NEW TITLE: Mathematics with Applications in Business and Social Sciences

Mathematics with Applications in Business and Social Sciences

The NEW title, Mathematics with Applications in Business and Social Sciences, covers content from fundamental algebra to finite mathematics and applied essential calculus. A primary emphasis is placed on showing students how to connect mathematics to real-world contexts.

Table of Contents

Chapter 0: Fundamental Concepts of Algebra 
0.1 Real Numbers
0.2 The Arithmetic of Algebraic Expressions
0.3 Integer Exponents
0.4 Radicals
0.5 Rational Exponents
0.6 Polynomials and Factoring
Chapter 1: Equations and Inequalities in One Variable 
1.1 Linear Equations in One Variable
1.2 Applications of Linear Equations in One Variable
1.3 Linear Inequalities in One Variable
1.4 Quadratic Equations in One Variable
1.5 Higher Degree Polynomial Equations
1.6 Rational and Radical Equations
Chapter 2: Linear Equations in Two Variables 
2.1 The Cartesian Coordinate System
2.2 Linear Equations in Two Variables
2.3 Forms of Linear Equations
2.4 Parallel and Perpendicular Lines
2.5 Linear Regression
Chapter 3: Functions and Their Graphs 
3.1 Introduction to Functions
3.2 Functions and Models
3.3 Linear and Quadratic Functions
3.4 Applications of Quadratic Functions
3.5 Other Common Functions
3.6 Transformations of Functions
3.7 Polynomial Functions
3.8 Rational Functions
3.9 Rational Inequalities
Chapter 4: Exponential and Logarithmic Functions 
4.1 Exponential Functions and Their Graphs
4.2 Applications of Exponential Functions
4.3 Logarithmic Functions and Their Graphs
4.4 Applications of Logarithmic Functions
Chapter 5: Mathematics of Finance 
5.1 Basics of Personal Finance
5.2 Simple and Compound Interest
5.3 Annuities: Present and Future Value
5.4 Borrowing Money
Chapter 6: Systems of Linear Equations; Matrices 
6.1 Solving Systems of Linear Equations by Substitution and Elimination
6.2 Matrix Notation and Gauss-Jordan Elimination
6.3 Determinants and Cramer’s Rule
6.4 Basic Matrix Operations
6.5 Inverses of Square Matrices
6.6 Leontief Input-Output Analysis
Chapter 7: Inequalities and Linear Programming 
7.1 Linear Inequalities in Two Variables
7.2 Linear Programming: The Graphical Approach
7.3 The Simplex Method: Maximization
7.4 The Simplex Method: Duality and Minimization
7.5 The Simplex Method: Mixed Constraints
Chapter 8: Probability 
8.1 Set Notation
8.2 Operations with Sets
8.3 Introduction to Probability
8.4 Counting Principles: Combinations and Permutations
8.5 Counting Principles and Probability
8.6 Probability Rules and Bayes’ Theorem
8.7 Expected Value
Chapter 9: Statistics 
9.1 Collecting Data
9.2 Displaying Data
9.3 Describing and Analyzing Data
9.4 The Binomial Distribution
9.5 The Normal Distribution
9.6 Normal Approximation to the Binomial Distribution
Chapter 10: Limits and the Derivative 
10.1 One-Sided Limits
10.2 Limits
10.3 More about Limits
10.4 Continuity
10.5 Average Rate of Change
10.6 Instantaneous Rate of Change
10.7 Definition of the Derivative and the Power Rule
10.8 Techniques for Finding Derivatives
10.9 Applications: Marginal Analysis
Chapter 11: More about the Derivative 
11.1 The Product and Quotient Rules
11.2 The Chain Rule and the General Power Rule
11.3 Implicit Differentiation and Related Rates
11.4 Increasing and Decreasing Intervals
11.5 Critical Points and the First Derivative Test
11.6 Absolute Maximum and Minimum
Chapter 12: Applications of the Derivative 
12.1 Concavity and Points of Inflection
12.2 The Second Derivative Test
12.3 Curve Sketching: Polynomial Functions
12.4 Curve Sketching: Rational Functions
12.5 Business Applications
12.6 Other Applications: Optimization, Distance, and Velocity
Chapter 13: Additional Applications of the Derivative 
13.1 Derivatives of Logarithmic Functions
13.2 Derivatives of Exponential Functions
13.3 Growth and Decay
13.4 Elasticity of Demand
13.5 L’Hôpital’s Rule
13.6 Differentials
Chapter 14: Integration with Applications 
14.1 The Indefinite Integral
14.2 Integration by Substitution
14.3 Area and Riemann Sums
14.4 The Definite Integral and the Fundamental Theorem of Calculus
14.5 Area under a Curve (with Applications)
14.6 Area between Two Curves (with Applications)
14.7 Differential Equations
Chapter 15: Additional Integration Topics 
15.1 Integration by Parts
15.2 Annuities and Income Streams
15.3 Tables of Integrals
15.4 Numerical Integration
15.5 Improper Integrals
15.6 Volume
Chapter 16: Multivariable Calculus 
16.1 Functions of Several Variables
16.2 Partial Derivatives
16.3 Local Extrema for Functions of Two Variables
16.4 Lagrange Multipliers
16.5 The Method of Least Squares
16.6 Double Integrals

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