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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
- Find the slope between two points and of a line.
- Estimate the limit of algebraic and trigonometric functions using tables and graphs.
- Find the limit of algebraic or trigonometric functions using algebra (cancellation and rationalization).
- Determine when the limit of a function does not exist.
- Finding one-sided limits.
- Using the definition of continuity, determine whether an algebraic function is continuous.
- For functions that are discontinuous, determine whether the function has removable or non-removable discontinuity. II. Differentiation
- Find the derivative of an algebraic function by finding the limit of the secant line.
- Determine where an algebraic function is differentiable.
- Find the derivative of algebraic and trigonometric functions using basic rules, the product rule, and the quotient rule.
- Find the second and third (higher) derivative of a function.
- Find the derivative of composite algebraic and trigonometric function using the chain rule.
- Determine whether a function is written in implicit or explicit form.
- Find the derivative of a function using implicit differentiation. III. Applications of the Derivative
- Find a related rate.
- Use related rates to solve real-world problems.
- Find a critical number of a function.
- Find the extrema on a closed interval using the first derivative.
- Apply Rolle’s Theorem in order to find all values of c in an open interval such that f^ (^ c)= 0.
- 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.
- Determine the intervals on which a function is increasing or decreasing.
- Apply the First Derivative Test to find relative extrema of a function.
- Determine intervals on which a function is concave upward or concave downward.
MATH 161 – CALCULUS I
STUDENT LEARNING OUTCOMES (continued)
- Find any points of inflection of the graph of a function.
- Apply the Second Derivative Test to find relative extrema of a function.
- Determine limits (finite and infinite) at infinity.
- Determine horizontal asymptotes, if any, of the graph of a function.
- Analyze and sketch the graph of a function.
- Solve applied minimum and maximum problems.
- Approximate a zero of a function using Newton’s Method.
- Find the tangent line approximation of a function.
- Compare the value of the differential, dy, with the actual change in y.
- Find the differential of a function using differentiation formulas. IV. Antidifferentiation
- Write the general solution of a differential equation.
- Find indefinite integral for antiderivatives.
- Use basic integration rules, including u-substitution, to find antiderivatives.
- Use Sigma Notation to write and evaluate a sum.
- Approximate the area of a plane region using Riemann Sums.
- Find the area of a plane region using limits.
- Evaluate a definite integral using limits.
- Evaluate a definite integral using properties of definite integrals.
- Find the area under a curve using the Fundamental Theorem of Calculus.
- Find the average value of function using the Mean Value Theorem for Integrals.
- 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
- 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
- Describe asymptotic behavior in terms of limits involving infinity E. Curve Sketching F. Max/Min Problems
- 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