Life Science Calculus (Applied Calculus) for Life Science Online Course for Academic Credit

Course: DMAT 202

Course Title: Applied Calculus for Life Sciences

Transcript Course Title (30 Characters Max:): Calculus for Life Sciences

Course Description: A single course in differential and integral calculus for management and business with emphasis on computational techniques and graphical analysis. Topics include a study of the algebraic and numerical aspects of linear, quadratic, polynomial, exponential, and logarithmic functions, function growth, derivative analysis and optimization, integration, applications to life sciences, and the Fundamental Theorem of Calculus. [3 Semester Credits]

Prerequisite: Successful completion of 3 years high school mathematics (C- or higher) or instructor consent.

E-Textbook: “Business Calculus & LiveMath” by Robert R. Curtis, Ph.D., adapted from Davis/Porta/Uhl “Calculus&Mathematica” courseware series

Software: LiveMath

PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 202 - Applied Calculus for Life Sciences

1.	Getting Started
	1.1	Email and Chat
	1.2	Learning About the Course
	1.3	Required Hardware
	1.4	Software Fundamentals

2.	The Big Picture
	2.1	Solving (easy) equations in 1 variable.
	2.2	What if you can't solve for x?
	2.3	Finding solutions numerically
	2.4	Finding solutions graphically
	2.5	Solving equations of more than 1 variable

3.	Functions
	3.1	Function notation
	3.2	Data sets
	3.3	Graphing functions
	3.4	Data sets and smooth curves
	3.5	Domain and Range
	3.6	Algebraic combinations of functions

4.	Linear Functions
	4.1	Algebraic definition
	4.2	Slope
	4.3	Graphing linear functions by hand
	4.4	Properties of linear functions
	4.5	Linear data sets

5.	Quadratic Functions
	5.1	Algebraic definition
	5.2	Graphing and Properties of Quadratic Functions
	5.3	Solving quadratic equations algebraically: Factoring
	5.4	Solving quadratic equations algebraically: Quadratic formula
	5.5	Solving quadratic equations numerically and graphically

6.	Power and Polynomial Functions
	6.1	Algebraic definition
	6.2	Graphing and Properties of Polynomial Functions
	6.3	Solving polynomial equations algebraically: factoring
	6.4	Solving polynomial equations numerically and graphically
	6.5	Radicals and fractional exponents

7.	Rational Polynomial Functions
	7.1	Algebraic definition
	7.2	Graphing and Properties of Rational Polynomial Functions
	7.3	Solving rational polynomial equations algebraically: factoring

8.	Exponential Functions
	8.1	Algebraic definition
	8.2	Graphing and Properties of Exponential Functions
	8.3	Solving exponential equations numerically and graphically
	8.4	Exponential Growth and Applications
	8.5	Data sets and exponential functions

9.	Logarithmic Functions
	9.1	Inverse Functions
	9.2	Algebraic Definition
	9.3	Graphing and Properties of Logarithmic Functions
	9.4	Solving exponential and logarithmic equations algebraically
	9.5	Solving logarithmic equations numerically and graphically
	9.6	Logarithmic Growth and Applications
	9.7	Data sets and logarithmic functions

10.	Growth:  Preparing for the Derivative
	10.1	Growth of Linear Functions
	10.2	Growth of Power Functions
	10.3	Growth of Exponential Functions
	10.4	Dominance of Growth of Functions
	10.5	Percentage Growth of Functions
	10.6	Global Scale:  Infinite Limits
	10.7	Data Functions and Interpolation
	10.8	Approximation of Functions by Linear Functions

11.	Exponential Functions and Natural Logarithms
	11.1	e = Euler's Number
	11.2	Natural Logarithm
	11.3	Growth Analysis
	11.4	Applications:  Carbon Dating
	11.5	Percentage Growth and Steady Growth of Exponential Functions
	11.6	Data Functions and Logarithmic Analysis
	11.7	Applications:  Compound Growth Rates
	11.8	Applications: World Population
	11.9	Applications: Growth and Half-Life Decay

12.	The Derivative of Polynomial, Exponential, Logarithmic, and Fractional Powers
	12.1	Instantaneous Growth Rates
	12.2	Definition of the Derivative
	12.3	Computing the Derivative Graphically
	12.4	Computing the Derivative Algebraically
	12.5	Computing the Derivative Numerically
	12.6	Average Growth Rate vs. Instantaneous Growth Rate
	12.7	Applications of the Derivative:  Spread of Disease
	12.8	Finding Maxima and Minima of Functions
	12.9	Relating a Function and Its Derivative

13.	Computing Derivatives
	13.1	Sum, Difference, Product, Quotient Rule
	13.2	Chain Rule
	13.3	Instantaneous Percentage Growth
	13.4	Growth Dominance

14.	Using Derivatives
	14.1	Finding Maxima and Minima
	14.2	Finding Good Representative Plots
	14.3	The Second Derivative

15.	Integration
	15.1	Measuring Area Under a Curve
	15.2	Definition of the Integral
	15.3	Properties of Integrals, Symmetry
	15.4	Integrals of Data Functions
	15.5	Numerical Methods:  Rectangles, Trapezoids
	15.6	Undefined Integrals
	15.7	Numerical Calculation of Integrals

16.	Fundamental Theorem of Calculus
	16.1	Derivative of an Integral
	16.2	Integral of a Derivative
	16.3	Fundamental Formula
	16.4	Properties of Integrals
	16.5	Indefinite Integrals and Antiderivatives
	16.6	u-Substitution

17.	Higher Dimensions
	17.1	Multivariable Functions
	17.2	Partial Derivatives
	17.3	Tangent Planes
	17.4	Optimization

In 2023, Distance Calculus introduced a new catalog of courses. The connection between the old courses and the new courses are given here:

New DMAT 202 = OLD DMAT 207 = OLD MATH 207

Legacy Course Description: This course covers fundamental notions of differentiation and integration of algebraic, exponential and logarithmic functions, with problems drawn from principally from business situations. Topics include optimization, related rates, and simple applications and methods of integration. While covering traditional analytic methods, this course also emphasizes graphical and numerical approaches. This course may not be taken for credit by mathematics majors, minors or core concentrators. No credit will be given to students who have previously received credit for MATH 213. (3 credits)

Legacy Detailed Course Syllabus in PDF

Course Description: This course covers fundamental notions of differentiation and integration of algebraic, exponential and logarithmic functions, with problems drawn from principally from business situations. Topics include optimization, related rates, and simple applications and methods of integration. While covering traditional analytic methods, this course also emphasizes graphical and numerical approaches. This course may not be taken for credit by mathematics majors, minors or core concentrators. No credit will be given to students who have previously received credit for MATH 213. (3 credits)

Prerequisite: High School Algebra
Detailed Course Syllabus in PDF

Nearly all collegiate students have completed "high school algebra". There is no mathematics placement exam. The Life Science Calculus (Applied Calculus) course starts with a very thorough "warm up" module on the important topics of high school algebra, with the added usage of the LiveMath software, which makes for an excellent "refresher" for student who have maybe be away from academic mathematics for some time.

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Life Science Calculus (Applied Calculus) - Academic Caveats

Some issues to consider when determining if Life Science Calculus (Applied Calculus) is for you.

• Terminal Course
  Life Science Calculus (Applied Calculus) does not lead to the higher Calculus sequence, and is not equivalent to the higher Calculus I course. Life Science Calculus (Applied Calculus) is usually the last math course a student takes as an undergraduate.
• No Trigonometry
  Life Science Calculus (Applied Calculus) does not include nor require Trigonometry. If your academic program requires a calculus course that includes trigonometry, you need to take the Calculus I course instead.
• No Multivariable Calculus
  Life Science Calculus (Applied Calculus) does not branch into the multivariable calculus topics - required by some majors/programs, especially Economics. If you need Multivariable/3D Calculus topics, you'll need to go through the higher Calculus I/II + Multivariable Calculus sequence.

Life Science Calculus (Applied Calculus) Student Academic Goals

One way to determine if Life Science Calculus (Applied Calculus) is the right course for you is to align yourself with examples of student profiles we usually encounter.

• Prepare for MBA or Other Graduate Program
  Many graduate programs, such as MBA's, have prerequisites that include "a single college-level Calculus course". The majority of our Applied Calculus students are seeking to satisfy such prerequisite requirements prior to starting their graduate school program. Our MBA-bound students tend to be highly-focused, goal-oriented students who complete their course work under very tight deadlines.
• Pharmacy, Nursing, Pre-Med
  Often these academic and training programs require "a single college-level Calculus course" as a prerequisite. Many students in these programs have strong mathematical skills, which aid them in completing the Applied Calculus course quickly. Some students in this category do have weaker mathematical backgrounds, requiring more time to achieve mastery and success in the Life Science Calculus (Applied Calculus) course.
• General Education Requirement
  Many students have "one more class" to finish to earn their baccelaureate degree, and Life Science Calculus (Applied Calculus) fits the bill for them.
  Warning: Many colleges/universities have a senior residency requirement where the last set of credits (usually 20-30 credits) must be completed at the college/university granting the degree, and cannot be "transferred in" from another school. Make sure you check with your college/university about such rules.
• Teacher Re-Certification
  Primary and secondary educators often are required to take courses for their certification and/or re-certification programs.
  Warning: Distance Calculus courses do not carry graduate-level credits. Some recertification programs require their teachers to complete graduate level credits. Calculus courses are inherently undergraduate-level courses.

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Life Science Calculus (Applied Calculus) Example Student Profiles

Case 1: MBA-Bound Student Needs Life Science Calculus (Applied Calculus)

Sally just got her acceptance letter from her MBA graduate school, but with notification that she needs to finish "a single collegiate-level differential and integral calculus course" by the start of MBA courses.

How fast can Sally finish the DMAT 202- Calculus for Life Science course?

MBA students tend to be highly-motivated and deadline-centered students, ready to "do what it takes" to get finished by the required date. Here are some scenarios for Sally:

Common Completion Timelines for DMAT 202- Calculus for Life Science
Hours Per Week Dedicated	Math Skills	Dedication	Completion Time	Advisory
5-10 hours/week	Weaker	1-2 hours/day	16 weeks	Reasonable
7-12 hours/week	Modest	2-3 hours/day	12 weeks	Reasonable
10-15 hours/week	Stronger	3-4 hours/day	8 weeks	Reasonable
15-20 hours/week	Strong	5-6 hours/day	6 weeks	Stretched
20-25 hours/week	Strong	5-7 hours/day	4 weeks	Stretched
20-25 hours/week	Strong	6-8 hours/day	3 weeks	Unreasonable, But Has Been Done
30-40 hours/week	Very Strong	8-10 hours/day	2 weeks	Unreasonable, But Has Been Done
40-50 hours/week	Very Strong	10-12 hours/day	9 days	World's Record

Case 2: Pharmacy Student Needs Life Science Calculus (Applied Calculus)

Marc is planning to go to Pharmacy School in a few months, and needs to finish the Life Science Calculus (Applied Calculus) course prior to the start of school. Marc has been away from academic mathematics for many years, and does not have a strong mathematics background, but makes up for such weaknesses with drive, energy, and dedication to achieving his goals.

How fast can Marc finish the DMAT 202- Calculus for Life Science course?

Marc will need to plan for extra time, especially at the beginning of the course, to get back into the swing of academic mathematics. The high school algebra review portion of the course (20 assignments) will be time well spent for Marc, as he revisits topics from high school that previously he did not have much success with. Marc is able to dedicate himself to the task, and is able to move more quickly through the Calculus curriculum (50 assignments). Here are some scenarios for Marc:

Common Completion Timelines for DMAT 202- Calculus for Life Science
Hours Per Week Dedicated	Math Skills	Dedication	Completion Time	Advisory
8-10 hours/week	Weaker	1-2 hours/day	15 weeks	Reasonable
15-20 hours/week	Weaker	2-3 hours/day	10 weeks	Reasonable
20-25 hours/week	Weaker	3-4 hours/day	8 weeks	Reasonable
20-25 hours/week	Modest	2-3 hours/day	8 weeks	Reasonable
25-30 hours/week	Modest	4-5 hours/day	6 weeks	Stretched
30-35 hours/week	Modest	5-6 hours/day	4 weeks	Stretched

Case 3: Working Parent Planning for Graduate Studies Needs Life Science Calculus (Applied Calculus)

Amelia is a parent of three children who also works full-time. Amelia has ambitious plans to return to graduate school in the next year to advance her career. Amelia cannot take a traditional classroom math course due to her schedule constraints.

How fast can Amelia finish the DMAT 202- Calculus for Life Science course?

We have many students like Amelia who are quite successful in Distance Calculus!

Amelia will probably do her math homework after her kids are asleep for the night, in the 10pm-midnight timeframe. The Mastery Learning format for Distance Calculus serves Amelia well, where she is able to spend extra time on those topics that are more challenging for her, without penalty or "falling behind" as she would in a traditional course.

When the children get sick and stay home from school, or life and work commands extra time, Amelia is able to take a break from Distance Calculus - usually for a few weeks, but perhaps for a few months, if needed - and return to her studies when her schedule permits. While such breaks do cause slower completion times, and "getting back in the swing of things" does require extra time and effort for Amelia, the flexibility of the asynchronous course format allows Amelia to finish the course when she can.

Case 4: 18-22 Year Old Student With Full Course Load Needs To Finish Life Science Calculus (Applied Calculus)

James is an undergraduate student at a university, carrying 15 semester credits - a full course load. James wants to add the Life Science Calculus (Applied Calculus) course to his course schedule, in order to complete a general education requirement.

What are the challenges that James will face with this plan?

In our experience, when a student is faced with "too many courses" at the same time, it is the asynchronous distance course that almost always is the course to suffer a lack of attention. With other synchronous course deadlines and examinations, it is natural that an asynchronous course such as Distance Calculus becomes the "pressure valve".

Students in these situations nearly always finish their Distance Calculus course during the winter break (December, January), spring vacation (April), and/or the summer vacation months (May-August). Even with the best of intensions, it is very difficult to complete a Distance Calculus course while taking 4 or 5 other courses simultaneously.

Younger students also have more difficulty with the flexible schedule of Distance Calculus. It is very easy to put off your course work "until all day Saturday" or "next week after my Philosophy exam", which snowballs into a huge amount of work leftover to an increasingly short amount of time. Planning for vacation times is the best approach for students in this category.

Life Science Calculus (Applied Calculus) Referenced Colleges/Universities

Over the past 26 years, Distance Calculus has enrolled thousands of students who successfully complete the Life Science Calculus (Applied Calculus) courses, and use this course record towards undergraduate and graduate programs at various colleges and universities in the U.S. and throughout the world.

Below is a list of schools that Distance Calculus students have utilized their Life Science Calculus (Applied Calculus) course credits earned towards these programs:

• University of Pennsylvania, Wharton School of Business
• London School of Economics
• Harvard University: Kennedy School of Government, Medical Schools
• Duke University, Fuqua School of Business, Law School, Graduate Programs
• Columbia University School of Business
• University of Pennsylvania Architectural School
• University of Michigan: MBA, Medical Schools, Graduate Programs
• Stanford University, MBA
• University of California, Berkeley
• Auburn University MBA Program
• University of North Carolina, MBA
• George Washington University School of Business
• Roger Williams University
• University of Minnesota, School of Public Health
• Montclair University
• Baylor University
• Eastern Illinois University
• University of Minnesota, Twin Cities
• University of Memphis
• State University at Buffalo, Law School
• Westminster College
• University of Mississippi
• Georgia Tech
• Wharton School of Business, University of Pennsylvania
• Harvard University, Kennedy School of Government
• Duke University - Fuqua School of Business
• Stanford University
• Princeton University
• University of California, Berkeley
• University of California, Santa Barbara
• University of Southern California
• Pennsylvania State University
• College of William & Mary
• University of Texas at Austin
• Drexel University
• University of Massachusetts
• Cornell University
• University of Wisconsin, Madison
• Carnegie Mellon University
• University of North Carolina, Chapel Hill
• Kings College, University of London
• Indiana University
• Rice University
• University of Georgia
• University of South Carolina
• University of Minnesota-Twin Cities
• Baylor University
• Loma Linda University
• University of Maryland
• Georgetown University
• University of West Florida
• Eastern Illinois University
• University of Virginia
• University of Maryland
• University of Nebraska
• University of Missouri
• University of Georgia
• Florida Atlantic University
• Washington State University
• University of New Orleans
• California State University, Sacramento
• California State University, Dominguez Hills
• Babson College
• Wheaton College
• Middlebury College
• George Washington University
• Roger Williams University
• Texas A&M University
• Oregon State University
• Illinois Institute of Technology
• Montclair University
• Hillsdale University
• Evangel University
• The Art Institute of Atlanta
• New Mexico Military Institute
• Athens State University
• American Graduate University
• Kaplan University
• University of Warwick
• Gordon College
• University of Memphis
• Endicott College
• University Of Mount Union
• Mesa State College
• Azusa Pacific University
• Thomas Edison State College
• State University at Buffalo Law School
• Murray State University
• University of Phoenix
• Webster University
• Northern Michigan University
• Western Michigan University
• Central Michigan University
• Fairleigh Dickenson University
• Whitman College
• Fairifield University
• Jacksonville State University
• University of Redlands
• Westminster College
• University of San Francisco
• Strayer University
• Vanderbilt University
• Howard University
• Middlebury College
• Valdosta State University
• American University
• Clarkson University
• Howard University
• Green Mountain College
• Whittier College
• Florida A & M University
• James Madison University
• Franklin University
• Woodbury University
• Quinnipiac University
• Webster University
• Western Michigan University

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Life Science Calculus (Applied Calculus): Academics

80% Computer Algebra, 20% Pencil/Paper, 0% Multiple Choice

Through the usage of a computer algebra system like LiveMath™ - you will never miss a minus sign again!

Although the driving of a computer algebra system requires some up-front time to learn and master, once completed (rather quickly for most students), the time saved from having to be a "minus sign accountant" adds to the productivity of your study time. If you have ever spent hours looking for that "little numerical error", you know what we mean.

Command of a computer algebra software system is a modern-day necessity of mathematical academics. It is important, however, to retain a meaningful command of paper/pen/pencil manual computations as well. Our blend of curriculum strives for an 80%/20% split between computer algebra usage and manual computation and written skills. With each module in our curriculum, a concluding Literacy Sheet assignment ensures that each student has written mathematical competency in the subject area.

The proctored final exam is a written exam away from the computer. It is these Literacy Sheet assignments, and the continuing bridge from modern computer algebra software back to classical, manual mathematics that prepares the student from this written final exam.

We do not have any multiple-choice work. We are a real collegiate-level course program - not a "canned" set of multiple-choice question sheets which are common from large publishers and degree-mill schools.

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Life Science Calculus (Applied Calculus) Example Curriculum

Videotext - A Modern Replacement of the Textbook

What is a videotext? It is like a textbook, except instead of being based upon printed information, this "text" is based upon video presentations as the core method of explaining the course topics. Instead of a huge, thick 1000-page Calculus textbook to lug around in your backpack, all of this new "videotext" can be loaded into your iPods or iPhones (and soon, the iPad!).

Example Videos are in MP4/H.264 format, which play in most modern browsers without additional software. When additional software is required, a backup Flash player will play the video. As a backup to Flash, you may also use iTunes and/or VLC.

Our videotext features two main types of videos:

• Screencast Videos using LiveMath™ Play Video
  

  Although we are anywhere from a few miles to a few thousand miles apart, watching these screencast videos is like sitting next to the course instructor, watching his computer, learning the topics of Calculus at the same time as learning how to drive the computer algebra and graphing software LiveMath™. These LiveMath™ screencast videos make up the majority of the video presentations in the videotext.

• ChalkTalk Videos: Manual Calculations Play Video
  

  While using a computer algebra software package is a very cool way to do Calculus computations and investigations, we must also pay attention to the classical side of Calculus, and the computations that can be completed by hand with paper/pen/pencil. To be a well-rounded Calculus student, you need to be able to do calculations in both technical and manual methods.

Life Science Calculus (Applied Calculus) Screencast Video Questions

One extremely powerful aspect of the Distance Calculus course technologies is the usage of screencast video (and audio) recordings made by the students and the instructors, exchanged just as easily as emails back and forth.

If a picture is worth a thousand words, then a screencast movie is worth a million words - and saves boatloads of time and effort.

Instead of trying to type out a math question about a particular topic or homework question, the ease of "turning on the screen recorder" and talking and showing your question - in the span of a few minutes - can save hours of time trying to convert your question into a typed (and coherent) narrative question.

Example Instructor Question/Answer Movie

When a student asks a question in a homework notebook, sometimes the best way to explain the answer is via a screen movie.

• Instructor Question/Answer Movie Play Video
  

• Instructor Question/Answer Movie Play Video
  

• Instructor Question/Answer Movie Play Video
  

• Instructor Question/Answer Movie Play Video
  

• Instructor Question/Answer Movie Play Video
  

• Instructor Question/Answer Movie Play Video
  

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Life Science Calculus (Applied Calculus) Example Student Work and Grading

The majority of course work occurs via the exchange of LiveMath™ notebooks - think Word Processing Files, but for mathematical computations instead of just text.

The student will "Hand-In" a notebook, and one of the instructors will grade, correct, give feedback, and/or give hints on the work in the notebook, and return the notebook to the student in his/her "GetBack" folder, where the student will view the instructor comments.

Sometimes the notebook is deemed "Complete" on the first revision. Sometimes the notebook must go back and forth between the student and instructor a number of times - 2, 3, 4, 5 times is rather common.

Coupled with the screencast video mechanism, sometimes the instructor or the student will submit a screen movie with the notebook, giving further explanation or questions in audio/video format.

Below are some example notebooks from actual students, showing the progression from starting notebook to completed notebook.

• LiveMath™ Homework Notebook #1 PDF Printout
  View PDF #1
  View PDF #2
  View PDF #3
  

• LiveMath™ Homework Notebook #2 PDF Printout View PDF
  

• LiveMath™ Homework Notebook #3 PDF Printout View PDF
  

• LiveMath™ Homework Notebook #4 PDF Printout View PDF
  

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Distance Calculus - Student Reviews

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