Chapter 1

• Introduction
• 1.0 The Process of Problem Solving
• 1.1 Functions
• 1.2 Mathematical Mocels and Formulation from Verbal Descriptions
• 1.3 Linear Functions and Models
• 1.4 Functions with One Concavity: Quadratic, Exponential, Power
• 1.5 Functions with Changing Concavity: Cubis, Quartic, Logistic
• Summary
   

Chapter 2

• 2.1 Average and Percent Rate of Change Over an Interval
• 2.2 Instantaneous Rate of Change at a Point
• 2.3 Derivative Notation and Interpretation, Marginal Analysis
• 2.4 The Algebraic Definition of Derivative and Basic Derivative Rules
• 2.5 Composite Functions and the Chain Rule
• 2.6 The Product Rule
• Summary

Chapter 3

• Introduction
• 3.1 Analysis of Graphs and Slope Graphs
• 3.2 Optimization – Algebraic Determination of Maxima and Minima
• 3.3 Testing of Critical Points, Concavity and Points of Inflection
• 3.4 Post-Optimality Analysis
• 3.5* Per-Cent Rate of Change at a Point, Elasticity, Average Cost
• Summary

Chapter 4

• Introduction
• 4.1 Continuous Probability Distributions
• 4.2 Approximating Area under Curves (Subinterval Methods)
• 4.3 Finding Exact Areas Using Limits of Sums
• 4.4 Recovering Functions from their Derivatives
• 4.5 The Fundamental Theorem of Calculus
• 4.6 Variable Limits of Integration and Medians, Improper Integrals
• 4.7* Consumer and Producer Surplus
• Summary

Chapter 5

• Introduction
• 5.1 Multivariable Functions and Models, 3-D Graphs
• 5.2 Formulating Models from Verbal Descriptions
• 5.3 Interest and Investments
• 5.4 The Time Value of Money (Present Value and Future Value) and Loans
• 5.5 Formulating SSE in Terms of Model Parameters
• Summary

Chapter 6

• Introduction
• 6.1 Multivariable Models from Data – Spreadsheets and Regression
• 6.2 Mean, Variance, Standard Deviation, MSE, Misuse of Statistics
• 6.3 R2, Standard Error, Misuse of Regression, Regression Assumptions
• 6.4* Investment Portfolios, Risk-Return Tradeoffs, Pareto Efficiency
• Summary

Chapter 7

• Introduction
• 7.1 Introduction to Matrices and Basic Operations
• 7.2 Matrix Multiplication
• 7.3 Systems of Linear Equations and Augmented Matrices
• 7.4 Matrix Equations and Inverse Matrices
• 7.5* Markov Chains
• Summary

Chapter 8

• Introduction
• 8.1 Rates of Change of Multivariable Functions
• 8.2 Finding Local Extrema of Multivariable Functions
• 8.3 Optimization using a Spreadsheet
• 8.4 Testing for Local and Global Extrema
• 8.5 The Method of Least Squares
• Summary

Chapter 9

• Introduction
• 9.1 Optimization with Equality Constraints: Lagrange Multipliers
• 9.2 Solving Linear Programs Graphically
• 9.3 The Simplex Method
• 9.4 Linear and Nonlinear Optimization on Spreadsheets Summary