calculus, applications of differentiation, and antidifferentiation and definite integration. Topics include fundamental theorem of calculus, definite integral, profit optimization in a monopoly, revenue from taxation, curve sketching, concavity and points of inflection, and rules for differentiation. The book examines the applications of integration and differentiation and integration of exponential and logarithmic functions, including exponential and logarithmic functions, differentiation and integration of logarithmic functions, and continuous compounding. The publication is a valuable source of data for researchers interested in the application of mathematics in financial analysis.

Preface

1. Equations and Graphs

1.1. Inequalities and Absolute Value

1.2. Coordinate Geometry

1.3. Distance in the Plane

1.4. Slope

1.5. Equations and Graphs

1.6. Demand and Supply Curves

1.7. Break-even Analysis

1.8. Higher Dimensional Spaces

2. Vectors and Matrices

2.1. Properties of Vectors

2.2. Vector Products

2.3. Properties of Matrices

2.4. Matrix Multiplication

2.5. Systems of Linear Equations

2.6. Matrix Inversion

2.7. Input-Output Analysis

3. Linear Programming

3.1. Linear Programs

3.2. Systems of Linear Inequalities

3.3. Two-Variable Programs

3.4. The Simplex Method

3.5. Duality and Minimisation Problems

4. Differential Calculus

4.1. Functions

4.2. Limits

4.3. Continuity

4.4. Slopes of Tangent Lines to a Curve

4.5 Derivatives

4.6 Rules for Differentiation

4.7 Composite Functions

4.8 Fractional Exponents

5. Applications of Differentiation

5.1. Maxima and Minima

5.2. Concavity and Points of Inflection

5.3. Curve Sketching

5.4. The Total Cost Function

5.5. Profit Optimisation in a Monopoly

5.6. Revenue from Taxation

5.7. The Effect of Taxation on Profit Optimisation

5.8. Inventory Models

6. Antidifferentiation and Definite Integration

6.1. Antidifferentiation

6.2. The Definite Integral

6.3. The Fundamental Theorem of Calculus

6.4. Areas Between Curves

7. Differentiation and Integration of Exponential and Logarithmic Functions

7.1. Exponential and Logarithmic Functions

7.2. Differentiaticfn and Integration of Logarithmic Functions

7.3. Differentiation and Integration of Exponential Functions

8. Applications of Integration

8.1. Antidifferentiation of Marginal Functions

8.2. Consumers' and Producers' Surplus

8.3. Simple and Compound Interest

8.4. Continuous Compounding

8.5. Simple Annuities

8.6. More General Annuities

8.7. Continuous Annuities

Table 8.1

Table 8.2

Table 8.3

Table 8.4

Answer Key—Selected Problems

Index