Content of MATH 1350

Design and Content of the new Math 1350 Survey of Calculus (2012)

The new MATH 1350 Survey of Calculus was designed in 2012 to adhere to the Transfer Assurance Guides (TAGS) for Business Calculus provided by the University System of Ohio.

General information about TAGS can be found at the following link: (TAGS).
The specific list of TAGS requirements for Business Calculus can be found at the following link: (Business Calculus).

The 4-semester-hour MATH 1350 replaces the Introduction to Calculus sequence MATH 163A (4-quarter-hour) and MATH 163B (3-quarter-hour). The table below shows how MATH 163A/B and MATH 1350 cover the topics listed in the TAGS. In the table, the nineteen grey rows are the "essential learning outcomes" stipulated by the TAGS. The remaining eleven white rows are the "optional topics" from the TAGS.

Notice in the table that the old MATH 163A/B covered seventeen of the nineteen essential topics and nine of the eleven optionial topics. Also notice, however, that six of the essential topics were taught in MATH 163B. Since fewer than ten percent of the students who took MATH 163A went on to take MATH 163B, most students were taught only eleven of the nineteen essential topics. (For example, pre-Business students were only required to take Math 163A.)

The new MATH 1350 covers all nineteen essential topics and two of the eleven optional topics in a single course. All students will be taught all of the essential topics.

General Category	Learning Outcomes The symbol * (in the gray rows) denotes essential learning outcomes from the TAGS. The symbol ** (in the white rows) denotes optional topics from the TAGS.	163	1350
1. Demonstrate an understanding of limits and continuity.	1.01 Determine limits analytically, numerically and graphically including one-sided limits and limits at infinity.*	163A	1350
1. Demonstrate an understanding of limits and continuity.	1.02 Analyze the limit behavior of a function at a point in its domain to determine if the function is continuous at that point. Determine intervals in which a function is continuous. Analyze and classify the discontinuities of a function.*	163A	1350
2. Demonstrate an understanding of derivatives and the ability to compute derivatives.	2.01 Use the limit definition of the derivative to determine the existence and to find the derivative of a given function.*	163A	1350
	2.02 Find the derivative of a function by identifying and applying the appropriate derivative formula.*	163A	1350
	2.03 Find higher order derivatives.*	163A	1350
3. Understand the interpretation of derivatives and their applications in a business environment.	3.01 Interpret the derivative as a rate of change.*	163A	1350
	3.02 Find the slope of the tangent line to the graph of a function at a given point.*	163A	1350
	3.03 Use the first derivative to determine intervals on which the graph of a function is increasing or decreasing and to determine critical points of the function.*	163A	1350
	3.04 Use the second derivative to determine intervals on which the graph of a function is concave upwards or concave downwards and to determine points of inflection.*	163A	1350
	3.05 Find and classify relative extrema and, on a closed interval, absolute extrema of a function.*	163A	1350
	3.06 Solve applied problems including marginal analysis applications.*	163A	1350
	3.07 Explain the relationship between marginal cost and average cost.*		1350
	3.08 Determine and discuss the elasticity of demand for a product.**
4. Understand the concept of integration and demonstrate ability to find indefinite and definite integrals and apply those results to the business setting.	4.01 Construct antiderivates analytically.*	163B	1350
	4.02 Find indefinite integrals using integration formulas and the method of substitution.*	163B	1350
	4.03 Find indefinite integrals using integration by parts.**	163B
	4.04 Identify definite integrals of functions as the areas of regions between the graph of the function and the x-axis.*	163B	1350
	4.05 Estimate the numerical value of a definite integral using a Riemann sum.**	163B	1350
	4.06 Understand and use the Fundamental Theorem of Calculus to evaluate definite integrals.*	163B	1350
	4.07 Use definite integrals to calculate the area of the region under a curve and the area of the region between two curves.*	163B	1350
	4.08 Determine present value and future value for an investment with interest compounded continuously.*	163B	1350
	4.09 Determine the average value of a function on an interval.**	163B	1350
	4.10 For given supply and demand functions find and interpret the consumer's surplus and the producer's surplus.*		1350
5. Demonstrate an understanding of functions of two variables	5.01 Find the domain of a function of two variables.**	163B
	5.02 Interpret contour diagrams for functions of two variables.**
	5.03 Compute partial derivatives of functions of two variables algebraically.**	163B
	5.04 Determine critical points for functions of two variables.**	163B
	5.05 Use the second derivative test to determine the nature of critical points of a function of two variables.**	163B
	5.06 Use the method of Lagrange multipliers to determine extreme values of functions of two variables subject to constraints.**	163B
	5.07 Solve applied problems involving the Cobb-Douglas production functions.**	163B

(page maintained by Mark Barsamian, last updated January, 2021)