Calculus
Using Microsoft Excelâ
Revathi Narasimhan
Kean University
Supplement to Calculus and its Applications and Brief Calculus with Applications, 10th Ed., by Goldstein, Lay and Schneider
Contents
Introduction 3
Scope of supplement 4
Integrating materials in class 5
To the student 6
Description of materials 7
References 11
Introduction
In any introductory mathematics course designed for non-mathematics majors, it is important for the student to understand and apply mathematical ideas in a variety of contexts. With the increased use of advanced software in all fields, it is also important for the student to effectively interact with the new technology. Our goal is to integrate these two objectives in a supplement for the texts Calculus and its Applications and Brief Calculus with Applications, by Goldstein, Lay and Schneider.
The package consists of interactive tutorials and projects in an Excel workbook format. The software platform used is the Microsoft Excel spreadsheet. It was chosen for the following reasons:
· suited to applications encountered in an applied calculus course
· widespread use outside of academia
· ease of creating reports with a professional look
Using a combination of specially designed projects and tutorials, students are able to analyze data, draw conclusions, and present their analysis in a professional format. The mathematical and computer skills learned with such an approach is an asset that they can carry with them to other courses as well as to their future places of employment.
In subsequent sections, we discuss the nature and scope of the supplement, its integration into a course, and descriptions of the projects and tutorials.
Scope of supplement
The package is divided into three portions - introduction to the software platform, interactive tutorials to reinforce ideas, and projects of more complexity.
Introduction to the software
Worksheets which contain just enough essentials about Excel to get the students started quickly have been written specifically for this course. The interactive nature of the worksheets lends itself to a quick learning curve so that the student can spend his or her time learning mathematics on Excel.
Tutorial worksheets
These worksheets illustrate a particular topic studied in calculus using the capabilities of Excel. These tutorials can be used as in-class activities in the course and can also be used as homework assignments. In addition to original problems in the tutorials, suitable problems from the text are also suggested. Instructors may find these tutorials helpful in designing lectures which incorporate computer presentations.
Projects
The project worksheets are more complex in scope and require a synthesis of the various topics covered in the course. Students are encouraged to work in groups and are required to turn in well formatted printouts using Excel and perhaps a word processor such as MS Word.
Integrating the materials in class
The topics chosen for the package were ones that would take full advantage of the capabilities of the spreadsheet software. The following objectives are stressed:
· algebraic, graphical, and tabular representation of equations and data
· exploratory experiments with data
· synthesis of mathematical ideas
· applications in a variety of contexts
· clear communication of results
The integration of mathematics, text, and graphics makes the spreadsheet highly suitable for problems which illustrate a particular concept rather than procedure. It is with this idea that the tutorials and projects in this package were created.
Prior knowledge of Excel is not required for use of this package. The introductory workbook discusses general features of Excel that students will need to master. All one has to do is to start up the software and open the intro.xls file. Other, more specific features are discussed as the need arises. It is advisable for the instructor to go through the tutorials and projects before making specific assignments for the students.
Students are encouraged to ask questions in class about their computer assignments. The questions related to the mathematical aspects of the projects are often discussed. Any particular technical issue involving the software is usually discussed with the student(s) outside of lecture.
Lectures involving computer and overhead presentations can benefit from many of the tutorials in the package. The content of the presentation should serve as a complement to the lecture. Examples of such presentations are numerical investigations of limits of functions and their derivatives. In our experience, short, to-the-point presentations tend to be more effective than those in which the presenter is working through multiple menu options, dialog boxes etc. Since the tutorials are available to the students, the presentation itself can be gone over by the student in his or her own time, thus reinforcing and expanding the ideas in the lecture.
A summary of the tutorials and projects is given at the end of this introduction to aid in planning a course syllabus integrating this package.
To the student
This collection of Excel tutorials and projects is intended to be a
supplement to your text, lecture, and homework. The way in which they will be incorporated in your syllabus will be determined by your instructor.
Before you begin any of the projects or tutorials, you should familiarize yourself with the Excel spreadsheet by going through the intro.xls workbook. It will contain enough material for you to get started. It is by no means an exhaustive reference to all the features of Excel. Other features will be introduced later as needed. You are encouraged to consult general references on Excel for additional information.
Whichever projects and tutorials are assigned, it is helpful to follow a few guidelines. Always print out and read through the worksheet to see what the main objective is. The tutorials are interactive; therefore you can enter data and do the assigned operations as you read. It is best to work on a copy of the Excel worksheets, keeping the original intact and stored elsewhere. Also, when doing problems assigned in the tutorial worksheets, it is best to do them on a empty workbook whose window is adjacent to the tutorial. Many of the tutorials are closely linked to the text. Therefore, it is important to refer to the text as well so that you can connect the material in this package to your lectures and regular homework.
The projects are more involved. Before you start the project on the computer, read through it and spend some time thinking about how you will approach your problem. Write an outline of the setup, tables, and functions which you will use. This is more efficient than simply starting to type at the computer right away. Over the course of working on the project, you will modify your work . This is expected and is normal. You will be asked not just to compute, but also to analyze and interpret your results. You should spend some time thinking about these issues as well. The final output should be of presentable quality and should be easy to understand.
If you encounter problems with the software while doing your work, you should consult the online help, which is very extensive. You should also look though the Troubleshooting worksheet in the intro.xls workbook. Some common errors and their fixes are listed here. Talk to your fellow students and consult your instructor. If all else fails, put is aside for a while and come back to it later to look at it in a new light.
Description of materials
All materials are in the form of Excel workbooks in MS Windows format. They should run on Excel 97/2000/XP and later versions under Windows 95/98/2000/XP. Each tutorial and project is in a separate worksheet within the corresponding workbook.
Some of the materials make use of tools which may not have been installed at your computer site at the time of software setup. These tools are the Solver and the Data Analysis Tools. If these do not appear as menu options under the Tools menu in Excel, you should have them installed through the setup program.
Introductory workbook Filename: intro.xls
In this workbook, basic concepts of Excel are introduced. An interactive tutorial is used to introduce concepts of formulas and graphs.
Chapter 0 Functions Filename: chap0.xls
Tutorial # / Title1 / Plotting Functions
2 / Polynomial Functions
3 / Rational Functions
4 / Power Functions
5 / Goal seeking using linear equations
6 / More Applications Using Goal Seek
Project # / Title
1 / Compound Interest
2 / Cost, Revenue, and Breaking Even
3 / Linear Depreciation
Chapter 1 The Derivative Filename: chap1.xls
Tutorial # / Title1 / Understanding slope: a depreciation model
2 / Numerically Investigating Limits
3 / Numerically Investigating Derivatives
4 / Derivative as a Rate of Change
Project # / Title
1 / Differentiability of the Absolute Value Function
2 / Velocity and Acceleration
3 / Minimal Average Cost
Chapter 2 Applications of the Derivative File: chap2.xls
Tutorial # / Title1 / Goal Seeking for Equations
2 / A Function and its Derivatives
3 / Optimization Problems using Goal Seek
Project # / Title
1 / Cost, Revenue, and Profit
2 / Pollutant Concentration
3 / Maximizing Profit
Chapter 4 Exponential and Natural Logarithm Functions File: chap4.xls
Tutorial # / Title1 / Exponential Functions
2 / Differentiation of Exponential Functions
3 / The Derivative of ln x
Project # / Title
1 / Graphs of Exponential Functions
2 / Analyzing Profit
3 / Population Growth
Chapter 5 Applications of the Exponential and Natural Logarithm Functions File: chap5.xls
Tutorial # / Title1 / Exponential Growth and Decay
2 / Calculation of Interest
3 / Applications in Economics
4 / Further Exponential Models
Project # / Title
1 / Interest Rates and Yields
2 / Effectiveness of Insect Repellent
Chapter 6 The Definite Integral File: chap6.xls
Tutorial # / Title1 / Areas and Riemann Sums
2 / Area Functions
Project # / Title
1 / Area of a Sector
2 / The Natural Logarithm Function
Chapter 7 Functions of Several Variables
File: chap7.xls
Tutorial # / Title1 / Optimization Using Solver - I
2 / Optimization Using Solver - II
3 / Method of Least Squares
Project # / Title
1 / Production Schedule
2 / Sports Statistics
3 / Rectangular rule for double integrals
Chapter 8 The Trigonometric Functions File: chap8.xls
Tutorial # / Title1 / Graphs of the Sine and Cosine Functions
2 / Limits Involving Trig Functions
3 / The Derivatives of Trig Functions
Project # / Title
1 / Analyzing Graphs of Trig Functions
2 / A Pollution Model
3 / Seasonal Business Cycle
Chapter 9 Techniques of Integration File: chap9.xls
Tutorial # / Title1 / Midpoint and Trapezoid Rules
2 / Simpson's Rule
Project # / Title
1 / Error Analysis for Approximate Integration
2 / Estimating Distance Traveled by a Rocket
Chapter 10 Differential Equations File: chap10.xls
Tutorial # / Title1 / Euler's Method
Project # / Title
1 / A Differential Equations Model
Chapter 11 Taylor Polynomials and Infinite Series
File: chap11.xls
Tutorial # / Title1 / Taylor Polynomials
2 / The Newton-Raphson Algorithm
Project # / Title
1 / Using Taylor Polynomials for Integration
2 / Approximating Roots
Chapter 12 Probability and Calculus File: chap12.xls
Tutorial # / Title1 / Expected Value and Standard Deviation
2 / Normal Random Variables
Project # / Title
1 / Statistical Analysis of Mutual Fund Data
2 / Standard Normal Distribution
References
Horton, W., Designing and Writing Online Documentation, John Wiley and Sons, New York, 1994.
Microsoft Corporation, Microsoft Excel User's Guide, Version 5.0, Redmond, WA, 1993.
Microsoft Corporation, Microsoft Excel Visual Basic User's Guide, Version 5.0, Redmond, WA, 1994.
Bureau of Labor Statistics, http://www.bls.gov
US Census Bureau, http://www.census.gov
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