### Nature of the Course

This course includes topics from differential equations and linear algebra that are useful in the Biological Sciences, topics which are not usually found in a second semester Calculus course. The course also gives an introduction to mathematical modelling of population growth, covering three mathematical models of population growth based upon: birth/death rates; limits to growth; and age distribution.

To include this material, the course excludes many topics that are needed in a third semester calculus course such as 251.

Math 138 is not a CALC2 equivalent course.

The only courses satisfying the CALC2 prerequisite are Math 152, 154, and 192. These are different versions of the second semester of the sequence Calculus for Mathematics and the Physical Sciences, a traditional second semester calculus course that prepares students for higher level mathematics courses. Students who may wish to take Math 251 should follow Math 135 with Math 152, not Math 138 (and not Math 136). This applies to students in certain programs in the Biological Sciences (in particular, Molecular Biology and Biochemistry), which require Math 251. More information on the transition from Math 135 to Math 152 can be found on the web page **Mathematics placement advice**.

**Math 138 will not serve as a prerequisite for Math 251** or any other course requiring a CALC2 prerequisite, except Math 250.**In summary:** **If you intend to take higher level courses requiring CALC2, do not take Math 136 or Math 138; take Math 152 instead.**

For a further discussion of Math 138, see **What is this course?**

### Text and Syllabus

Since Spring 2014, this course uses *CALCULUS Special Edition, Chapters 5-8,11,12,14 *(Sixth Edition), by K. Smith, M. Strauss and M. Toda and published by Kendall Hunt (ISBN# 9781465240798). This is a custom edition for Rutgers University, extracted from the larger (and more expensive) text CALCULUS by Smith, Strauss and Toda.

The course also requires two supplements to the textbook:

- A
**Rutgers supplement**, with two parts, on A. Population Growth Models and B. Linear Algebra. - A UMAP Supplement, Population Projection, by Edward L. Keller. You will need a username and a password to access this material; they will be supplied to you in the lectures.

Here is the current **departmental syllabus** for the course. Your instructor will supply his or her own version of this syllabus.

In the course catalog, this course (640:138) is called * Calculus II for the Biological Sciences* and is listed as covering: Transcendental Functions, techniques of integration, elementary differential equations and their applications to Biological Sciences, and an introduction to Linear Algebra. Only the first two of these topics are common to the other Calculus II courses (640:136 and 640:152).

### So what is this course?

The first third of Math 138 is an abridged version of the first half of Calculus 136, skimping on techniques of integration. The second third covers linear differential equations. The Exponential Growth model of explosive population growth comes early. After Spring Break, the Logistic Population Growth Model is covered. This also uses a differential equation to model limits to growth. The final third of the course builds to a different kind of model: the Leslie Model, in which population is modeled by something called a *Markov Process.*

Historically, Math 138 was created in 1974 as a spin-off from the Unified Calculus sequence 135-136, which still exists. The purpose was to emphasize those parts of Calculus relevant to Biology. Since the late 1980's it has been organized around three models for population growth. The sequence 135-136/138 was re-designed again in 1997, emphasizing the early introduction (in 135) of transcendental functions and the use of Graphing Calculators. In 2004, a new textbook was chosen, and supplements put on line. We have come a long way.

Currently, in Spring 2006, textbook for this course is a *Calculus and Its Applications*, a **custom text, for Rutgers University**, published by Pearson Custom Publishing. The text is based primarily on *Calculus, Third Edition*, by Strauss, Bradley and Smith, but also contains material from *Calculus & Its Applications*, by Goldstein, both published by Prentice Hall.

The course also requires two supplements to the textbook:

- A
**two-part supplement**, developed at Rutgers, on*A. Population Growth Models*and*B. Linear Algebra*. - A UMAP module
*Population Projection*, by Edward L. Keller.

This course has always had supplementary material accompanying the standard textbook. In the 1970's there were 5 supplements covering: semilog graph paper, quantitative measurement, exponential and logistic growth (as applied to cells), and sedimentation. In 1983, the course was redesigned, with input from the Biology department. The number of supplements grew to 11, with material on partial fractions, hyperbolic functions, complex numbers and the Population Projection supplement we still use. Some of the present Rutgers supplementary material dates to a further re-emphasis on Linear Algebra and Differential Equations in the late 1980's, again with the encouragement of the Biology department. In 1997, the Differential Equations supplement was added, chapter 16 of a larger textbook * Calculus: Early Transcendental Functions*, to allow students to save money with the smaller 10-chapter textbook. In 1998, the Linear Algebra material was redesigned and is now somewhat tailor-made for this class.

### Catalog Description

01:640:138. CALCULUS II FOR THE BIOLOGICAL SCIENCES (4)

For biological sciences majors.

Prerequisite: CALC1. Credit restrictions: CR2.

Techniques of integration, elementary differential equations and their applications to biological sciences, and an introduction to linear algebra.

### Current Semester

### Topics in Mathematics for the Liberal Arts (01: 640: 103, Summer 2017 )

##### Topics in Mathematics for the Liberal Arts (section B6)

Index Number: 01495Credits: 3

Professor: ROEMER

Schedule:

- [L] Wed 6:00PM-8:00PM TIL-127 (LIV)
- [L] Fri 6:00PM-8:00PM TIL-127 (LIV)
*By Arrangement*

##### Topics in Mathematics for the Liberal Arts (section H6)

Index Number: 01376Credits: 3

Professor: GULICK

Schedule:

*By Arrangement*- [L] Thu 6:00PM-8:00PM SC-104 (CAC)
- [L] Mon 6:00PM-8:00PM SC-104 (CAC)

##### Topics in Mathematics for the Liberal Arts (section HA)

Index Number: 00592Credits: 3

Professor: AMODIO

Schedule:

- [L] Thu 1:15PM-3:25PM HH-A1 (CAC)
- [L] Tue 1:15PM-3:25PM HH-A1 (CAC)
- [L] Fri 1:15PM-3:25PM HH-A1 (CAC)
- [L] Mon 1:15PM-3:25PM HH-A1 (CAC)