You are welcome to come to office hours with any kind of
question (see the home page for times) -- we are here to help you and ready to explain
the same thing as many times as necessary. You can also
email the instructor or course assistant if you have
The Office of the Vice Provost for Teaching and Learning
offers free drop-in and individual appointment tutoring in
the following Math courses: Math 19, 20, 21, 41, 42, 51,
52, 53. To schedule an individual appointment, visit
view our drop-in schedule and to view information about
tutoring for other courses, visit tutoring.stanford.edu.
Some graduate students also offer their services to tutor
for Math 19, you can find their names and email address on
of private tutors maintained by the math
department. Beware, private tutors tend to be
The Stanford Math Department has developed two mini-courses
to help you review or learn trigonometry, and exponentials
and logarithms. The mini-courses are a quick and
to-the-point review of certain areas of precalculus that a
sizeable proportion of students need to brush up on before
taking calculus. They consist of short videos followed by
supplementary videos and exercises from Khan
Academy. While they typically will not cover every single
important aspect of a topic, they are a fast way to get to
a good place before starting calculus.
The Stanford Math Department has developed an online
learning tool to help you acquire the precalculus
skills you will need for the Math 20 series. This resource
is an in-depth, time-intensive survey of most precalculus
topics you will encounter at Stanford. It is recommended
for students who feel that they need extensive extra
practice across a wide range of precalculus topics, or who
need to learn precalculus topics from scratch. There is a
fee for use of the software ($34 for 6 weeks of help, $82
for 18 weeks of help).
The precalculus topics go through Module 12, but you
might want to also work on the topics of Modules 15 and 16
as they will be important for us this year.
Another interesting resource for this class is Khan Academy, a
website which hosts short, very helpful lectures. We
highly recommend you spend some time looking through their
Algebra lectures. We also expect their Calculus lectures
will be very helpful throughout the course. They have a
very popular sequence hosted at iTunesU. Some sample
sessions are given below. You may not need all (or any) of
these or you may need more. Try some out and don't
hesitate to contact any member of the teaching staff if
you have any questions. If you are feeling either bold or
highly confused, you can start from the beginning with a
very thorough set of diagnostic exercises that can help
pinpoint where you should be focusing. To do the
diagnostic exercises, start at the
exercise dashboard (and be patient, it starts with
arithmetic and finishes at calculus).
The following is a list of video topics we think will be particularly
helpful to Math 19-20-21 students. This list may or may not be updated
as the course progresses.
Trigonometry: You might now be best served by the Stanford Mini-Course on Trigonometry.
For all trig videos on Khan Academy, you can see the Basic Trigonometry Homepage and the Trig identities and examples Homepage. For maximum success, work out the exercises.
Rational inequalities: For all videos having to do with rational expressions, you can see the Rational Expressions Homepage. For maximum success, work out the exercises.
- quadratic inequalities (2 parts)
- functions (4 parts/)
- domain of a function
- rational inequalities (2 parts)
- function inverses (4 parts)
- algebraic long division
- limits: introduction, examples (5 parts)
- squeeze theorem
- proof:lim (sin x)/x
- exponential growth
- parametric equations
- logarithmic scale
- function inverses
Work through all of the videos, including sequences and series! There
is not so much here and getting these short, concise summaries will
help your overall comprehension.