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Discipline: MathematicsSub-discipline:General Course Title: Single Variable Calculus I Late TranscendentalsMin. Units 4 semesterGeneral Course Description: A first course in differential and integral calculus of a single variable: functions; limits and continuity; techniques and applications of differentiation and integration; Fundamental Theorem of Calculus. Primarily for Science, Technology, Engineering & Math Majors.
Number: Math 211 (from TCSU, CAN 18)Suffix: Any rationale or comment
Required Prerequisites or Co-Requisites
Prerequisite: Precalculus, or college algebra and trigonometry, or equivalent.
Advisories/Recommended Preparation
Course Content:
1. Definition and computation of limits using numerical, graphical, and algebraic approaches
2. Continuity and differentiability of functions
3. Derivative as a limit
4. Interpretation of the derivative as: slope of tangent line, a rate of change
5. Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule
6. Derivatives of trigonometric functions
7. Implicit differentiation with applications, and differentiation of inverse functions
8. Higher-order derivatives
9. Graphing functions using first and second derivatives, concavity and asymptotes
10. Maximum and minimum values, and optimization
11. Mean Value Theorem
12. Antiderivatives and indefinite integrals
13. Applications of integration to areas and volumes
14. Definite integral; Riemann sum
15. Properties of the integral
16. Fundamental Theorem of Calculus
17. Integration by substitution
Laboratory Activities: (if applicable)
Course Objectives: At the conclusion of this course, the student should be able to:
1. Compute the limit of a function at a real number;
2. Determine if a function is continuous at a real number;
3. Find the derivative of a function as a limit;
4. Find the equation of a tangent line to a function;
5. Compute derivatives using differentiation formulas;
6. Use differentiation to solve applications such as related rate problems and optimization problems;
7. Use implicit differentiation;
8. Graph functions using methods of calculus;
9. Evaluate a definite integral as a limit;
10. Evaluate integrals using the Fundamental Theorem of Calculus; and
Use the definite integral to find areas and volumes
Methods of Evaluation:
Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.
Sample Textbooks, Manuals, or Other Support Materials
A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.
FDRG Lead Signature: Date: [For Office Use Only] Internal Tracking NumberDescriptor Guide Sheet
Discipline: The discipline has been determined and is entered.
Subdiscipline: You may decide that a sub-discipline will serve your discipline best. For example, biology faculty may or may not decide to identify subdivisions (cellular vs. organismic, or marine, or ecology/environmental). Discipline faculty will determine what best serves their needs.
General Course Title: Insert a course name in this field that is generally used and will be widely recognized. It need not be the actual course title at all colleges or universities but should describe the topic of the course.
Minimum Units: Indicate the minimum number of units expected of this course, based on semester configuration; we will later offer a conversion into quarter units.
Proposed Number: Use the numbering protocol to assign a tentative number to the course; like the sub-discipline or general course title, during your drafting stages, this number can be changed.
Proposed Suffix: If desirable, add an L after the number in the box to indicate a lab; or an S to indicate this course is part of a sequence.
Rationale or Comment: Use this space to provide explanation to the field about the number; during the drafting stage, you may also use this space to record a request for an additional suffix or modification of the numbering protocol.
Required Prerequisites or Co-Requisites: List any courses required to be completed prior to taking the listed course; if there is not agreement among segmental faculty about the prerequisites, you might consider describing a similar course without those prerequisites or listing only Advisories/Recommended Preparation (see below). A co-requisite does not mean in the CCCs what it may mean for the 4-year institutions.
Advisories/Recommended Preparation: These recommendations for courses, experiences, or preparation need not be validated; they can be good-faith and generally accepted recommendations from discipline faculty that further the students chances of success in this or subsequent courses.
Course Content: Count content should list all the expected and essential topics of the course. If this course is a lab/lecture combination, the Lab content should be spelled out separately.
Course Objectives: List the course objectives, competencies, or skills that the students should be able to demonstrate upon completion of the course. Community college faculty should be attentive to explicitly linking the objectives to the topics covered. If this course is a lab/lecture combination, again the learning objectives should be spelled out separately and be linked to the topics covered in the lab component of the course. Use additional sheets as needed.
Methods of Evaluation: List those methods you anticipate would be used to observe or measure the students achievement of course objectives (e.g., quizzes, exams, laboratory work, field journals, projects, research, demonstrations, etc.)
Textbooks: Recent (published within the past 5-6 years) college-level texts, materials, software packages can be suggested here. While texts used by individual institutions and even individual sections will vary, enter examples of representative work. If this is a lab course or a lab/lecture section, remember to include an example of a lab manual.
FDRG Leads Signature and Date: When the descriptor template has been finalized by the FDRG is in final form and is ready for posting, the Lead should send this completed and signed document to Katey Lewis at HYPERLINK "mailto:Katey@asccc.org" Katey@asccc.org who will post the descriptor and solicit review and comment prior to finalizing the descriptor for the next phase of the C-ID Project.
Prerequisite or co-requisite course need to be validated at the CCC level in accordance with Title 5 regulations; co-requisites for CCCs are the linked courses that must be taken at the same time as the primary or target course.
Advisories or recommended preparation will not require validation but are recommendations to be considered by the student prior to enrolling.
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