MATHS 165: Calculus 1 (4)

Syllabus

 

1.    Prerequisites:  Maths 111 and 112; or sufficient background in algebra and trigonometry as evidenced by the student’s high school record, SAT/ACT scores, and/or score on the Mathematics Placement Test.

 

2.     Course Description: MATHS 165 Calculus 1 (4 credit hours). Differential calculus of algebraic and transcendental functions and applications, antidifferentiation and the Riemann integral.  The course includes the use of graphing calculators and computer software. 

 

3.    Course Objectives:  MATHS 165 serves as an introduction to the subject of calculus.  The student is expected to master the manipulation of mathematical symbols and gain an understanding and appreciation of mathematical thinking.  These tools are used to give the student a new way of looking at today’s world at a collegiate level. Calculus provides a framework to propel oneself  from a static view of the world to a more dynamic model, opening up a much wider array of scenarios and associated problem solving techniques.  Often this work is most effectively achieved in a cooperative environment. Applications to a wide variety of fields are stressed to enhance the student's appreciation and ability to apply the techniques of calculus to solve problems in the real world.

 

4.    Course Rationale: Calculus is a primary foundation of collegiate and higher mathematics.  It is essential that every serious student of mathematics have a solid basis for further study in the field.  Although some students will come to Ball State with an adequate calculus background from high school, most students planning to major in mathematics, engineering, physics, chemistry or a related subject need this sequence.  (Those students who have successfully completed an Advanced Placement (AP) calculus course or other sufficiently rigorous high school calculus course may qualify to begin in a subsequent calculus course.)

 

• MATHS 165 provides a thorough introduction to the ideas of differential and integral calculus which provide the mathematical foundation for much of modern science and technology.  Students will learn to use the formal language of calculus to give precise expression to a range of real-world problems. They will also conquer the mechanics of calculus that enable one to progress from a careful mathematical statement of a problem to its solution.

 

• Differential calculus addresses the difficulties of dealing with “changing rates of change.”  Important and useful rates of change abound.  For instance, speed and inflation rates are rates of change in distance and market basket costs, respectively, over time.  Though it is an easy matter to compute the average speed for a hour-long trip or the average interest rate over a month,  it is more difficult to decide what the speed or inflation rate is at a given instant.  Problems in physics or economics are relatively easy when speeds or inflation rates never change. This, however, is not life as we know it.  We are forced to deal with rates of change that are continuously changing.

 

• The derivative of a function is the instantaneous rate of change in that function.  For instance, the derivative of a distance function represents instantaneous velocity.  Learning to express rates as derivatives and conquering the mechanical manipulation of derivatives enables one to solve a wide range of problems.  Just as a ball thrown straight up into the air reaches it highest point when its velocity is zero, a function achieves its greatest value when its derivative is zero. This is the central idea used in solving a wide range of important optimization problems.

 

• Integral calculus deals with how quantities accumulate. If you travel at a fixed speed for a given amount of time, it is easy to determine how far you have traveled. But, if your speed is continually changing can you figure out how far you have traveled?  Similarly, if interest rates have varied over the past year, can you determine how your money has accumulated?  The same ideas that allow you to solve these problems also enable you to find volumes of curved figures or the amount of work required to boost a rocket into orbit.  The definite integral, which is used to solve these problems,  is the second area of focus in MATHS 165.

 

5.                 Course Content:  The topics to be covered are listed in the course description. They constitute the standard first semester calculus course offered by nearly every college and university. The students are expected to attend class regularly and to study the material and examples in the text as well as those presented in class.

 

It is expected that the student will master and utilize a graphing calculator and the computer algebra system Mathematica. Relevant portions of the Departmental Mathematica Tutorial will be incorporated into the course.  Additional applications of Mathematica will be included.  The program Mathematica, as well as the Departmental Mathematica Tutorial and sample Mathematica labs, are available on any Departmental lab computer. 

 

Also, this course satisfies the University Core Curriculum requirement in mathematics. It addresses the following overall and foundational Goals of the University Core Curriculum Program.  These goals, in ranked order, are:

 

Overall Goals:

 

1.          To recognize the common problems of living by drawing on knowledge of historical and contemporary events and the cultural heritage related to these events.

 

Operationalized:  To recognize problems that often arise in areas such as mathematics, natural sciences, and industry by using the theory and techniques of introductory calculus.

 

2.          To solve  the common problems of living by drawing on knowledge of historical and contemporary events and the cultural heritage related to these events.

 

Operationalized: To solve problems that often arise in areas such as mathematics, natural sciences, and industry by using the theory and techniques of introductory calculus.

 

3.          To communicate at a level acceptable for college graduates.

 

Operationalized: To use the language and notation of calculus at a level acceptable for college graduates.

 

 

Foundational Goals: 

 

1.          To provide basic academic and intellectual tools, especially the ability to communicate.

 

Operationalized: To provide a thorough introduction to the ideas of differential and integral calculus, which form an important part of the intellectual tools used in modern science and technology. Students will learn to use the formal language of calculus to give precise expression to a range of real-world problems.

 

2.          To provide a basic understanding of civilization.

 

Operationalized: To become familiar with both the pragmatic and the aesthetic impact calculus has had on our civilization.

 

5.                    Course Format: Lecture/discussion.

 

6.                    Method of Evaluating Student Performance:  Typical components are homework assignments, projects, in-class exams, and student presentations. The evaluation and weight of these components are at the discretion of the instructor. Students may be evaluated on their understanding of the content material for the course, their ability to solve problems related to the course material, and on their ability to communicate mathematically to others verbally or in writing.

 

 

7.                    Evaluation of the Course:  The instruction of the course is evaluated by departmental student evaluations and peer evaluation. The course is reviewed and revised periodically by the Departmental Undergraduate Programs Committee. Assessment techniques used in evaluating the course may include student focus groups, pre-post tests on student attitudes and values of mathematics, and pre-post tests for problem solving.  Similar assessment techniques may be given to a sample group of students one year after completion of the course.  The department plans to work in conjunction with the University Core Curriculum Subcommittee and the Office of Academic Assessment to design the evaluation instruments, and to develop and implement the assessment process.

 

 

 

Last revised:  MAK, Fall 2005