MATH 170
Calculus I
4 semester credits
Catalog Description
MATH 170 CALCULUS I (4-0-4)(Area III). Definitions of limit, derivative, and integral. Computation of the derivative, including logarithmic, exponential and trigonometric functions. Applications of the derivative, approximations, optimization, mean value theorem. Fundamental theorem of calculus, brief introduction to the applications of the integral and to computations of antiderivatives. Intended for students in engineering, mathematics and the sciences.
Prerequisites
MATH 143 and MATH 144 or MATH 147 or satisfactory placement exam score. The mathematics placement examination covers the materials covered in our MATH 147 course and covered in the usual math analysis courses in local high schools. This algebraic material is the minimum needed to be able to solve and/or simplify the exercises which are used to demonstrate and apply calculus concepts. Students may also satisfy the prerequisite by a suitable score on the ACT or SAT examinations.
Jurisdiction
This course is governed by a department committee which determines the text, the pace and the emphasis of the course.
Learning Objectives
Our first semester calculus course has the usual objectives of a calculus course which is used by other disciplines on campus. As a service course taken primarily by non-majors, MATH170 stresses neither the aesthetic side of mathematics nor the idea that of mathematics as the study of patterns.
Through the course of the semester, successful students will be expected
Assessment of Learning Objectives
Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:
Core Outcomes
After successfully completing MATH170, students will be able to demonstrate the following competencies in order to fulfill specific requirements set by the Core Philosophy and Goals Statement:
Topics and approximate timetable
The following table is based on a typical semester schedule-60 class meetings of 50 minutes each. The actual time spent on each topic will vary slightly from semester to semester and instructor to instructor.
Text
The current text is University Calculus by Joel Hass, Maurice Weir and George Thomas, Addison-Wesley (2007). Other texts in recent years are Calculus, Early Transcendentals by James Stewart. Brooks/Cole Publishing Company, Calculus, Concepts and Contexts, James Stewart, Brooks/Cole and Calculus from Graphical, Numerical and Symbolic Points of View, Ostebee and Zorn, Saunders Publishing Company.
Format, Student Activities, and Grades
Class meetings involve a combination of lecture, questions and discussion and sometimes small group activities; the instructor chooses the appropriate mix. Homework is an important part of the course; some exercises may involve extensions of ideas in the text to new situations, rather than just routine applications. Some examinations may be partially take-home. The instructor chooses the exact grading scheme, but a typical distribution might be:
Letter grades are based on a scale in which 90% of the total possible
points guarantees an A, 80% a B, 70% a C, and 60% a D, with the
instructor having the discretion to lower these cut-offs if warranted.
Calculus I
4 semester credits
Catalog Description
MATH 170 CALCULUS I (4-0-4)(Area III). Definitions of limit, derivative, and integral. Computation of the derivative, including logarithmic, exponential and trigonometric functions. Applications of the derivative, approximations, optimization, mean value theorem. Fundamental theorem of calculus, brief introduction to the applications of the integral and to computations of antiderivatives. Intended for students in engineering, mathematics and the sciences.
Prerequisites
MATH 143 and MATH 144 or MATH 147 or satisfactory placement exam score. The mathematics placement examination covers the materials covered in our MATH 147 course and covered in the usual math analysis courses in local high schools. This algebraic material is the minimum needed to be able to solve and/or simplify the exercises which are used to demonstrate and apply calculus concepts. Students may also satisfy the prerequisite by a suitable score on the ACT or SAT examinations.
Jurisdiction
This course is governed by a department committee which determines the text, the pace and the emphasis of the course.
Learning Objectives
Our first semester calculus course has the usual objectives of a calculus course which is used by other disciplines on campus. As a service course taken primarily by non-majors, MATH170 stresses neither the aesthetic side of mathematics nor the idea that of mathematics as the study of patterns.
Through the course of the semester, successful students will be expected
- To develop an understanding of the derivative and how it can be used in solving problems.
- To understand the relationship between the derivative and the graph of a function.
- To be sufficiently practiced in basic algebra to set up and solve equations and inequalities involving functions and their derivatives.
- To recognize that the integral is an operator which can be approximated through Riemann sums and is (in a sense) an anti-derivative of the integrand.
- To have mastered the basic formulae for differentiation and integration.
Assessment of Learning Objectives
Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:
- Periodic problem sets for homework serve both as learning and assessment tools. Classroom activities may vary depending on students' performances on homework assignments.
- Problems given on in-class examinations are designed to give students the opportunity to demonstrate their ability to apply rules and formulae to the solution of simpler problems.
- Instructor-optional take-home examinations designed to evaluate the students ability to solve more complicated and time-consuming problems. These problems give students the opportunity to demonstrate their ability to use technology to solve problems that are not amenable to simple analytic techniques.
Core Outcomes
After successfully completing MATH170, students will be able to demonstrate the following competencies in order to fulfill specific requirements set by the Core Philosophy and Goals Statement:
- Critical Thinking/Problem Solving Skills
Clearly identify and analyze a problem, identify possible solutions and give the rationale for a preferred solution
Students will identify in homework and on tests their abilities in applying calculus theory and concepts to problems.
- Communication Skills
Write clearly
Students are expected to provide interpretations and explanations of their solutions to problems that are posed to them in class and on homework. Their grammar, sentence structure, punctuation and spelling are considered in the evaluation of their work.
- Cultural Perspective
Mathematics is a culturally independent discipline which is studied and advanced by people of all cultures, races, and nationalities. - Breadth of Knowledge and Intellectual Perspective
Articulate relevant basic assumptions, concepts, theoretical constructs, and factual information.
Throughout the course, students are expected to explain their assumptions and interpret their results in the theoretical framework of calculus.
Understand and apply relevant discipline-specific methodologies and strategies of inquiry.
Students will demonstrate their facility in applying techniques of calculus to problems designed to test their understanding of the concepts.
Topics and approximate timetable
The following table is based on a typical semester schedule-60 class meetings of 50 minutes each. The actual time spent on each topic will vary slightly from semester to semester and instructor to instructor.
| Limits and continuity | 10 |
| Derivative rules for polynomials and transcendental functions. | 15 |
| Implicit differentiation, related rates, and approximations | 8 |
| Applications of the derivative | 13 |
| Introduction to Riemann sums, integration and antidifferentiation. | 9 |
Text
The current text is University Calculus by Joel Hass, Maurice Weir and George Thomas, Addison-Wesley (2007). Other texts in recent years are Calculus, Early Transcendentals by James Stewart. Brooks/Cole Publishing Company, Calculus, Concepts and Contexts, James Stewart, Brooks/Cole and Calculus from Graphical, Numerical and Symbolic Points of View, Ostebee and Zorn, Saunders Publishing Company.
Format, Student Activities, and Grades
Class meetings involve a combination of lecture, questions and discussion and sometimes small group activities; the instructor chooses the appropriate mix. Homework is an important part of the course; some exercises may involve extensions of ideas in the text to new situations, rather than just routine applications. Some examinations may be partially take-home. The instructor chooses the exact grading scheme, but a typical distribution might be:
| Homework | 14% |
| 4 examinations | 56% |
| Final Examination | 30% |
| Total | 100% |
Updated 19 Aug 2005
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