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Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences


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Part I. ALGEBRA0. Review of Algebra0.1 Sets of Real Numbers0.2 Some Properties of Real Numbers0.3 Exponents and Radicals0.4 Operations with Algebraic Expressions0.5 Factoring0.6 Fractions0.7 Equations, in Particular Linear, Equations0.8 Quadratic Equations 1. Applications and More Algebra1.1 Applications of Equations1.2 Linear Inequalities1.3 Applications of Inequalities1.4 Absolute Value1.5 Summation Notation1.6 Sequences 2. Functions and Graphs2.1 Functions2.2 Special Functions2.3 Combinations of Functions2.4 Inverse Functions2.5 Graphs in Rectangular Coordinates2.6 Symmetry2.7 Translations and Reflections2.8 Functions of Several Variables 3. Lines, Parabolas, and Systems3.1 Lines3.2 Applications and Linear Functions3.3 Quadratic Functions3.4 Systems of Linear Equations3.5 Nonlinear Systems3.6 Applications of Systems of Equations 4. Exponential and Logarithmic Functions4.1 Exponential Functions4.2 Logarithmic Functions4.3 Properties of Logarithms4.4 Logarithmic and Exponential Equations Part II. FINITE MATHEMATICS5. Mathematics of Finance5.1 Compound Interest5.2 Present Value5.3 Interest Compounded Continuously5.4 Annuities5.5 Amortization of Loans5.6 Perpetuities 6. Matrix Algebra6.1 Matrices6.2 Matrix Addition and Scalar Multiplication6.3 Matrix Multiplication6.4 Solving Systems by Reducing Matrices6.5 Solving Systems by Reducing Matrices (continued)6.6 Inverses6.7 Leontief's Input-Output Analysis 7. Linear Programming7.1 Linear Inequalities in Two Variables7.2 Linear Programming7.3 Multiple Optimum Solutions7.4 The Simplex Method7.5 Degeneracy, Unbounded Solutions, and Multiple Solutions7.6 Artificial Variables7.7 Minimization7.8 The Dual 8. Introduction to Probability and Statistics8.1 Basic Counting Principle and Permutations8.2 Combinations and Other Counting Principles8.3 Sample Spaces and Events8.4 Probability8.5 Conditional Probability and Stochastic Processes8.6 Independent Events8.7 Bayes's Formula 9. Additional Topics in Probability9.1 Discrete Random Variables and Expected Value9.2 The Binomial Distribution9.3 Markov Chains Part III. CALCULUS10. Limits and Continuity10.1 Limits10.2 Limits (Continued)10.3 Continuity10.4 Continuity Applied to Inequalities 11. Differentiation11.1 The Derivative11.2 Rules for Differentiation11.3 The Derivative as a Rate of Change11.4 The Product Rule and the Quotient Rule11.5 The Chain Rule 12. Additional Differentiation Topics12.1 Derivatives of Logarithmic Functions12.2 Derivatives of Exponential Functions12.3 Elasticity of Demand12.4 Implicit Differentiation12.5 Logarithmic Differentiation12.6 Newton's Method12.7 Higher-Order Derivatives 13. Curve Sketching13.1 Relative Extrema13.2 Absolute Extrema on a Closed Interval13.3 Concavity13.4 The Second-Derivative Test13.5 Asymptotes13.6 Applied Maxima and Minima 14. Integration14.1 Differentials14.2 The Indefinite Integral14.3 Integration with Initial Conditions14.4 More Integration Formulas14.5 Techniques of Integration14.6 The Definite Integral14.7 The Fundamental Theorem of Integral Calculus14.8 Approximate Integration14.9 Area between Curves14.10 Consumers' and Producers' Surplus 15. Methods and Applications of Integration15.1 Integration by Parts15.2 Integration by Partial Fractions15.3 Integration by Tables15.4 Average Value of a Function15.5 Differential Equations15.6 More Applications of Differential Equations15.7 Improper Integrals 16. Continuous Random Variables16.1 Continuous Random Variables16.2 The Normal Distribution16.3 The Normal Approximation to the Binomial Distribution 17. Multivariable Calculus17.1 Partial Derivatives17.2 Applications of Partial Derivatives17.3 Implicit Partial Differentiation17.4 Higher-Order Partial Derivatives17.5 Chain Rule17.6 Maxima and Minima for Functions of Two Variables17.7 Lagrange Multipliers17.8 Lines of Regression17.9 Multiple Integrals

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