Lectures are where I will introduce and explore the material. Throughout the semester, I'll do my best to make you part of the process, giving you the chance to try problems yourself and ask questions. If there's something you feel unsure of, don't feel nervous about putting your hand up. If you are thinking it, then so are lots of other people in the room. I'm here to guide you towards proper understanding, not deliver dry uninterupted monologues. The more like a back and forth conversation, the better!

LEC 001: 9.30am-11.00am TT, Wheeler Auditorium

LEC 002: 2.00pm-3.30pm TT, Wheeler Auditorium

Both lectures will be identical and you are welcome to attend either, although it would be best to attend your offical section for the first few weeks. The second lecture will be livestreamed.

Attendance at lecture is not mandatory, although I strongly advise that you go.

Don't fall behind, keep a steady pace so you understand what everyone's talking about in the next lecture/discussion section. Even then, reviewing right before your next Math 1B class always helps refresh your memory and help you better build on concepts.

1B student, Fall 2022

Here are the in-person lecture notes.

Every week you will have three hours of discussion session led by a GSI or UGSI (graduate or undergraduate student instructor). It's in these sessions that you'll really explore the material as a group (around 25 students in each section). In discussion section you'll work together to solve challenging problems. This is where you'll really learn how to master the material. Here's some advice about how to get the most out of discussion section:

• Learning Mathematics can be really challenging. As with almost anything in life, making it a social experience will make the process much more rewarding and productive. View discussion section as a way to both learn the material and potentially find people to work with outside of class.
• Don't be nervous about asking questions (or answering them) in group discussions. Even if you're not correct, lots of other people will definitely be thinking the same thing and it'll be a learning experience for the group. There are often many ways to approach a problem and hearing other peoples' perspectives can dramatically deepen your understanding.
• Your GSI will frequently split the main group into smaller groups where you'll work on problems more collaboratively. Be an active participant in these. Even if you're not completely confident in your approach, still share it.

For a discussion section schedule go to the folllowing links: Section 001 and Section 002.

You can only attend the section you are officially enrolled in. If you have enrollment questions contact: enrollment@math.berkeley.edu

You'll be following fixed worksheets in your discussions. After you've had section, they'll be posted here along with solutions.

Attendance at discussion section is not mandatory, although I strongly advise that you go.

Take advantage of discussion and office hours to practice more problems. You really do most of the learning in homework and discussion, just attending lectures isn't enough!

1B student, Spring 2020

Here is contact information for all GSIs and UGSIs.

In addition to lectures and discussion section, you will have access to daily office hours. Office hours are you're chance to talk to me or a GSI/UGSI. They are a really good way to get to know your instructors better and get help with any aspect of the course. These are also a space for you to work in small study groups at your own pace if you'd like.

In office hours you can talk about any aspect of the course (and beyond). If you've spent time on a homework problem and have stalled, come to office hours; If you're unsure about your academic trajectory, come to office hours; If you want to learn what mathematics research is about, come to office hours; If you're struggling with the course and don't know what to do, come to office hours; If you think you might need a reference from a professor in the future, come to office hours; If you just want a chat, come to office hours.

Go to as many office hours as you can! I only started going after doing badly on the second midterm. I should have been attending from the start. It would have made a big difference.

1B student, Spring 2019

I'll be having office hours 2pm-4pm MWF. As a default GSI/UGSI office hours are in-person, although some will be conducted online via Zoom.

Here is a link with the full office hour schedule.

Math 1B is a continuation of Math 1A. From the get-go, that means it assumes a good knowledge of that course (or an equivalent, e.g. AB Calculus).

Before that though, there are various pre-calculus topics (trigonometry, and algebra with inequalities and absolute values especially) which you'll want to have a solid grasp of. Here's a complete pre-calculus course that I've designed to help you. I'll let you know which specific topics to review as we go through the semester.

If you want a lightning quick overview, here's a pre-calculus cheatsheet.

It's inevitable that you'll have forgotten details over the break (or longer), so to help you review foundational topics, I've recorded a complete collection of videos lessons for the whole of Math 1A. To access them, go to this link and click on the Syllabus, Videos and Lecture Notes tab. This is obviously a lot of material, but you should look at the three review videos when you have the time.

You'll also find a review video in the Schedule and Videos tab below. It's important that you look at this before the first day of class.

The textbook for this course is: Stewart, Single Variable Calculus: Early Transcendentals for UC Berkeley, 8th edition (ISBN: 9781305765276, Cengage).

This is a custom edition containing chapters 1-9, 11 and 17 of Stewart's "Calculus: Early Transcendentals", 8th edition. The regular edition is also fine, it just contains extra chapters covered in math 53. The 7th edition is also acceptable, but you will need to watch for differences in the numbering of assigned homework problems. In chronological order, we'll cover material in chapters 7, 11, 9, 17

Even though it's probably something you aren't used to doing, I strongly recommend reading the textbook throughout the semester. It provides more detail than can possibly be covered in lectures (either in-person or recorded), and is a habit you want to get into now. Future courses will not have videos to fall back on and reading the textbook will be absolutely vital.

Reading the textbook alongside the lectures really helps. When you're stuck on a homework problem try to find a similar example in the book.

1B student, Spring 2018

Here is the homework schedule.

Homework assignments are due each Wednesday at 11.59pm on Gradescope. Here are instructions for how to upload your work. Your two lowest homework scores will be dropped.

Each assignemnt will be graded on a combination of completeness and correctness. More specifically you will get three points for submitting solutions to all exercises. In addition, each week a randomly selected question will be graded (out of three points) for correctness. Your two lowest scores will be dropped. You may discuss the homework problems with your classmates, but you must write your solutions on your own. Make use of discussion sections, office hours, study groups, etc. if you need assistance, but in the end, you should still write up your own solutions.

Lectures are where new concepts are introduced, but homework is where most of the real learning happens. It's where you internalize the abstract ideas and discover for yourself how they can be used to solve problems. From my experience the main distinction between those who succeed in this course and those who don't, is how they treat the homework. Here's some advice about how to approach it:

• Be organized. Don't leave things for the last moment. (You'll struggle to complete the homework assignment if you start on the night before it is due.) Work consistently in small installments. Some homework can take 6 hours to complete properly.
• As you progress through the homework you'll notice it increasing in difficulty. The more difficult problems are often the most important, giving you the opportunity to really master the material. If you're struggling with a challenging problem you should spend at least 30 minutes on your own, thinking about it in depth. Even if you fail to make a breakthrough, this is still more worthwhile than giving up after a couple of minutes and talking to a peer or consulting an answer scheme. In future courses you'll be solving problems that require days (or weeks) of dedicated thought. Now is the time to hone this skill.
• If you've spent serious time exploring a problem and are still struggling, then is the time to seek help: Speak to your peers, come to my or a GSIs office hours, go to the SLC and talk to a tutor. The last thing you should do is look at a solution manual. Actively speaking to someone about a problem is much better than passively reading a solution.

Homework Solutions will be made available shortly after submission at this link.

Take the homework seriously. It will really help on exams as practice. In addition, doing more problems on the homework for subjects you are weak in will help as well

1B student, Spring 2019

In addition to homework, roughly every week, you will have either a quiz or project.

Quizzes will take place on Thursday (LEC001) or Friday (LEC002), roughly every two week in discussion section. They will last about 15 minutes and be closely related to the homework submitted that week. Your lowest score will be dropped from your grade.

Projects will give you the opportunity to explore certain topics in more depth, perhaps exploring interesting real-world applications, or more subtle questions what we don't have time to cover in lectures. They will be due on Friday, roughly every two weeks on Gradescope. Here are instructions on how to upload your work. Your lowest score will be dropped from your grade.

The projects (and later their solutions) will available at this link.

What	When
Quiz 1	Week 2
Project 1	Week 3
Quiz 2	Week 4
Project 2	Week 6
Quiz 3	Week 7
Project 3	Week 8
Quiz 4	Week 9
Project 4	Week 12
Quiz 5	Week 13
Quiz 6	Week 14
Project 5	Week 15

There will be no make-up quizzes, unless there are exceptional circumstances.

Here a link containing practice exams. These are very similar to the actual exams. Make sure you study them carefully.

Spend a lot of time studying the practice exams. Don't leave it till the day before to look at them. They are hard, but the real exams are basically the same.

1B student, Fall 2021

There will be two midterms and a final. There will be no make-up exams, unless there are truly exceptional circumstances.

Because of the grading scheme, you can miss one midterm, for whatever reason, without penalty. On the other hand, missing both midterms will seriously harm your grade and make it much more difficult to pass the course.

As per university policy, if you do not sit the final exam, you automatically fail the course. Please check the dates now to make sure that you have no unavoidable conflicts!

Here is the schedule:

• Midterm 1: Thursday February 15, in class (Wheeler Auditorium)
• Midterm 2: Thursday March 21, in class (Wheeler Auditorium)
• Final Exam: LEC 001 Wednesday May 8, 11.30am-2.30pm (Exam Location TBD); LEC 002 Monday May 6, 11.30am-2.30pm (Exam Location TBD).

Calculators and notes will NOT be allowed for the exams.

To obtain full credit for an exam question, you must obtain the correct answer and give a correct and readable derivation or justification of the answer. Unjustified correct answers will be regarded very suspiciously and will receive little or no credit. The graders are looking for demonstration that you understand the material. To maximize credit, cross out incorrect work. We will be scanning all exams so you will get them back electronically.

After each midterm, there will be a brief window when you can request a regrade. If you are unsure about making a regrade request consult myself or your GSI beforehand. Regrade requests may result in a lowering of your grade. As per university policy, final exams cannot be regraded.

DSP students requiring accommodations for exams must submit to the instructor a "letter of accommodation" from the Disabled Students Program. Due to delays in processing, you are encouraged to contact the DSP office before the start of the semester.

Cheating is unacceptable. Any student caught cheating will be reported to higher authorities for disciplinary action.

In Math 1A or elsewhere, you studied functions of a single variable, limits, and continuity. You learned about derivatives, which describe how functions change, and which can be used to help find maxima and minima of functions. You also learned about integrals which describe the aggregate behavior of a function over an interval, such as the area under a curve or the average of a varying quantity. The derivative and the integral are tied together in the fundamental theorem of calculus, one version of which relates the integral of the derivative of a function over an interval to the values of the function at the endpoints of the interval.

In this course we will continue the study of calculus in three parts as follows:

• The first part of the course is about techniques of integration (sections 7.1 to 7.8 of the book). As you should already know, differentiation is relatively straightforward: if you know the derivatives of elementary functions, and rules such as the product rule and the chain rule, then you can differentiate just about any function you will ever come across. Integration, on the other hand, is hard. Sometimes it is even impossible to integrate a given function explicitly in terms of known functions. We will introduce a collection of useful tricks with which you can integrate many functions. The hard part is to figure out which trick(s) to use in a given situation. For integrals which we cannot evaluate explicitly, we will learn how to find good approximations to the answer.
• The second part of the course is about sequences and series (chapter 11 of the book). This can be regarded as the general theory of approximating things. This part of the course is subtle and involves new ways of thinking. It may be a lot harder than the first part, especially if you have seen some of the first part before.
• The third part of the course is an introduction to ordinary differential equations (chapters 9 and 17 of the book). Here one tries to understand a function, given an equation involving the function and its derivatives. ("Ordinary" means that we consider functions of a single variable. Functions of several variables enter into "partial" differential equations, which you can learn about in a more advanced course.) The theory of differential equations is perhaps the most interesting part of calculus, is the subject of much present-day research, and has many real-world applications. Our study of differential equations will make use of most of the calculus we have done so far.

When	What	Where
Week 1 (1/15 - 1/19)	Review (Make sure you look at this before the first lecture) Video
	Integration by Parts Video	7.1
	Rational Integrals Video	7.4
Week 2 (1/22 - 1/26)	Trigonometric Integrals Video	7.2
	Trigonometric Substitution Video	7.3
Week 3 (1/29 - 2/2)	Strategies of Integration Video	7.5
	Approximate Integration Video	7.7
Week 4 (2/5 - 2/9)	Errors and Approximate Integration Video	7.7
	Improper Integrals Video	7.8
Week 5 (2/12 - 2/16)	Sequences and Series Video	11.1, 11.2
	Midterm 1 (In class, Thursday 2/15)
Week 6 (2/19 - 2/23)	Divergence and Integral Tests Video	11.2, 11.3
	Comparison and Alternating Series Tests Video	11.4, 11.5
Week 7 (2/26 - 3/1)	The Ratio and Root Tests Video	11.6
	Strategies for Series Testing Video	11.7
Week 8 (3/4 - 3/8)	Power Series Video	11.8
	Representing Functions as Power Series Video	11.9
Week 9 (3/11 - 3/15)	Taylor Series Video	11.10
	Errors and Taylor Polynomials Video	11.10
Week 10 (3/18 - 3/22)	Differential Equations and Direction Fields Video	9.1, 9.2
	Power Series Review Video Video
	Midterm 2 (In class, Thursday 3/21)
Week 11 (3/25 - 3/29)	Spring Break!
Week 12 (4/1 - 4/5)	Separable Equations Video	9.3
	Models of Population Growth Video	9.4
	Linear First-Order Equations Video	9.5
Week 13 (4/8 - 4/12)	Complex Numbers Video
	Second-Order Homogeneous Linear Equations Video	17.1
Week 14 (4/15 - 4/19)	Second-Order Nonhomogeneous Linear Equations Video	17.2
Week 15 (4/22 - 4/26)	Series Solutions Video	17.4
	Something Fun	17.2
Week 16 (4/29 - 5/3)	RRR week
Week 17 (5/6 - 5/10)	Final Exams

Grades are calculated as follows:

Homework	10%
Projects and Quizzes	10%
First Midterm	20%
Second Midterm	20%
Final Exam	40%

If your final exam score is higher than your lowest midterm exam score, then it will replace it, thus accounting for 60% of your grade. This means you can miss a midterm for any reason whatsoever and it will not necessarily adversely effect your grade.

Your final letter grade will ultimately be decided by your ability to demonstrate a crisp understanding of the material and the ability to apply it to a diverse set of problems. Broadly speaking I will be looking for the following criteria for each letter grade:

• A-/A/A+: A clear demonstration that the central concepts have been fully understood; Computational techniques (and their many subtleties) have been mastered and can be applied accurately to a diverse problem set; A strong understanding of how the abstract concepts can be applied to many real world applications.
• B-/B/B+: Demonstration that the central concepts have been reasonably understood, but perhaps with minor misunderstandings; Core computational techniques have been reaonably understood (but generally not key subtleties) and can be applied fairly accurately to a fairly large problem set; Reasonable understanding of how the abstract concepts can be applied to some real world applications.
• C-/C/C+: Demonstration that the central concepts have been vaguely understood, but with major misunderstandings; Core computational techniques have been poorly understood and can be a applied accurately only in the most standard examples; Weak understanding of how the abstract concepts can be applied to even basic real world applications.

To be as fair as possible, I will also take into account the historic average of the class. This means that if I set an exam which is very difficult it will be taken into account in the final letter grades.

Please note: incomplete grades, according to univlersity policy, can be given only if unanticipated events beyond your control (e.g. a medical emergency) make it impossible for you to complete the course, and if you are otherwise passing (with a C- or above).

Enrollment: For question about enrollment contact Marsha Snow, or email enrollment@math.berkeley.edu.

The Student Learning Center provides support for this class, including full adjunct courses, review sessions for exams, and drop-in tutoring. This is a truly fantastic resource. I definitely recommend you take advantage of it.