Single Variable Calculus James Stewart

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Martha Weitz

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Aug 3, 2024, 11:44:14 AM8/3/24

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Single-variable calculus textbooks focus on functions of a single independent variable, while multi-variable calculus textbooks also cover functions with multiple independent variables. Single-variable calculus is typically taught in high school or early college, while multi-variable calculus is usually a more advanced topic.

Yes, a strong understanding of algebra is crucial for understanding calculus. Many concepts in calculus involve manipulating equations and solving for variables, which require a solid foundation in algebra.

No, it is not recommended to use a single-variable calculus textbook to learn multi-variable calculus. While there may be some overlap in topics, multi-variable calculus introduces new concepts and techniques that are not covered in single-variable calculus.

Most calculus textbooks require a strong understanding of algebra, trigonometry, and pre-calculus concepts. Some may also require knowledge of basic geometry and limits. It is important to check the specific prerequisites listed by the textbook before using it.

When choosing a calculus textbook, consider your level of understanding and the level of the course you are taking. Look for textbooks with clear explanations, plenty of examples and practice problems, and a format that works well for your learning style. It can also be helpful to read reviews and compare different textbooks before making a decision.

Differential and integral calculus of functions of one independent variable. Topics include the basic analytic geometry of graphs of functions, and their limits, integrals and derivatives, including the Fundamental Theorem of Calculus. Also, some applications of the integral, like arc length and volumes of solids with rotational symmetry, are discussed. Applications to the physical sciences and engineering will be a focus of this course, as this course is designed to meet the needs of students in these disciplines. Course Note(s): Not for credit. Not eligible for financial aid. Prerequisite(s): Pre-calculus (e.g., AS.110.105 or equivalent)

The course materials are divided into weekly modules which can be accessed in Canvas. A module will have several sections, including the overview, lectures, practice problems, online homework, online quizzes, and supplemental material. During weeks of an exam, the exam will be found online in the module. You should check regularly the calendar in Canvas for due dates, the discussion board, and the announcements page for updates and reminders.

Main concepts of calculus are derivatives (rates of change of a function) and integrals (which, in particular, provide a way to recover a function from the knowledge of its derivative). Knowledge and the ability to work with these concepts is essential for further studies of mathematical subjects, as well as for applications of mathematical techniques in other sciences. This course will focus on understanding calculus concepts, analytical reasoning and developing crucial skills in order to calculate, analyze, interpret and communicate the results clearly.

Homework is online and is assigned for each week. There are three attempts at each online homework problem set. The highest of the attempts is counted as the grade. Your lowest homework grade will be dropped.

There will be 2 mid-term exams. The exams are online and use Respondus Lock Down Browser and Webcam. There will be a cumulative final exam the last week of class. All exams are due by end of day Sunday of the exam week.

There will be a short online quiz each week. There are two attempts at the quiz and the questions are pulled randomly during each attempt. The higher of the two attempts counts for the grade. Your lowest quiz grade will be dropped.

Collaboration Policy:
Collaboration on homework is allowed and encouraged. However, each student must write up his/her solutions to the problems individually and in his/her own words - copying from another student's paper is prohibited. Homework is an essential part of learning the course material. Failing to give it proper attention will significantly harm your performance on the exams and your overall grade for the class.

Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar ( -services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.

Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.

If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

I just recently learned the the definition of differentiable at a point in my multi-variable calculus class. The analogy between the multi-variable definition and that of the single variable uses the fact that the difference between the exact value of the function and the value of the tangent line approximation of the function goes to $0$ as $\Delta x$ goes to $0$. Later I forgot the definition, but I used this intuitive idea to come up with the following definition: