This 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 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.
You 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.
The most representative exams for us are those from Fall 2013 and Fall 2012. 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 2012 and 2013), 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 problem.
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.