Arts and Support Service - Calculus I - Lab | MATH 161, Lab Reports of Calculus

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STATE UNIVERSITY OF NEW YORK

COLLEGE OF TECHNOLOGY

CANTON, NY

COURSE OUTLINE

MATH 161 – CALCULUS I

Prepared by: MARY GFELLER SCHOOL OF LIBERAL ARTS & SUPPORT SERVICES DEPARTMENT OF MATHEMATICS MAY 2006

MATH 161—CALCULUS I

A. TITLE: Calculus I B. COURSE NUMBER: MATH 161 SHORT TITLE: Calculus I C. CREDIT HOURS: 4 D. WRITING INTENSIVE (OPTIONAL): N/A E. COURSE LENGTH: 15 weeks F. SEMESTERS OFFERED: Fall semester G. HOURS OF LECUTRE, LABORATORY, RECITATION, TUTORIAL, ACTIVITY: This course will consist of four 50-minute lecture/recitation/computer lab H. CATALOGUE DESCRIPTION: This course is the first of a three-semester sequence of Calculus courses developed for students in Engineering Science who expect to transfer to a four-year engineering college upon completion of the program. Other qualified students may also take this sequence. Topics include: Quick review of functions and graphs; limit and continuity; the derivative and its properties; differentiation of algebraic and transcendental functions; curve sketching; related rates; applied extrema problems; other applications of differentiation; numerical methods; antidifferentiation. Four hour lecture per week. I. PRE-REQUISITES/CO-REQUISITES: College Algebra (MATH 121) with indication of strength, or Course III with a 4th^ year of high school mathematics, or at least 75 on Test B or permission of instructor. Recommended: College Trigonometry (MATH 131). J. GOALS (STUDENT LEARNING OUTCOMES): see attached. K. TEXTS: Members of the Mathematics Department who will be teaching the course will select the appropriate text. Audio-visual aids and computer software will be used when appropriate and available. L. REFERENCES: None M. EQUIPMENT: Smart classroom (Computer projection and access to the Internet)

MATH 161 – CALCULUS I

STUDENT LEARNING OUTCOMES

Students will be able to: I. Functions and Limits

1. Find the slope between two points and of a line.
2. Estimate the limit of algebraic and trigonometric functions using tables and graphs.
3. Find the limit of algebraic or trigonometric functions using algebra (cancellation and rationalization).
4. Determine when the limit of a function does not exist.
5. Finding one-sided limits.
6. Using the definition of continuity, determine whether an algebraic function is continuous.
7. For functions that are discontinuous, determine whether the function has removable or non-removable discontinuity. II. Differentiation
8. Find the derivative of an algebraic function by finding the limit of the secant line.
9. Determine where an algebraic function is differentiable.
10. Find the derivative of algebraic and trigonometric functions using basic rules, the product rule, and the quotient rule.
11. Find the second and third (higher) derivative of a function.
12. Find the derivative of composite algebraic and trigonometric function using the chain rule.
13. Determine whether a function is written in implicit or explicit form.
14. Find the derivative of a function using implicit differentiation. III. Applications of the Derivative
15. Find a related rate.
16. Use related rates to solve real-world problems.
17. Find a critical number of a function.
18. Find the extrema on a closed interval using the first derivative.
19. Apply Rolle’s Theorem in order to find all values of c in an open interval such that f^ (^ c)= 0.
20. Apply the Mean Value theorem to find the all values of c in an open interval such that (c, f(c)) is on the tangent line at x = c.
21. Determine the intervals on which a function is increasing or decreasing.
22. Apply the First Derivative Test to find relative extrema of a function.
23. Determine intervals on which a function is concave upward or concave downward.

MATH 161 – CALCULUS I

STUDENT LEARNING OUTCOMES (continued)

10. Find any points of inflection of the graph of a function.
11. Apply the Second Derivative Test to find relative extrema of a function.
12. Determine limits (finite and infinite) at infinity.
13. Determine horizontal asymptotes, if any, of the graph of a function.
14. Analyze and sketch the graph of a function.
15. Solve applied minimum and maximum problems.
16. Approximate a zero of a function using Newton’s Method.
17. Find the tangent line approximation of a function.
18. Compare the value of the differential, dy, with the actual change in y.
19. Find the differential of a function using differentiation formulas. IV. Antidifferentiation
20. Write the general solution of a differential equation.
21. Find indefinite integral for antiderivatives.
22. Use basic integration rules, including u-substitution, to find antiderivatives.
23. Use Sigma Notation to write and evaluate a sum.
24. Approximate the area of a plane region using Riemann Sums.
25. Find the area of a plane region using limits.
26. Evaluate a definite integral using limits.
27. Evaluate a definite integral using properties of definite integrals.
28. Find the area under a curve using the Fundamental Theorem of Calculus.
29. Find the average value of function using the Mean Value Theorem for Integrals.
30. Find the area under the curve using the Trapezoidal Rule and Simpson’s Rule.

MATH 161 – CALCULUS I

DETAILED OUTLINE (continued) III. Applications of the Derivative A. Related Rates B. Critical Points, Extrema, and Inflection Points

1. Know corresponding characteristics of the graphs of f, f , and f 

C. Concavity

1. Points of inflection as places where concavity changes

2. The relationship between the concavity of f and the sign of f 

D. Limits at Infinity and Asymptotic Behavior

1. Describe asymptotic behavior in terms of limits involving infinity E. Curve Sketching F. Max/Min Problems
2. Optimization involving area of rectangle and business problems G. Newton’s Method H. The Differential IV. Antidifferentiation A. Indefinite Integrals B. Basic Integration Rules C. Area Under a Curve using Riemann Sums D. Fundamental Theorem of Calculus E. Numerical Integration