Calculus I developed by Dr. Arek Goetz is a fully online course. It is run only through an acredited by Western Association of Schools and Colleges university. Since its inception over 1000 students have successfully completed the class. The course isopen to all students with sufficient background in algebra,
notions of functions, and in elementary trigonometry. Welcomed are
students from domestic or international universities as well as
professionals who are preparing for graduate schools. The course has been
particularly popular among students preparing to enter medical schools
as many medical schools require at least one semester of calculus,
pharmacy, and MBA programs.
Transcripts & Transfer of credit units
Transcripts, whether official or unofficial are only available through the university through which the student takes the course.
Prerequisites and Pretest
To qualify for the course students need to take this self pretest based on algebra, notions of functions, and basic trigonometry.
Before committing to the class all students should review algebra.
Letters of recommendation to your future school
In the past students competing for admission to top medical schools or MBA programs, requested letters of recommendation. Professor Goetz will gladly write a letter if requested by a student whose contributions to online learning are substantial and meaninful.
How is this program different from other online calculus courses?
The class offers 4 semester units. Dr. Goetz's online calculus course is in 11th semester of existence. Hundreds of students from major US
universities and some from other parts of the world successfully
complete the class every year. The course is designed and taught by a research
mathematician with an National Science Foundation track record. The
communication among students is facilitated by an intuitive formula
generator - Students focus on exchanging ideas, not on learning how to
type set mathematics.
Stimulating social learning experience
The course has 25 new lessons. Students spend on average between 6-9 interactive hours per module. In each of the 25 lessons, students (i) interact with a high quality video lecture and at times take a quiz directly related to the lecture. The lectures can be either streamed in high definition over the internet, or preloaded for an off line viewing on laptops, ipads, and android phones or iphones. At anytime students can pause the lecture and ask questions on the forum monitored by the instructor. (ii) Students interact with the live course notes and read the textbook. (iii) Students begin solving homework problems on first their own and then engage in an online discussion with the instructor and other students by offering hints and asking questions. (iv) Submitted homework assignments are human graded and promptly returned with instructor or instructor teaching assistant's comments. Correct solutions to the assignments are then provided. The course combines the best proven methods in a traditional mathematics class together with a new social online learning environment that links students located at remote locations. The forum is actively moderated by the professor.
Students meet online. There are no required in class
meetings. There is one proctored event: a comprehensive final examination. Students take the exam at their home institution
or work place, or at other locations with a proctor at their
The course offers a flexible schedule. The student does not have to be present
at specific hours. However, there are homework deadlines and the student needs
to commit to working on the course and participating in discussion at
least once every two or three days.
Most students need between 5 to 7 hours per lesson -
for most lessons. This includes all: interacting with the video lecture, analyzing the notes, thinking and working on homework problems, and sharing ideas on
the forum. (The summer session is intensive: there are 3 lessons per week, 2
lessons in the Fall and Spring).
The final course grade is based on homework (including
quizzes), the student's online contributions, and the final exam. The computer
picks the weights in your favor according to these ranges.
(a) homework includingquizzes (50%-60%)(b) a comprehensive final
examination (20%-30%)(c) the student's online activity (remaining
weight) - responses and hints to other students' questions,
For example, if the student does not perform well under the time pressure of
the final exam, you could minimize the final exam contribution (down
to 20%) and instead ensure that your homeworks and your online
contributions are meaningful and substantial. In trully exceptional circumstances the professor may apply a slightly different grading scheme.
A final course grade can only be assigned if there is a record
of all three: a proctored final, a record of homeworks and the student's consistent online activity.
Is this course for you?
Students who succeeded in this course
tend to be independent, self-motivated, being able to adhere to a
regular schedule, students who were comfortable with algebra. Post
baccalaureate students preparing for medical schools and MBA as well
as high school students passionate about math also tend to do well.
The online course is not easier than a regular class, but it is often
more convenient. Students who are looking for a course that offers an
easy A with little learning should not apply, nor should students who
event remotely consider submitting somebody else's work. In cases of
proven cheating, we remove the student from the class without a refund
and we notify the student's school. In cases where the final grade
needs to be based on a limited or nonuniform track record, we
investigate the integrity of the records, for example we schedule a
skype/video conference with a student. Please read what students who
succeeded in this class before are saying. Also, please note that in
the summer the course is quite intensive and there are three lessons
About the author
Dr. Goetz is an active researcher in Dynamical Systems, an academic instructor, and an e-learning entrepreneur. Goetz graduated from the University of Illinois at Chicago in 1996 with a doctoral degree in mathematics. Since then he held visiting positions at Boston University, the University of Exeter, University of Marseille, Institut des Hautes Etudes Scientifiques (IHES) in France, and Instituto Nacional de Matematica Pura e Aplicada (IMPA) in Brazil. Dr.Goetz holds a tenured full professorship at San Francisco State University. He is a recipient of two National Science Foundation Grants for his research in Dynamical Systems with geometric singularities. He delivered over a hundred research talks at conferences and universities worldwide. An experienced academic instructor, Goetz is also the founder of Mangoroot, a multimedia internet platform for communicating and learning mathematics over the internet. The platform was used to successfully teach over a thousand of calculus students located in various locations in the US and abroad.
His passion to convey mathematics to his students takes him to remote places on the planet such as volcanoes and glaciers in Ecuador where he shoots multimedia calculus clips which are then incorporated in the teaching content.
Syllabus: Learning outcomes and list of topics
The central object of the study in calculus is the concept of a function. Functions are used to describe
the real world around us. Calculus I introduces two fundamental concepts which enable us to describe and investigate functions. These
are the derivative and the integral. The derivative
describes how a function changes at a particular time. The integral
carries information about the history of a function. Both, the
derivative and the integral are defined using limits. Calculus I
covers: Limits, Continuity, Asymptotes, The tangent problem, Rates of
Change, Derivatives (including trigonometric and transcendental
derivatives), Graphs, and their shapes, Optimizations, Riemann Sums,
Integrals including two parts of the Fundamental Theorem of Calculus.
List of topics.
Review of quadratic, exponential and logarithmic functions
Two fundamental problems in Calculus and Introduction to limits
Long term behavior and asymptotes
Rates of change
Derivatives of Polynomials and the Exponential Function
The Product and Quotient Rules
Derivatives of Trigonometric Functions
The Chain Rule
Derivatives of Logarithmic Functions
Exponential Growth and Decay
Minimum and Maximum Values
The Mean Value Theorem and Shapes of a Graph
Local Extrema and Inflection Points
Shapes of Graphs
Estimates of areas under graphs
The Area Function
Definite Integrals and Antiderivatives
Applications of the Fundamental Theorem of Calculus
At the conclusion of the course, students will be able to :
Evaluate a variety of limits including limits at infinity,
one-sided limits, and limits of indeterminate forms. Identify
discontinuities in functions presented algebraically or graphically;
Apply the definition of derivative to calculate and estimate
derivatives from formulas graphs, or data;
Differentiate sums, products and quotients of composite polynomial,
trigonometric, exponential, and logarithmic functions;
Discuss the conceptual relations between derivatives rates of
change, and tangent lines in the context of an applied example,
Analyze and solve exponential growth and decay differential equations;
Analyze graphs of functions by using asymptotes, first and second
Solve applied optimization problems and justify answers;
Estimate a definite integral with a Riemann sum and supply a sketch;
Evaluate simple definite integrals using the Fundamental Theorem of
Calculus; Differentiate integrals.
The studnet be provided with a free set of interactive
multimedia notes and the student will to print the pdf lesson notes (about the
total of 120 pages). The notes are the base material, not a full textbook.
In expensive used major textbooks should be used to supplement the notes.