## Course Content and Outcome Guide for MTH 251

- Course Number:
- MTH 251
- Course Title:
- Calculus I
- Credit Hours:
- 4
- Lecture Hours:
- 30
- Lecture/Lab Hours:
- 0
- Lab Hours:
- 30
- Special Fee:

#### Course Description

Includes limits, continuity, derivatives and applications of derivatives. Graphing calculator required. TI-89 Titanium or Casio Classpad 330 recommended. Prerequisites: MTH 112 or CMET 131; and their prerequisite requirements. Audit available.#### Addendum to Course Description

This is the first course of four courses in the Calculus sequence. Lab time shall be used by students to work on group activities - the activities to be used during lab are on the mathematics department home page.

#### Intended Outcomes for the course

Upon successful completion students should be able to:

• Analyze real world scenarios to recognize when derivatives and limits are appropriate, formulate problems about the scenarios, creatively model these scenarios (using technology, if appropriate) in order to solve the problems using multiple approaches, judge if the results are reasonable, and then interpret and clearly communicate the results.

• Appreciate derivatives and limit-related concepts that are encountered in the real world, understand and be able to communicate the underlying mathematics involved to help another person gain insight into the situation.

• Work with derivatives and limits in various situations and use correct mathematical terminology, notation, and symbolic processes in order to engage in work, study, and conversation on topics involving derivatives and limits with colleagues in the field of mathematics, science or engineering.

• Enjoy a life enriched by exposure to Calculus.

#### Course Activities and Design

#### Outcome Assessment Strategies

- at least two in-class exams, one of which is a comprehensive final
- proctored exams should be worth at least 50% of the overall grade
- a closed book/closed note/no technology exam over derivative formulae
- laboratory reports (graded homework with an emphasis on proper notation and proper documentation) ,

- Take-home examinations
- Quizzes
- Attendance

- A team project with a written report and/or in-class presentation
- Participation in discussions
- In-class group activities

#### Course Content (Themes, Concepts, Issues and Skills)

__Context Specific Skills__

- Students will learn to evaluate limits graphically, numerically, and symbolically.
- Students will learn the formal definition of the first derivative and find algebraic derivative using both this definition and the traditional shortcut formulas associated with derivatives.
- Students will learn to learn and apply the relationships between functional behavior and first and second derivative behaviors.
- Students will learn to model and solve several types of applications using derivatives.

__Learning Process Skills__

- Classroom activities will include lecture/discussion and group work.
- Students will communicate their results in oral and written form.
- Students will apply concepts to real world problems.
- The use of calculators and/or computers will be demonstrated and encouraged by the instructor where appropriate. Technology will be used (at least) when graphing curves and estimating limits.

**COMPETENCIES AND SKILLS**

**REQUIRED STUDENT COMPETENCIES:**

**1 Limits and Continuity**

**2 The Derivative**

**3 Symbolic Differentiation**

**4 APPLICATIONS OF THE DERIVATIVE**

**Documentation Standards for Mathematics**

- Every solution must be written in such a way that the question that was asked is clear
*simply by reading the submitted solution*. - Any table or graph that appears in the original problem
*must*also appear*somewhere*in your solution. - All graphs that appear in your solution
*must*contain axis names and scales. All graphs must be accompanied by a figure number and caption. When the graph is referenced in your written work, the reference must be by figure number. Additionally, graphs for applied problems must have units on each axis and the explicit meaning of each axis must be self-apparent either by the axis names or by the figure caption. - All tables that appear in your solution
*must*have well defined column headings as well as an assigned table number accompanied by a brief caption (description). When the table is referenced in your written work, the reference must be by table number. - A brief introduction to the problem is almost always appropriate.
- In applied problems, all variables and constants
*must*be defined. - If you used the graph or table feature of your calculator in the problem solving process, you
*must*include the graph or table in your written solution. - If you used some other non-trivial feature of your calculator (e.g., SOLVER), you must state this in your solution.
- All (relevant) information given in the problem
*must*be stated somewhere in your solution. - A sentence that orients the reader to the
*purpose*of the mathematics should usually*precede*symbol pushing. - Your conclusion
*shall not*be encased in a box, but rather stated at the end of your solution in complete sentence form. - Remember to line up your equal signs.
- If work is word-processed
**all**mathematical symbols must be generated with a math equation editor.