Vector Calculus for Engineers

Although I earned a BS degree in chemical engineering in 1999 and have taken multivariable calculus, Professor Jeffrey Chasnov’s Vector Calculus for Engineers was a great challenging learning process.

I found the time needed to complete the course could be long or short. Initially, I started out as I do with all my courses and tried to solve all problems without looking at the solutions. Since the course is compressed, much is covered in a short period. There were new topics that I had to learn, and I was rusty on other topics. So, week 3 sent me a message. Don’t be afraid to learn from the solutions to meet the deadlines. This is very important for week 4, which was the most challenging week for me.

When learning from the solutions, one MUST figure out the missing steps to ensure competence on the weekly assessments. This takes knowledge of physics and mathematics for some problems, and just mathematics for other problems. In engineering, we were taught to always draw our system. I found this to be true in this course as well. At times, one cannot just memorize the equations given, and there are many great equations and tricks given, but one must take the extra step to figure out how the equations were derived. As a simple example, the last problem in the notes integrates the circle over dr and one must remember that s = r(theta) and ds = r d(theta) to get the problem fully. This is knowledge from trigonometry and basic calculus, and Professor Chasnov expects one to use known physics and mathematical relationships to solve problems. Obviously, this includes material learned in Vector Calculus for Engineers.

I found the time required to complete problems was longer than suggested, and I put in 6 hours a day on some days, but my average was near 4 hours a day. Most weekly assessments took me much longer than 45 minutes to complete. Week 4 took me 4.5 hours but note that I shot for 100% on each assessment on first attempt. Also, I have an illness that causes shaky hands so my writing can be bad. This is a huge factor in later weeks where much algebra is needed to solve the problems. Week 5 had excellent applications.

Overall, Professor Jeffrey Chasnov put together a very useful course for engineers, physicists, and people who want to learn vector calculus. He does expect familiarity with mathematics and physics, and I am happy I had refreshed my algebra, trigonometry, single variable calculus, and physics using Coursera. I also used MITx and MIT OCW. I now have more confidence going into my study of computational fluid dynamics (CFD) and fluid dynamics

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**Course Review: Vector Calculus for Engineers (HKUST via Coursera)**

*Rating: ★★★★☆ (4/5)*

I recently completed the *Vector Calculus for Engineers* course offered by the Hong Kong University of Science and Technology (HKUST) on Coursera, and overall, I was impressed with the content and structure. Here are my thoughts:

### **Course Content:**
The course does an excellent job of covering key concepts in vector calculus, which are crucial for students in engineering and physical sciences. The topics include vector fields, line integrals, surface integrals, divergence, curl, and Green's, Gauss', and Stokes' theorems, among others. The explanations were clear, and the progression from one topic to the next felt natural.

What I particularly appreciated was the emphasis on real-world applications. As an engineering student, it's easy to get bogged down in the abstract aspects of mathematics, but this course did a fantastic job of relating the concepts to practical engineering problems like fluid dynamics, electromagnetism, and more.

### **Instructor & Presentation:**
The course is taught by knowledgeable instructors who break down the complex topics into manageable segments. The teaching style is engaging, and the use of visual aids, such as diagrams and animations, helped reinforce the material. The pace of the lectures was appropriate, though some sections were a bit dense and required additional review on my part.

One of the highlights of the course was the integration of interactive examples and exercises. The quizzes after each module really helped in reinforcing the concepts and provided a great way to check my understanding as I moved through the course.

### **Hands-On Experience:**
This course strikes a nice balance between theory and practice. There are assignments that encourage you to apply the theoretical concepts to practical problems, which really enhanced my learning experience. However, I feel that more real-world problem sets could have been incorporated to give students more opportunities for applied learning.

### **Difficulty Level:**
I would classify this course as intermediate in terms of difficulty. It’s suitable for those with a basic understanding of multivariable calculus, though I would recommend some familiarity with topics like partial derivatives and integrals beforehand. For those without prior knowledge in these areas, certain sections might be challenging, but the course does provide enough review to help you get up to speed.

### **Course Platform:**
The course is hosted on Coursera, which makes it convenient for remote learning. The platform is user-friendly, and the video quality is excellent. The discussion forums were a helpful resource, and I found the interaction with fellow learners to be quite enriching.

### **Conclusion:**
Overall, *Vector Calculus for Engineers* is a solid, well-structured course that serves as a great introduction to the application of vector calculus in engineering. It’s both informative and challenging, and I feel more confident in my understanding of the subject after completing it. I would highly recommend this course to anyone pursuing a degree in engineering, physics, or any related field.

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I recently completed the *Vector Calculus for Engineers* course offered by the Hong Kong University of Science and Technology (HKUST) on Coursera, and overall, I was impressed with the content and structure. Here are my thoughts:

### **Course Content:**
The course does an excellent job of covering key concepts in vector calculus, which are crucial for students in engineering and physical sciences. The topics include vector fields, line integrals, surface integrals, divergence, curl, and Green's, Gauss', and Stokes' theorems, among others. The explanations were clear, and the progression from one topic to the next felt natural.

What I particularly appreciated was the emphasis on real-world applications. As an engineering student, it's easy to get bogged down in the abstract aspects of mathematics, but this course did a fantastic job of relating the concepts to practical engineering problems like fluid dynamics, electromagnetism, and more.

### **Instructor & Presentation:**
The course is taught by knowledgeable instructors who break down the complex topics into manageable segments. The teaching style is engaging, and the use of visual aids, such as diagrams and animations, helped reinforce the material. The pace of the lectures was appropriate, though some sections were a bit dense and required additional review on my part.

One of the highlights of the course was the integration of interactive examples and exercises. The quizzes after each module really helped in reinforcing the concepts and provided a great way to check my understanding as I moved through the course.

### **Hands-On Experience:**
This course strikes a nice balance between theory and practice. There are assignments that encourage you to apply the theoretical concepts to practical problems, which really enhanced my learning experience. However, I feel that more real-world problem sets could have been incorporated to give students more opportunities for applied learning.

### **Difficulty Level:**
I would classify this course as intermediate in terms of difficulty. It’s suitable for those with a basic understanding of multivariable calculus, though I would recommend some familiarity with topics like partial derivatives and integrals beforehand. For those without prior knowledge in these areas, certain sections might be challenging, but the course does provide enough review to help you get up to speed.

### **Course Platform:**
The course is hosted on Coursera, which makes it convenient for remote learning. The platform is user-friendly, and the video quality is excellent. The discussion forums were a helpful resource, and I found the interaction with fellow learners to be quite enriching.

### **Conclusion:**
Overall, *Vector Calculus for Engineers* is a solid, well-structured course that serves as a great introduction to the application of vector calculus in engineering. It’s both informative and challenging, and I feel more confident in my understanding of the subject after completing it. I would highly recommend this course to anyone pursuing a degree in engineering, physics, or any related field.

I can only deliver a mixed review. The course presents a generous amount of material, and all the basics are covered, but the presentation, especially in the final week, is perfunctory at best, grinding through derivations and leaving many steps for the student simply to "look up". Therefore, I recommend the course only as a review for anyone who already knows the material; trying to learn the details for the first time from this rushed and compressed presentation is likely to be frustrating, if not discouraging.

This is a likely related to Coursera's pressure to cram course contents into 4-week lumps as much as of anything else. That said, the lectures are well-organized trips through the standard derivations of results in Cartesian and spherical coordinate systems, but the motivation of the utility of scalar and vector products as projections and volumes is left behind once it has been given that perfunctory treatment in the early lectures. The course makes no attempt to get beyond dimension that can treated with analytic geometry of planes and 3-space; we do see the fluxes on cube faces and on the boundary of spheres; sadly, these treatments are too rushed. Vector calculus is a rich and beautiful subject, but don't come here to try to learn it for the first time.

I found the Vector Calculus for Engineers course on Coursera to be an excellent learning experience. The system is designed very well, making the overall process of studying and navigating the material straightforward and easy to follow.
The instructor's teaching methodology is particularly effective; I found the concepts to be presented in a way that is highly understandable and easy to grasp. This clarity is crucial for a complex topic like vector calculus. Furthermore, the inclusion of practice exercises is a significant strength. These exercises are invaluable for reviewing and reinforcing comprehension, which ultimately solidifies the knowledge required for engineering applications. Overall, it's a well-structured and beneficial course.

A great refresher course if you already know vector calculus and would like to take a cursory glance to brush up the concepts. I didn't have the in-depth knowledge of the topic but tackling it on your own can at first seem daunting. It had been something of a personal challenge for me. This course seemed to offer a practical grasp of the topics in four weeks. I figured if I could manage this, I will be able to gather enough courage to independently study the topic in more detail. Thanks to the incredible instructor, Professor Chasnov, the material didn't seem too hard. But I should mention that I am a physics major and I was already comfortable with working with vectors and had a good enough grasp on Calculus 2. My only complaint was with problems in lecture 41 which I personally thought could have done with an additional video on how to apply the theorems to Navier Stokes equation. I think I was looking a bit more information for the physical meaning behind the problem and how the theorems exactly help us. Something you can find out online... but that would require putting in additional hours, if you are up for it. I certainly had to work a lot more than what the course suggests is the time required to complete a given week.

All in all, I would definitely recommend this course to anyone who wants to get a working understanding of using multivariable calculus.