MATH 171: Calculus and Analytic Geometry I
Prerequisites: One of the following:
1) A grade of C or better in MATH 138 or another approved college-level precalculus course including some trigonometry.
2) A passing score on a placement exam approved by the department of Mathematics and Statistics.
Credit hours: (4)
This course lays the foundational concepts of calculus: the limit, differentiation and integration. It includes techniques for finding limits, derivatives and integrals of algebraic functions, exponential, logarithmic, trigonometric, and inverse funtions. Applications of the derivative include curve sketching, velocity and acceleration, optimization, and L'Hopital's Rule. Integration includes the area under a curve and the Fundamental Theorem of Calculus. This course has been approved for credit in the Mathematical Sciences Area of the CORE Curriculum. Students may not receive credit for both MATH 171 and the sequence MATH 168:169 and may not receive credit for both MATH 171 and MATH 151.
Detailed Description of Course
The following topics will be covered for algebraic, exponential, logarithmic, trigonometric, and inverse functions:
1) The concept of the limit of a function, including one-sided limites, infinite limits, and limits at infinity
2) Techniques for evaluating limits
3) Continuity of a function
4) The definition of the derivative of a function, tangent lines, and rates of change
5) Differentiation of techniques, including the Power Rule, Product Rule, quotient Rule, and Chain Rule
6) Implicit differentiation and logarithmic differentiation
7) Differentiation of an inverse function
8) Curve sketching including asymptoms, intervals of increase and decrease, concavity, relative extrema, and points of inflection
9) The Mean Value Theorem and Rolle's Theorem
10) Applications of the derivative, including velocity and acceleration, optimization, and related rates.
11) L'Hopital's Rule
12) Antidifferentiation and the indefinite integral
13) Sigma notation, Riemann sums, area under a curve, and the definite integral
14) The Fundamental Theorem of Calculus
15) Antidifferentiation with substitution
16) Average value of a function
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:
1) Interpret relationships among numeric, symbolic and graphical information as applied to the real world;
2) Solve problems using numeric, symbolic and graphical information
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. Students may not receive credit for both MATH 171 and the sequence MATH 168:169 and may not receive credit for both MATH 171 and MATH 151.
Review and Approval
November 2, 2017