MAT-231 Objectives
MAT-231 Calculus for Management Science
Instructional Objectives
- Define a function.
- Graph a function by point – by – point method.
- Find the domain of a given function.
- Use function notation to simplify expressions.
- Define Cost, Price-Demand, Revenue and Profit Functions.
- Learn to graph all elementary functions.
- Discuss transformations of functions (Vertical and Horizontal Shifts; Reflections, Expansions and Contractions).
- Define and graph a linear function.
- Define the slope of a line.
- Learn how to use the concept of a linear function in application problems.
- Define and discuss quadratic functions and their properties.
- Graph quadratic function.
- Apply quadratic functions to business problems.
- Define polynomial and rational functions.
- Find the domain for a given rational function.
- Find vertical and horizontal asymptotes of rational functions.
- Define and graph an exponential function.
- Understand the properties of exponential functions.
- Solve exponential equations.
- Solve application problems involving finance, money growth, population growth etc.
- Find the inverse of a function.
- Identify and graph logarithmic functions.
- Use the product, quotient and power properties of logarithms.
- Evaluate common and natural logarithms.
- Use the change of base formula.
- Solve logarithmic equations.
- Solve problems that can be modeled by logarithmic equations, such as, finance and social sciences.
- Find rate of change, instantaneous rate of change.
- Define slope of secant line and tangent line.
- Evaluate limits by using difference quotient.
- Evaluate limits algebraically.
- Find derivative using the definition of difference quotient.
- Discuss the graphs of nonexistence of the derivative.
- Find the derivative of a constant function.
- Find the derivative functions by using power rule and derivative of sum and differences.
- Define Marginal Cost Function and solve application problems.
- Find derivatives of functions using product and quotient rule.
- Apply chain rule and general power rule to determine the derivatives of functions.
- Solve applied problems pertaining to marginal analysis in business and economics.
- For a given function, find the continuity properties.
- Find limits at infinity and infinite limits.
- For a given function, find intervals where function is increasing and where function is decreasing.
- Use first derivative test to find all local extrema.
- For a given function, find intervals where a graph is concave up and where a graph is concave down.
- For a given function, find all inflection points.
- Use second derivative test to find local maxima and minima.
- For a given function, find absolute maxima and minima.
- Use second derivative test for absolute maximum and minimum.
- Optimize revenue and profit.
- Optimize area and perimeter.
- Optimize Inventory Costs, Rental Income and Agricultural output.
- Find the derivatives of logarithmic and exponential functions.
- Revisit the chain rule to differentiate logarithmic and exponential functions.
- Differentiate expressions implicitly.
- Solve application problems pertaining to related rates and motion.
- Solve application problems pertaining to related rates and business.
- Find the antiderivative of a given function (algebraic forms).
- Find the antiderivative of a given function (exponential and logarithmic forms).
- Solve application problems involving antiderivative functions.
- Find the antiderivative of a function using substitution.
- Evaluate the definite integrals.
- Solve application problems involving definite integrals.
- Find area between a curve and the X- axis.
- Find area between two curves.
- Find the index of income concentration.
- Find the future value of a continuous income stream.
- Find consumers’ and producers’ surplus.
- Find antiderivative using the technique of integration by parts.