Mathematics 168
MATH 168: Calculus I with Integrated Precalculus I (GE)
Prerequisites: Either 1) a grade of C or better in MATH 125, or 2) a passing score on a placement exam approved by the Department of Mathematics and Statistics.
Credit hours: (3)
The sequence MATH 168: MATH 169 covers the topics covered in MATH 171 but also includes topics from algebra and trigonometry that MATH 171 assumes as prerequisite. MATH 168 covers limits and derivatives of algebraic, exponential, and logarithmic functions and applications of the derivative, including curve sketching, velocity and acceleration, optimization, and related rates.
Note(s): General Education and Scientific and Quantitative Reasoning designated course. Students with credit for MATH 138 or MATH 171 may not receive credit for MATH 168.
Detailed Description of Course
This course will cover the following topics:
1.Review of functions, including domain and range, graphs, and transformations
2.Review of linear, quadratic, polynomial, algebraic, and rational functions
3.The concept of the limit of a function, including one-sided limits, infinite limits, limits at infinity, and asymptotes
4.Techniques for evaluating limits
5.Continuity of a function
6.The definition of the derivative of a function, tangent lines, and rates of change
7.Differentiation techniques
a.Power Rule
b.Product Rule
c.Quotient Rule
d.Chain Rule
e.Implicit differentiation
8.Curve sketching including asymptotes, intervals of increase and decrease, concavity, relative extrema, and points of inflection
9.The Mean Value Theorem and Rolle's Theorem
10.Inverse functions and their derivatives
11.Limits and derivatives of exponential and logarithmic function
12.Applications of the derivative, including velocity and acceleration and optimization, and related rates.
Detailed Description of Conduct of Course
Instructors will use a combination of lectures, group work and computer laboratory sessions. Some may require students to present homework problems to the rest of the class on a regular basis. Software packages and graphing utilities will be used on solving problems and as illustrative aids.
Student Goals and Objectives of the Course
Students are expected to learn the basic principles of Calculus and Analytic Geometry and to demonstrate the use of these principles in problem solving. In addition to paper and pencil problem solving, students will use appropriate graphing calculator and computer algebra system technology.
Students will be able to use the tools of mathematics and quantitative reasoning to conceptualize and solve problems.
Students will be able to:
a.interpret relationships among numeric, symbolic, and graphical information as applied to the real world.
b.solve problems using numeric, symbolic, and graphical information.
Assessment Measures
Graded tasks may include tests, quizzes, homework exercises, papers, class participation and attendance. Students will be required to demonstrate literacy in the use of mathematical software packages and/or graphing calculators as effective tools in problem solving.
Other Course Information
This course is primarily intended for freshman and sophomore students, especially those majoring in mathematics, computer science, the natural sciences, psychology, or economics who need to take Calculus I but are not placed into MATH 171. Students may not receive credit for both MATH 168 and either MATH 171 or MATH 151.
Review and Approval
November 2, 2017
March 01, 2021