Learning Outcomes for Math 1350 Survey of Calculus
Concepts Covered in Chapter 2 and 3 of Our Textbook
- Find limits analytically, numerically and graphically including one-sided limits and limits at infinity.*
- 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.*
- Find the derivative of a function using the limit definition.*
- Find the derivative of a function by identifying and applying the appropriate derivative formula.*
- Understand the interpretation of the derivative as the slope of a line tangent to a graph and as a rate of change.*
- Understand the business terminology of demand, cost, price, revenue, and profit, and solve applied problems including marginal analysis applications. Explain the relationship between marginal cost and average cost.*
Concepts Covered in Chapter 4 of Our Textbook
- Find higher order derivatives of a function.*
- 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.*
- 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.*
- Find and classify relative extrema of a function.*
- Find the absolute extrema of a continuous function on a closed interval.*
Concepts Covered in Chapter 5 and 6 of Our Textbook
- Find antiderivatives and indefinite integrals using integration formulas and the method of substitution*
- Identify definite integrals of functions as the areas of regions between the graph of the function and the x-axis.*
- Estimate the numerical value of a definite integral using a Riemann sum.**
- Use the Fundamental Theorem of Calculus to evaluate definite integrals.*
- Use definite integrals to calculate the area of the region under a curve and the area of the region between two curves.*
- Use definite integrals to calculate the average value of a function on an integral.**
- Find present value and future value for an investment with interest compounded continuously.*
- 4.10 For given supply and demand functions, find and interpret the consumer's surplus and the producer's surplus.*