Math 105B

Syllabus

Course:  Math 105B

Title:  Advanced Mathematics for Science and Engineering II

Credit Hours:  4

Prerequisites:  Math 105A.

Instructor: Ali Behzadan (You may click on your instructor's name to send an email to your instructor.)

Tentative List of Topics:  Concepts and examples of partial differential equations (PDE). Notion of well-posed problems. Basics of wave equations and diffusion equations. Fourier series, orthogonal expansions, and eigenvalue problems. Separation of variables for PDEs. Series solutions of ODEs (if time allows). A more detailed list of topics scheduled to be covered can be found  here.

The main objective will be to have a clear understanding of certain basic ideas and techniques in the analytical study of linear partial differential equations. Students will be able to articulate the fundamental questions in the study of PDEs and explain various types of PDEs. They will be able to demonstrate understanding of various solution techniques and solve problems and carry out calculations especially with examples that are important throughout mathematics and physics.

Textbook:  There is no required textbook. Lectures do not follow any particular textbook; we will draw material from a variety of sources including the following references:

• Partial Differential Equations: An Introduction, Second Edition, by W. A. Strauss; Wiley, (2007).
• Advanced Engineering Mathematics (Sac State Custom Edition, Copyright Year 2013), by E. Kreyszig.

You should regard the notes you take in class as your primary source; the textbook is a companion source, for those moments when I have been incomplete in class, or when you want to read further in a topic that interests you.

Homework:  Homework is a very important part of the course and in order to fully master the topics it is essential that you work carefully on every assignment and try your best to complete every problem. We will have two different kinds of homework assignments in this class: Gradescope homework and "paper-and-pen" homework.

• "Paper-and-Pen" Homework:  The "paper-and-pen" homework assignments will be announced on the course homework page. You should make every effort to complete the "paper-and-pen" homework assignments and seek help with problems you have not been able to solve.
• Gradescope Homework:   Each week you will be asked to complete at least one or two homework assignment(s) in Gradescope. Gradescope homework questions can be multiple choice, multiple answer, or fill-in-the-blank style. The due date for each assignment will be announced in class and posted to Gradescope.
• Late homework will not be accepted.
• You will be automatically enrolled in this course at Gradescope by August 29th.
• Your login will be your university email, and your password can be changed (or set) here.

Course Readings:  Please carefully study the lecture notes of the previous lecture at least twice before the next lecture and bring your questions to my office hours. You are responsible for material in the notes whether or not it is discussed in the lecture. Reviewing the material covered in the previous lesson will provide a framework to which the new information can be attached in the next lesson. Research has proven that new information can be more easily understood when it can be integrated with previous information and organized into larger schemata. I recommend that you summarize the key points that are taught in each lecture on a separate sheet of paper.

Lectures:   You are responsible for material presented in the lecture whether or not it is discussed in any notes or textbook. The lectures will emphasize ideas and concepts, rather than just computational examples. You should expect questions on the exams that will test your understanding of concepts discussed in the lectures.

Attendance: Your assumption should be that you are a responsible teacher who is teaching the course. So it does not make sense to miss any class or arrive late or leave early. Attendance is worth 5 points; lectures for which attendance data is recorded will be weighted equally. In order to receive the attendance score, please arrive on time (it will help if you make sure to be in class at least 5 minutes early) and please do not leave class early. Missing more than five lectures will result in an automatic "F" in the course (if you miss more than five lectures, then your course letter grade will be F). This policy may appear to be harsh, but please know that the aim of our attendance policy is by no means to add to your stress. The goal is to ensure that everyone is keeping up with the course. Many of us have the habit of procrastination. It has been repeatedly proven to me that it is less likely for my students to fall behind if they attend the lectures. Your education is of paramount importance and I care about you and your education.

• Note: If for reasons of illness, injury, or emergency health issues, you will not be able to regularly attend the lectures, you must email me by the end of Week 1. I will help you in any way I can. I promise together we will find an alternative method for calculating your attendance score.

Announcements:   It is absolutely essential that you check your Sac State email and course announcements on Canvas at least once a day. I may give you important information with 24 hours' notice. Also please check our course homework page regularly for possible updates.

Exams:  There will be two midterm exams and a final exam. The exams will be either in-class or take-home (this will be decided later). For take-home exams you may be contacted after the exams have been graded to set up a zoom meeting to eliminate any cheating suspicions.

• Midterm Exam 1: Wednesday 10/05/2022
• Midterm Exam 2: Wednesday 11/16/2022
• Final Exam: Dec 16 (Friday) 8:00 - 10:00 am.

Grading:  Your Math 105B weighted average will be calculated as follows:

• 5% Attendance,  20% Homework,   35% Midterm Exams,   40% Final Exam

After your weighted average is calculated, letter grades will be assigned based on the following grading scale:

A	A-	B+	B	B-	C+	C	C-	F
≥95	[91,95)	[87,91)	[83,87)	[80,83)	[77,80)	[73,77)	[70,73)	[0,70)

In addition,

you must pass the final examination (score≥70) in order to pass the course,

your score on each single paper-and-pen homework assignment must be greater than or equal to 70 (out of 100) in order to pass the course,

your average score on midterm exams must be greater than or equal to 70 (out of 100) in order to pass the course,

your average score on any four consecutive Gradescope homework assignments must be greater than or equal to 50 (out of 100) in order to pass the course,

you must receive a perfect score on the "Syllabus/Introductory Email Quiz" to pass the course.

There will be no curve. Your score will be solely based on your own performance and not how others perform in class. Also your final percentage grade will NOT be rounded up. So 94.9999% is an A-. Please do not be more concerned with your grade than with what you learn. Remember "Grades don't measure your intelligence, age doesn't define your maturity and disabilities don't define your worth."

Note: Please notice that outside factors, including the need for a certain grade for admission/retention in any academic program, scholarship or transfer credit, graduation requirements or personal desire for a specific grade DO NOT appear in the above calculations. Your letter grade will be determined solely based on your performance as described above. Financial aid status, delay in graduation, etc. cannot be used as reasons for a grade change. Such requests are absolutely unacceptable and will be processed as a form of academic dishonesty.

Grade Recording Errors:  This course will have a Gradescope page; your homework and midterm grades will be recorded on the Gradescope page (or the Canvas page) for our class. Please always make sure that your grades have been inputted and inputted correctly. Keep all of your returned exams. If there is any mistake in the recording of your scores, you will need the original exam in order for us to make a change. In particular, if there is any mistake in the recording of your exam or homework scores, you must notify me within two days after the score was posted to Gradescope page (or the Canvas page) for our class (otherwise your request will not be considered).

Make-up Exams:  Make-up exams will not be given. You cannot take any exam early or late. In particular, it is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in this class if you cannot take the final exam at the scheduled time.

Extra Credit:  Each pen-and-paper homework assignment contains some questions marked in bold. You will get extra credit if you come to my office hours and explain your solutions to the bold questions of the week. For each successful presentation you will earn 1/2 point extra credit which will be added directly to your final grade.

Be on Time:  Please arrive on time; in fact, it will help if you make sure to be in class at least 5 minutes early. Also please do not leave class early.

Office Hours:   I have scheduled a large number of office hours. Study the lecture notes regularly and make sure to bring your questions to my office hours. There is nothing that I like more than talking with you about math. In the unlikely case that all my office hours will conflict with your classes, you must let me know by the end of Week 1 so that we investigate the issue and possibly schedule even more office hours.

How to Succeed in My Course:   The main purpose of my Math 105B class is not to measure how smart you are compared to others. Your grades will not be curved and your score will be solely based on your own performance and not how others perform in class. The main objective of my class is to ensure that you will learn the basics of partial differential equations, and to achieve that goal it is absolutely essential that you do the following:

• 1- Please attend EVERY SINGLE class and be engaged by active listening. You must not arrive late or leave early.
• 2- Please carefully study the lecture notes of the previous lecture at least twice before the next lecture and bring your questions to my office hours. Please study every lecture line by line and try to understand every detail. Please make sure that you fully understand the meaning of each statement and the purpose of each single statement in the lecture notes and bring your questions to my office hours.
• 3- You must spend adequate time on each homework assignment and bring your questions to my office hours.

Spend Sufficient Time on the Course:  Since Math 105B is worth 4 credits, you should be willing to spend at least 12 hours per week on the course during a regular semester.

Electronic Devices:   Please do NOT use devices such as laptops, tablets, cell phones for non-class-related purposes while in class.

Academic Dishonesty:   Academic dishonesty is considered a serious offense at CSUS.  All problems in exams should be solved using terminology, ideas, and methods that were introduced in lecture. If in any of your solutions you use ideas, notation, or techniques that have not been discussed in lecture, that will be considered as cheating.  Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.   It is in your best interest to maintain your academic integrity. (Click here for more information.)

Lastly,  I believe that we are so incredibly fortunate to live in this wonderful place and have the opportunity to work or study at CSUS. If you share this sentiment, if you believe in the power of honesty and integrity, if you believe in the power of hard work and determination, and if you believe in lifting people up and not tearing them down, please do take my class. I will stop at nothing to help you succeed in this class.