page might be updated as the course progresses, including both review
materials and lectures and sources to help with new material.
Here are some handouts:
- A handout on the basic functions you are responsible for knowing
- A handout on exponents, radicals, and factoring, to help you catch up on some topics we will not cover in class. If you need more help on these topics, please visit the Khan Academy website for short helpful videos on these topics.
- A trig circle, with all of the values of sine and cosine which we expect you to know.
- A handout on trig identities. You are expected to memorize these.
- A handout on logarithm rules, with all of the log rules which we expect you to know.
are welcome to come to office hours with any kind of question -- we are
here to help you and ready to explain the same thing as many times as
necessary. You can also email your instructor or a Course Assistant if
you have any concerns.
Stanford offers free drop in
tutoring for Math 19 through the Center for Teaching and Learning
(CTL). All of the information is on the Undergraduate tutoring website.
Some graduate students also offer their services to tutor for Math 19, you can find their names and email address on the list of private tutors maintained by the math department. Beware, private tutors tend to be expensive.
Material covered for a given midterm in the past does not
necessarily correspond to the material covered in Math 19 this quarter
(even in Fall 2014), so bear this in mind when using these to
study for exams.
We will not provide solutions
other than the ones already available here, but you are welcome to ask
any instructor or course assistant to show you correct solutions to any
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
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).
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.
Accelerated Calculus for Engineers
program is administered by the School of Engineering, but it is not
only for engineering students. Students must apply to enroll in ACE;
you may find the application on the ACE website. Students who are admitted to the ACE program must participate in mandatory weekly discussion sections.
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.