Course Content and Outcome Guide for MTH 253
- Course Number:
- MTH 253
- Course Title:
- Calculus III
- Credit Hours:
- Lecture Hours:
- Lecture/Lab Hours:
- Lab Hours:
- Special Fee:
Course DescriptionIncludes infinite sequences and series (emphasis on Taylor series), an introduction to differential equations, and vectors in three space. Graphing calculator required. TI-89 Titanium or Casio Classpad 330 recommended. Prerequisites: MTH 252 and its prerequisite requirements. Audit available.
Addendum to Course Description
This is the third course of four courses in the Calculus sequence.
Intended Outcomes for the course
Upon completion of this course the learner should be able to do the following in the outside world:
¢ Appreciate elementary differential equation, vector, and series 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 elementary differential equations, vectors, and series in various situations and use correct mathematical terminology, notation, and symbolic processes in order to engage in work, study, and conversation on topics involving vectors and series with colleagues in the field of mathematics, science or engineering.
¢ Enjoy a life enriched by exposure to Calculus.
Outcome Assessment Strategies
- at least two proctored exams, one of which is a comprehensive final that is worth at least 25% of the overall grade
- proctored exams should be worth at least 60% of the overall grade
- at least one of the exams should require the use of technology
- Take-home examinations
- Graded homework problems
- 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)
- Students will learn to determine the convergence status of a given series.
- Students will learn estimation techniques for convergent series.
- Students will learn to model functions with Taylor series and use Taylor Series to solve application problems.
- Students will learn to model and solve several types of applications using vectors.
- Students will learn to recognize a differential equation, draw and read a slope field, and algebraic solve simple differential equations.
- 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 estimating convergent series.
The goal is to use vectors, in the plane and 3-space, to represent quantities that have direction as well as magnitude.
multiplication graphically and symbolically.
- 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.