Calculus

Course Description

This course demonstrates and examines various concepts of differential calculus. It assists in understanding the basic concepts of differential calculus. These concepts are used to apply differential calculus in business, economics, and science coursework. Applications to real-world problems are emphasized throughout the course. Specific applications to disciplines such as statistics, accounting, finance, and economics are included in this course. A variety of other applications, such as geometry, personal finance, science, and engineering are also presented.

Topics and Objectives

Calculus as an Object Oriented Math

• Develop an understanding of a mathematical function as an object
• Differentiate the form of various functions and their graphs.
• Explain basic concepts of slope, tangent, asymptote, and limit.
• Use binomial expansion to compute derivative of a function.

Limit of a Function as an Object

• Identify the right and the left limit of a function at a given point.
• Define the discontinuity of a function at a given point.
• Compute the derivatives of linear, quadratic, and polynomial functions.

Derivative as an object

• Solve various applied problems by using derivatives.
• Graph the first derivative of various functions and find their root.
• Compute the derivatives of rational, exponential, logarithmic, and radical functions.

Computing Derivatives of Mixed Functions

• Find the derivative of the sum and difference of two functions.
• Find the derivative of the ratio and the product of two functions.
• Find the derivative of the composition of two functions.

Summarize the Basic Concepts of Differential Calculus

• Summarize the Concepts of Continuity, Rate, Limit, Derivative, Tangent of a Function.
• Summarize the Product and Quotient Rules of Differentiations.

Integration as an area under a curve

• Define an area under a curve as an integral of a function.
• Evaluate definite integrals.
• Apply product, quotient, and chain rules to compute integrals of various functions.
• Use integral calculus to solve applied problems.
• Use definite integrals to compute the area bounded by two curves.

Application of integral calculus in business and economics

• Apply integral calculus in business and economics.
• Define probability density functions.
• Compute the expected value for a given density function.
• Use the integral of density functions to solve applied problems.

Numerical Integration

• Compute the probabilities by using the uniform, exponential, normal density functions.
• Apply numerical integration to evaluate definite integrals.
• Use numerical integration built in Excel function to compute integrals of various density functions, and answer applied probability questions.

Summarize the Basic Concepts of Integral Calculus

• Summarize the Concepts of Infinite Sum, Integral, and Rules of Integration.
• Summarize the Product and Quotient Rules of Integration.