Quantitative Analysis

- acknowledgements…

First of all, I would like to thank Lynn Dietrich (director of the Math Learning Center at Monmouth University, West Long Branch, New Jersey, USA) for her help in producing this tutorial text. Without her help, many typographical errors might not have been caught before submitting the final draft.

I would also like to extend my thanks to Sophie Tergeist (bookboon.com Ltd. – Davenport House, 16 Pepper Street, London E14 9RP, United Kingdom) for her constant patience in answering my numerous questions during the production of this text.

- explanation of how the textbook is organized…

This tutorial textbook has been organized into 4 chapters (units) with several individual tutorial lessons within each chapter. As presented in the table of contents, each of the tutorials has been listed separately with its objective and its starting page. For coding purposes: “Tutorial N.M” means that the tutorial is the Mth lesson in chapter N.

I attempted to present each of the tutorials as if a person (teacher, tutor) was sitting next to the reader talking each of the concepts through. My goal was to make sure that each of the lessons was fully explained but still fully understandable. Hopefully this goal was met.

- description of whom I believe might be interested in using these tutorials…

The purpose of this tutorial textbook is to present mathematical skills (algebraic concepts) and their various applications that may be important to students of management (business) science. The applications included should allow readers to view math in a practical setting relevant to their intended careers.

1. Equations, Inequalities & Linear Programming 
   1. Tutorial 1.1: Solve one-step linear equations in one variable
   2. Tutorial 1.2: Solve two-step linear equations in one variable
   3. Tutorial 1.3: Solve multi-step linear equations involving like-terms
   4. Tutorial 1.4: Solve multi-step linear equations involving parentheses
   5. Tutorial 1.5: Solve multi-step linear equations in one variable where the variable appears on each side of the equation
   6. Tutorial 1.6: Solve multi-step linear inequalities in one variable
   7. Tutorial 1.7: Graph the solution of multi-step linear equations or inequalities in one variable on a number line
   8. Tutorial 1.8: Graph a line that passes through two given points
   9. Tutorial 1.9: Graph a linear equation using its x- and y-intercepts
   10. Tutorial 1.10: Graph an equation (in slope-intercept form) using its slope and y-intercept
   11. Tutorial 1.11: Graph a linear equation (in standard form) using its slope and y-intercept
   12. Tutorial 1.12: Determine the slope of a line passing through 2 given points
   13. Tutorial 1.13: Use the slope-intercept formula to write the equation of a line with a given slope and point
   14. Tutorial 1.14: Use the point-slope formula to write the slope-intercept form of an equation of a line with a given slope and point
   15. Tutorial 1.15: Write the standard form of an equation of a line with a given slope and point
   16. Tutorial 1.16: Write an equation of a line that passes through two given points
   17. Tutorial 1.17: Determine whether the lines for a pair of equations are parallel, perpendicular or coincide with each other
   18. Tutorial 1.18: Write the equation of a line through a given point that is parallel to a given line
   19. Tutorial 1.19: Write the equation of a line through a given point that is perpendicular to a given line
   20. Tutorial 1.20: Solve a system of linear equations by graphing
   21. Tutorial 1.21: Solve a system of linear equations by substitution
   22. Tutorial 1.22: Solve a system of linear equations by elimination
   23. Tutorial 1.23: Solve a system of three equations in three variables
   24. Tutorial 1.24: Solve applications involving systems of equations
   25. Tutorial 1.25: Find the marginal cost, the marginal cost revenue and the marginal cost profit of given linear total cost functions, linear total revenue functions and linear profit functions
   26. Tutorial 1.26: Evaluate linear total cost functions, linear total revenue functions and linear profit functions
   27. Tutorial 1.27: Write the equations for linear total cost functions, linear total revenue functions and linear profit functions by using information given about the functions
   28. Tutorial 1.28: Find the break-even point for the given cost and revenue functions
   29. Tutorial 1.29: Evaluate and graph supply and demand functions
   30. Tutorial 1.30: Write the equation (in slope-intercept form) of a supply or a demand function
   31. Tutorial 1.31: Determine the market equilibrium for a given scenario
   32. Tutorial 1.32: Graph a linear inequality in two variables
   33. Tutorial 1.33: Solve a system of linear inequalities in two variables
   34. Tutorial 1.34: Name the vertices for the feasible solution region for the given system of linear inequalities
   35. Tutorial 1.35: Use the vertices for the feasible solution region for a given system of linear inequalities to determine the optimal (minimum or maximum) value of a given linear function that is subject to constraints as defined by the given system of inequalities
   36. Tutorial 1.36: Use graphing to determine the optimal maximum value of a linear function subject to constraints
   37. Tutorial 1.37: Use graphing to determine the optimal minimum value of a linear function subject to constraints
   38. Tutorial 1.38: Solve applications involving linear programming
2. Matrices & Array Operations 
   1. Tutorial 2.1: Determine the number of rows or columns in a matrix
   2. Tutorial 2.2: Determine the order (dimensions) of a matrix
   3. Tutorial 2.3: Identify square matrices
   4. Tutorial 2.4: Identify the element (entry) at a given location (MRC)
   5. Tutorial 2.5: Determine a zero matrix with a given order (dimensions)
   6. Tutorial 2.6: Find the transpose of a matrix
   7. Tutorial 2.7: Determine the negative of a matrix
   8. Tutorial 2.8: Use matrices to present and interpret given data
   9. Tutorial 2.9: Add matrices
   10. Tutorial 2.10: Subtract matrices
   11. Tutorial 2.11: Use matrix addition/subtraction to solve real-world business applications
   12. Tutorial 2.12: Multiply a matrix by a scalar (real number)
   13. Tutorial 2.13: Find the product of given matrices
   14. Tutorial 2.14: Complete matrix multiplication involving zero matrices
   15. Tutorial 2.15: Complete multiplication involving identity matrices
   16. Tutorial 2.16: Use matrix multiplication to solve business applications
   17. Tutorial 2.17: Write the augmented matrix for a system of equations
   18. Tutorial 2.18: Use a reduced matrix to determine the solutions for a given system
   19. Tutorial 2.19: Use matrices to solve systems with unique solutions
   20. Tutorial 2.20: Use matrices to solve systems with non-unique solutions
   21. Tutorial 2.21: Find the inverse of a 2 × 2 square matrix
   22. Tutorial 2.22: Use 2 × 2 inverse matrices to solve systems of equations
   23. Tutorial 2.23: Use row operations to find the inverse matrix of a square matrix
   24. Tutorial 2.24: Use N × N inverse matrices to solve systems of equations
   25. Tutorial 2.25: Use matrix inverses to solve real-world applications
   26. Tutorial 2.26: Use a computer spreadsheet to determine the number of rows and columns contained in a matrix and thereby determine the order of the matrix
   27. Tutorial 2.27: Use a computer spreadsheet to determine the transpose and/or the negative of a matrix
   28. Tutorial 2.28: Use a computer spreadsheet to add or subtract matrices
   29. Tutorial 2.29: Use a computer spreadsheet to complete a scalar multiplication
   30. Tutorial 2.30: Use a computer spreadsheet to complete a matrix multiplication
   31. Tutorial 2.31: Use a computer spreadsheet to solve systems of equations involving row operations
   32. Tutorial 2.32: Use a computer spreadsheet to determine the inverse and/or determinant of a matrix
   33. Tutorial 2.33: Use a computer spreadsheet to solve a system of equations involving inverse matrices
3. Quadratic & other Special Functions 
   1. Tutorial 3.1: Factor a polynomial expression by finding its greatest common monomial factor
   2. Tutorial 3.2: Factor a polynomial expression by grouping
   3. Tutorial 3.3: Factor a polynomial expression (x2 + bx + c) as a product of binomials
   4. Tutorial 3.4: Factor a polynomial expression (ax2 + bx + c) as a product of binomials
   5. Tutorial 3.5: Factor “special” polynomial expressions through patterning
   6. Tutorial 3.6: Use factoring to complete business applications
   7. Tutorial 3.7: Solve quadratic equations by factoring
   8. Tutorial 3.8: Solve quadratic equations by completing the square
   9. Tutorial 3.9: Derive the quadratic formula by completing the square
   10. Tutorial 3.10: Solve quadratic equations using the quadratic formula
   11. Tutorial 3.11: Determine the number and the nature of the solutions for a quadratic equation
   12. Tutorial 3.12: Solve business applications involving quadratic functions
   13. Tutorial 3.13: For any quadratic function
   14. Tutorial 3.14: Use quadratic functions to find market equilibrium
   15. Tutorial 3.15: Use quadratic functions to find break-even point(s)
   16. Tutorial 3.16: Maximize quadratic revenue and/or profit functions. Minimize quadratic cost functions
   17. Tutorial 3.17: Use quadratic functions to solve real-world applications
   18. Tutorial 3.18: Identify the graphs of basic functions
4. Mathematics of Finance 
   1. Tutorial 4.1: Find the amount of interest for a simple interest loan or investment
   2. Tutorial 4.2: Find the future value for a simple interest investment
   3. Tutorial 4.3: Find the amount that was invested into an account where simple interest is used
   4. Tutorial 4.4: Find the simple interest rate earned on an investment
   5. Tutorial 4.5: Find the time needed for an account with a simple interest rate to reach a desired future value
   6. Tutorial 4.6: Find the future value for an account that is compounded periodically
   7. Tutorial 4.7: Find the amount of interest earned for an account that is compounded periodically
   8. Tutorial 4.8: Find the amount that was invested into an account that is compounded periodically
   9. Tutorial 4.9: Find the interest rate for a periodically-compounded account
   10. Tutorial 4.10: Solve an exponential equation using logarithms
   11. Tutorial 4.11: Find the time needed for an account that is compounded periodically to reach a certain future value
   12. Tutorial 4.12: Find the future value for an account when interest is compounded continuously
   13. Tutorial 4.13: Find the amount that was invested into an account that is compounded continuously
   14. Tutorial 4.14: Find the interest rate for an account that is compounded continuously
   15. Tutorial 4.15: Find the time needed for an account that is compounded continuously to reach a specified amount
   16. Tutorial 4.16: Find the annual percentage yield (APY) of money in an account where the interest is compounded periodically
   17. Tutorial 4.17: Find the annual percentage yield (APY) of money in an account where the interest is compounded continuously
   18. Tutorial 4.18: Compute the future value of an ordinary annuity
   19. Tutorial 4.19: Compute the payment amounts required in order for an ordinary annuity to have a specified future value
   20. Tutorial 4.20: Find out how long it will take for an ordinary annuity to reach a savings goal
   21. Tutorial 4.21: Compute the future values of an annuity due
   22. Tutorial 4.22: Compute the payment amounts required in order for an annuity due to have specified future values
   23. Tutorial 4.23: Find out how long it will take for an annuity due to reach a savings goal
   24. Tutorial 4.24: Compute the present value of an ordinary annuity
   25. Tutorial 4.25: Compute the payments for a specified present value for an ordinary annuity
   26. Tutorial 4.26: Compute the present value of an annuity due
   27. Tutorial 4.27: Compute the payments for a specified present value for an annuity due
   28. Tutorial 4.28: Compute the present value of a deferred annuity
   29. Tutorial 4.29: Compute the payments for a specified present value for a deferred annuity
   30. Tutorial 4.30: Find the regular payments to amortize a debt
   31. Tutorial 4.31: Find the amount that can be borrowed for a specified payment
   32. Tutorial 4.32: Find the unpaid balance of a loan