MTH230 Calculus

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.

Review All Topics From Weeks One through Five.

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.

• 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.

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.
• Apply 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, rules of integration, and Tangent of a Function.
• Summarize the Product and Quotient Rules of Integration.

Review All Topics From Weeks One Through Ten.