605.156.81 - Calculus for Engineers

Expanded Course Description

Engineers rely on calculus to design bridges, analyze circuits, optimize mechanical systems, and even develop new technologies in AI. This course is structured to provide you with the mathematical fluency and analytical mindset necessary for success in your engineering career. By the end of the semester, you’ll have a solid grasp of calculus concepts and their engineering applications, preparing you for more advanced coursework and real-world problem-solving.

This course will be fast-paced and rigorous, but don’t worry—you won’t be tackling it alone! We’ll provide structured support through engaging lectures, collaborative problem-solving sessions, and hands-on applications to reinforce key concepts.

So, if you’re ready to think critically, solve complex problems, and push your mathematical skills to the next level, welcome aboard! Let’s dive into the language of engineering and unlock the power of calculus together.

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the course menu. A module will have several sections including the overview, video lectures and content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

This course is designed with computer engineers in mind, emphasizing practical applications and problem-solving techniques that are directly relevant to AI/computer engineering disciplines. We will move quickly through the core concepts, but with a focus on understanding, application, and mastery, ensuring that you not only learn the material but also know how to use it in real-world contexts.

Key Topics Include:

• Limits and Continuity: Understanding the foundation of calculus and the behavior of functions.
• Differentiation: Learning how rates of change govern motion, optimization, and engineering systems.
• Integration: Exploring accumulation, area, and volume, with applications in physics and engineering.
• Applications of Derivatives and Integrals: Real-world problem-solving, including optimization, work, and energy.
• Sequences and Series: Mastering infinite processes and their applications in engineering analysis.

• Precalculus Review: Functions
• The Limit of a Function
• Continuity, Limits at Infinity, and the Derivative
• Finding Derivatives
• Applications of Derivatives & Intro to Antiderivatives
• Definite Integral
• Fundamental Theorem of Calculus
• Substitution Rule
• Sequences & Series
• Tests for Series Convergence
• Taylor & Power Series
• Applications of Integrals
• Techniques of Integration
• Improper Integrals

Course Goals

The goal of this course is to equip engineering students with a comprehensive and accelerated mastery of the core concepts from Calculus 1 and Calculus 2—spanning derivatives, integrals, sequences, series, and their real-world applications—while fostering advanced problem-solving skills, critical thinking, and the ability to apply mathematical principles to complex engineering challenges in areas such as physics, robotics, systems optimization, and dynamic process modeling.

Course Learning Outcomes (CLOs)

• Differentiate functions of one variable using limits, derivative rules, and implicit differentiation, and interpret derivatives in the context of rates of change and engineering applications.
• Apply derivatives to solve problems involving optimization, related rates, linearization, and motion, including real-world engineering scenarios.
• Evaluate definite and indefinite integrals using fundamental integration techniques such as substitution, integration by parts, and partial fractions.
• Apply the Fundamental Theorem of Calculus to connect differentiation and integration, and interpret integrals as accumulation functions in physical and engineering contexts.
• Use integrals to solve applications involving area, volume, arc length, surface area, work, fluid pressure, and other engineering-related quantities.
• Analyze sequences and series, including tests for convergence, power series, and Taylor/Maclaurin series, and apply them to function approximation.
• Model and solve problems using differential equations and integrals in contexts such as population growth, electrical circuits, heat transfer, and mechanical systems.
• Interpret and communicate mathematical reasoning clearly, using symbolic, graphical, numerical, and verbal representations to support engineering problem-solving.

Textbooks

Required Text: Single Variable Calculus: Early Transcendentals, 8th Edition, James Stewart, Brooks-Cole, February 2015, ISBN-10: 1305270339, ISBN-13: 978-1305270336. Chapters covered: 1-11.

Other Materials & Online Resources

Calculator Policy: Calculators are not allowed, nor needed, on exams, including the final. Some homework assignments may require the use of a scientific calculator for rounding purposes, otherwise a calculator is not necessary for the course.

Student Coursework Requirements

It is expected that each module will take approximately 7–10 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2–3 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 3–4 hours per week), and problem set assignments (approximately 2–3 hours per week).

Homework

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.

Exams: 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.

Quizzes: 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.

Discussion Forums:  Each week you are to post your initial response to the discussion by Thursday night and respond to at least two classmates by end of day Sunday. Your lowest discussion forum grade will be dropped. 

Grading Policy

Assignments are due according to the dates posted in the Canvas course site. Students may check these due dates in the Course Calendar or the Assignments in the corresponding modules. Grades will post no later than one week after assignment due dates. A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week. A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

The following grades are used for this course: A+, A, A– (excellent), B+, B, B– (good), C (unsatisfactory), F (failure), I (incomplete). A grade of F indicates the student’s failure to complete or comprehend the course work.

A course for which an unsatisfactory grade (C or F) has been received may be retaken. The original grade is replaced with an R. If the failed course includes laboratory, both the lecture and laboratory work must be retaken unless the instructor indicates otherwise. A grade of W is issued to those who have dropped the course after the refund period but before the drop deadline. The transcript is part of the student’s permanent record at the university. No grade may be changed except to correct an error, to replace an incomplete with a grade, or to replace a grade with an R.

The Whiting School assumes that students possess acceptable written command of the English language. It is proper for faculty to consider writing quality when assigning grades.

For incomplete grades, please see the Graduate Programs catalogue for the Whiting School of Engineering.

The course grading scale is the following:

100–98 = A+
97–94 = A
93–90 = A−
89–87 = B+
86–83 = B
82–80 = B−
79–70 = C

Course Evaluation

Final grades will be determined by the following weighting:

10% Discussions (lowest grade dropped)
10% Homework  (lowest grade dropped)
15% Quizzes  (lowest grade dropped)
20% Midterm Exam 1 
20% Midterm Exam 2
25% Final Exam   (in addition to the final, this replaces a lower midterm grade.)

All assignments are due according to the dates in the Calendar.

Late submissions will be reduced (no exceptions without prior coordination with the instructors).

Exams (50% of Final Grade Calculation, 30% for Midterms and 20% for Final)

The midterm exams will be available in Module 7 and Module 11. The final exam will be available in the last Module. You will have one week to complete the exams and they will be due by 11:59PM on the last day of the module from which it was released.

Course Policies

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.

Generative AI Policy:
This course assumes that work submitted for a grade by students – all process work, drafts, brainstorming artifacts, final works – will be generated by the students themselves, working individually or in groups as directed by class assignment instructions. This policy indicates the following constitute violations of academic honesty: a student has another person/entity do the work of any substantive portion of a graded assignment for them, which includes purchasing work from a company, hiring a person or company to complete an assignment or exam, and/or using generative AI tools (such as ChatGPT)."

Academic Policies

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 (https://ep.jhu.edu/student-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. This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University is committed to providing welcoming, equitable, and accessible educational experiences for all students. If disability accommodations are needed for this course, students should request accommodations through Student Disability Services (SDS) as early as possible to provide time for effective communication and arrangements.  For further information about this process, please refer to the SDS Website.

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.  For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

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).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.