# Calculus from 1973 to 1983

During this time, most students completed their calculus courses in the Department of Mathematics within the College of Arts and Sciences and a small number of students took calculus courses at College IV (Kirkhof College) in a modular, self-paced format. Following are the course descriptions for the courses in the calculus sequence for the Department of Mathematics:

**201 ****Calculus**** I**

First course in **calculus**. Differentiation and integration of rational and algebraic functions.

**202 ****Calculus**** II**

Continuation of **Mathematics 201. **Differentiation and integration of elementary transcendental functions. Integration techniques. Prerequisite: **Mathematics 201.**

**203 ****Calculus**** III**

Indeterminate forms, infinite series and multivariate calculus. Continuation **of Mathematics 202. **Prerequisite: **Mathematics 202.**

College IV, which opened its doors in 1973, originally operated using a pedagogical model featuring self-paced instruction, mastery learning, and modular design of a liberal arts curriculum. During its first two years of existence, Dr. Carl Arendsen was developing the self-paced mathematics curriculum at College IV. Most of the work done during that time focused on the precalculus courses, but calculus modules were offered for the 1975-76 academic year. Most of the modules for Calculus I and Calculus II were developed by Dr. Arendsen and Dr. Philip Pratt of the College of Arts and Sciences, and most of the modules for Calculus III were developed by Dr. Ted Sundstrom after he joined the faculty of College IV in 1975. Following are the first descriptions of courses in the calculus sequence at College IV. These descriptions appeared in the 1976-77 catalog.

**Mathematics 32: Calculus and Analytic Geometry I**

Analytic geometry, differentiation and integration of rational functions including applications.

**Mathematics 34: Calculus and Analytic Geometry II**

Continuation of the 57-32 series. Differentiation and integration of the elementary transcendental functions, polar coordinates and integration techniques.

**Mathematics 36: Calculus and Analytic Geometry III**

Continuation of the 57-34 series. Applications of integration, determinate forms, infinite series and multivariate calculus.

As with most classes at College IV at that time, the key was the “learning module,” which was a unit of study pertaining to a small but definable portion of the course. Grand Valley was on the quarter system at that time. Each of these courses was a five-credit course, and each course was divided into a sequence of one-half credit or one-credit modules. Each module contained learning objectives, which stated the expected goals to be achieved by the student, a study guide for the materials used to achieve an understanding of the material, and a self-test for the student to check on her or his understanding of the material. Students would work through the modules on their own but could get individualized instruction with the instructor during designated office hours. Click here to see an example of a Calculus III module developed by Dr. Ted Sundstrom.

When a student was confident that he or she had mastered the material, that student would take a so-called mastery test over the material. Successfully completing the mastery test at the 90% level granted the student the credit for that module. Students who failed to master the material would meet with the faculty member for help in determining their weakness and obtain assistance from the faculty member. After working on the material again, students could take another form of the mastery test for that module. When a student passed the mastery test, he or she would be awarded credit for that module and would be allowed to continue to the next module.

**A Four Course Calculus Sequence**

From 1975 to 1983 (when the colleges were combined), the College of Arts and Sciences continued to teach calculus in a traditional lecture-discussion format and College IV (Kirkhof College) continued to offer students the option of completing calculus in a self-paced, modular format. The vast majority of students completed their calculus courses in the College of Arts and Sciences.

There were two major changes in the descriptions of the courses in the calculus sequence during this time. One was a change from a three-course calculus sequence to a four-course calculus sequence for the 1977-78 academic year. In the College of Arts and Sciences, the first two courses in the sequence were not changed. Basically, the five-credit course was divided into two three-credit courses with some additional material.

**203 Calculus III**

Multiple integrals and applications of them. Parametric equations and polar coordinates. Prerequisite: 202. Three hours credit. Offered fall, winter and spring terms.

**204 Calculus IV**

Limits, Rolle's Theorem, Mean Value Theorem, sequences and series, series of functions and Taylor series. Prerequisite: 202. Three hours credit. Offered fall, winter and spring terms.

College IV made a similar change and including numbering changes for its modules.

**5941 Calculus I**

A first course in calculus with emphasis on differentiation and integration of rational and algebraic functions. Prerequisite: 5922. Five hours credit.

**5942 Calculus II**

Differentiation and integration of the elementary transcendental functions, integration techniques, applications of the integral, indeterminate forms, improper integrals, parametric equations and polar coordinates. Prerequisites: 5923and 5941. Five hours credit.

**5943 Calculus III**

An introduction to some numerical methods used in calculus including Taylor polynomials, numerical integration, sequences and series, power series and Taylor series. Prerequisite: 5942. Three hours credit.

**5944 Calculus IV**

An introduction to multivariate calculus. Topics include partial differentiation, multiple integration, vector calculus, line integrals, Green's theorem and an introduction to differential equations. Prerequisite: 5942. Four hours credit.

There were some differences in the descriptions for Calculus III and Calculus IV between CAS and CIV and Calculus IV was four credits in CIV as opposed to three credits in CAS. These four-course calculus sequences were short-lived, however, due to the fact that Grand Valley decided to change to the semester calendar beginning with the 1980-81 academic year. The calculus sequence became a sequence of three courses of 5, 4, and 4 credits. Following are the descriptions for the calculus courses in CAS.

**201 Calculus and ****Analytic ****Geometry ****I.***** **Analytic geometry. Differentiation and integration of functions of a single variable with applications. Prerequisite: 120. Five credits.

**202 Calculus and Analytic Geometry II. **Differentiation and integration of parametric equations, polar coordinates, techniques of integrating functions of a single variable, three-dimensional analytic geometry, partial differentiation, and multiple integration. Prerequisite: 201. Four credits.

**203 Calculus and Analytic Geometry III. **A study of vector algebra and vector analysis including physical applications; infinite sequences and series, convergence tests, power series, Taylor's theorem, and numerical approximations; indeterminate forms and limit theorems. Prerequisite: 202. Four credits.

At that time, due to small enrollment in the calculus courses, Kirkhof College offered only the first course in the calculus sequence. Following is the description of Calculus I for Kirkhof College.

**201 Calculus and Analytic Geometry I**. A first course in calculus including some analytic geometry. Differentiation and integration of rational, algebraic, exponential, logarithmic, and trigonometric functions. Prerequisite: MAT 113. Five credits.

The course descriptions for Calculus II and Calculus III were changed for the 1982-83 academic year. They were changed so that Calculus III would essentially become a multi-variable calculus course.

**202 Calculus and Analytic Geometry II. **Integration techniques, parametric equations and polar coordinates, indeterminate forms, improper integrals and vector algebra. Prerequisite: 201. Four credits. Offered fall and winter semesters.

**203 Calculus and Analytic Geometry III. **Partial differentiation, multiple integration, sequences and series, convergence and remainder theorems, power series and Taylor series. Prerequisite: 202. Four credits. Offered fall and winter semesters.

**The Use of the Hand-Held Calculator**

During the late 1970’s and early 1980’s several faculty members became interested in the use of hand-held calculators in the teaching of mathematics. Two faculty members who were especially interested in this were Dr. Virginia Muraski in CAS and Dr. Ted Sundstrom in Kirkhof College. Beginning in the 1979-80 academic year, Dr. Sundstrom required the students to use a calculator in some algebra courses and to use a full scientific calculator for the precalculus course. (A full scientific calculator was one that had the exponential, logarithmic, and trigonometric functions built in.) The work on the precalculus course was done with Prof. Leon Ablon, who was a faculty member at the College of Staten Island and was a visiting faculty member at Kirkhof College during the 1977-78 academic year. The first documented requirement for the use of a scientific calculator in a calculus course was the course description for Calculus I in Kirkhof College for the 1981-1982 academic year.

**201 Calculus and Analytic Geometry I. **A first course in calculus including some analytic geometry. Differentiation and integration of rational, algebraic, exponential, logarithmic, and trigonometric functions. A full scientific calculator is required. Prerequisite: MTH 118. Offered on sufficient demand. Five credits.

The use of calculators in the calculus sequence by some faculty members continued after the colleges merged in 1983. This eventually led to the use of graphing calculators in the calculus sequence beginning in the late 1980’s.