MATH140 Calculus I
Department of Science, Technology, Engineering & Mathematics: Mathematics
Course Number and TitleMATH140 Calculus I
Number of Credits4 credits
Minimum Number of Instructional Minutes Per Semester3000 minutes
PrerequisitesMath Placement Test score of 11 or MATH125 (C or better)
Other Pertinent InformationAt least four one-hour tests, quizzes, and a two-hour comprehensive departmental final examination will be given.
Catalog Course DescriptionThis is the first course in the calculus sequence for physical science, business, computer science, mathematics, and engineering students. Topics include: limits, the rate of a function, derivatives of algebraic and basic trigonometric functions, applications of derivatives, integration, and applications of the definite integral.
Required Course Content and Direction
Learning Goals:Course Specific:
The student will be able to:
- demonstrate understanding of the concept of limit.
- evaluate limits.
- demonstrate understanding of the concept of continuity.
- evaluate derivatives of algebraic and trigonometric function.
- demonstrate correct use of implicit differentiation to find a derivative.
- apply concepts of differentiation to problems in curve sketching, related rates, straight line motion.
- apply concepts of differentiation to science, business, and economics.
- find indefinite integrals.
- solve elementary differential equations.
- apply the definition of the definite integral and its properties.
- evaluate definite integrals.
- accurately use the definite integral for applications, such as average value, areas, volumes of solids of revolution, length of plane curves.
Core Learning Goals:
Math or Science: The student will be able to:
- develop the ability to analyze, interpret, and apply quantitative information.
Core Learning Objectives:
Math or Science: The student will be able to:
- accurately translate descriptive problems into mathematical formulas and solve them. (1)
Critical Thinking/Problem Solving: The student will be able to:
- demonstrate an understanding of solving problems by:
- recognizing the problem
- reviewing information about the problem
- developing plausible solutions
- evaluating the results
These skills are developed in VII.B.3 and VII.B.5.
Planned Sequence of Topics and/or Learning Activities:The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lesions required to study the topic.
- Limits and Continuity (8 lessons)
- Geometric Interpretation of Limits
- Evaluating Limits
- Limit Theorems
- One-Sided Limits
- The Derivative (12 lessons)
- Geometric Interpretation - Tangent Line to a Curve
- Definition of Derivative
- Velocity, Acceleration, and Other Rates of Change
- Finding Derivatives, Using the Limit Definition
- Finding Derivatives, Using the Formulas
- Product and Quotient Rules
- Derivatives of Basic Trigonmetic Functions
- Chain Rule and Composite Functions
- Implicit Differentiation
- Higher Order Derivatives
- Applications of the Derivative (12 lessons)
- Straight Line Motion
- Related Rates
- Increasing and Decreasing Functions
- Relative and Absolute Extrema
- Concavity and Inflection Points
- 2nd Derivative Test
- Optimization Problems
- Integration (9 lessons)
- Indefinite Integrals
- Differential Equations
- Summation Notation
- Finding Areas and Definite Integrals by Definition
- Fundamental Theorem of Integral Calculus
- Properties of the Definite Integral
- Using Substitution to Evaluate Integrals
- Applications of Integration (7 lessons)
- Area Under a Curve
- Average Value of a Function
- Area Between Curves
- Volumes of Revolution - Disk and Shell Method
- Length of a Plane Curve
Assessment Methods for Core Learning Goals:All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students and, for the core, formal assessment open-ended questions reflecting theoretical and applied situations.
Reference, Resource, or Learning Materials to be used by Students:Departmentally selected textbook and graphing calculator. Details provided by the instructor of each course section. See Course Format.
Teaching Methods EmployedPrimary teaching methods are lecture, recitation, problem solving, and class discussion as appropriate.
Review/Approval Date - 3/06; Core Goals/Objectives added 12/04