Calculus 3, part 1 of 2
A total of 47.5 hours of lectures
This is an academic level course for university and college engineering. Due to its size, it is divided into two parts. This page describes the first of those two parts.
Level - Intermediate
You need to be familiar with Calculus 1 and Calculus 2 and some Linear Algebra before you can make full use of this course.
Curriculum
Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.
Calculus 3, part 1 of 2
Get the outline
A detailed list of all the lectures in part 1 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.
Get Calculus 3 part 1 on Udemy
When you buy the course on Udemy, you get access to it for life. There is just a one-time fee. The prices do vary a lot on Udemy, but if you use our link by clicking on this panel, you will get the best current price. See also our page on “coupon codes” in the menu (the current code is TPOT_SEP26).
Course Objectives & Outcomes for part 1
Describe position, velocity, speed and acceleration; compute arc length of parametric curves; arc length parametrization.
Several variants of the Chain Rule, involving different kinds functions. You will also learn how to apply these variants of the Chain Rule for problem solving.
Optimization of functions of several variables, both on open domains and on compact domains (Lagrange multipliers on the boundary, etc.).
How to solve problems in multivariable calculus (illustrated with more than 200 solved problems) and why these methods work.
Parameterize some curves (straight lines, circles, ellipses, graphs of functions of one variable, intersections of two surfaces).
Limits, continuity and differentiability for functions of several variables. Theory, geometric intuitions, and lots of problem solving.
Several variants of the Implicit Function Theorem, with various geometrical interpretations; problem solving.
Reviews (86)
Ilir S.
Udemy student
The course is very very nice! It covered some very important calculus topics and i cant wait to start the second part! I used to hate calculus because of the way i was taught in University, but now I'm enjoying every bit of it. Thank you Hania for the great effort you have put behind this.
Francisco O.
Udemy student
What can I say the value of this course it is not only contained in the material, I have learned a lot from Hania's courses, simply the careful of developing of the subject is outstanding. Here in this course many of the topics seen in calc 1 and 2 with some features of linear algebra really start making more practical sense. With help of these previous background the problems of surfaces and level curves become richer and less difficult to grasp.
Isael B.
Udemy student
Great Professor
Alex
Udemy student
Very clear and coherent so far. She really takes the time to explain all odds and ends of all examples and proofs. This is a very complete course.
Nathan B.
Udemy student
I've found that even when I understand the theory and KNOW how to solve the problems (or think I do), I STILL benefit from watching the solutions, because there's often some clever algebraic trick that I wouldn't have thought of, or would have taken me a long time to realize. Thank you for making these videos and taking the time to work through the examples to solidify the theory. I'm such a nerd, I binge your math videos instead of Netflix!
Wais A.
Udemy student
Very thorough covers everything
Jesus A.
Udemy student
Very good as usual.
Anurag P.
Udemy student
great experience so far. she explains the concepts intuitively.
William P.
Udemy student
yes very special teacher
Vasanth G.
Udemy student
I am really enjoying this course, after watching Cal 1 and 2 by the same teacher.
Marcelo S.
Udemy student
A Professora explica o conteúdo da matéria de forma detalhada, o que possibilita o entendimento do conteúdo em outros idiomas. Até o presente momento, foi uma das melhores aulas que tive nesta plataforma de ensino.Machine translation: The teacher explains the course material in detail, which makes it possible to understand the content in other languages. So far, it has been one of the best classes I've taken on this learning platform.
Gary E.
Udemy student
This course is well presented. She explains the concepts very clearly and in an order that flows well. Thank you for your work putting these courses together.
NARAYAN R.
Udemy student
This course is truly outstanding! The instructor is exceptional—her deep expertise in the subject shines through in every lesson. She is a remarkably talented educator, with a teaching style that sets her apart. Her contributions to Udemy and its students are invaluable!
Ishan A.
Udemy student
This is ultra amazing course . So detailed, so much in depth explanation .
Mike H.
Udemy student
Great course, alot of knowledge, documentations, and instructions. I primarily focus on Computer Graphics and deal with vectors, so expanding my knowledge into Calculus beyond linear algebra. Even in Machine Learning you will encounter Gradients and partial derivatives with N Dimension features, Training and learning. So this math stuff appears everywhere even in Computer Science.
Debbie C.
Udemy student
Great explanations and graphics that help reinforce the topics. I highly recommend this course.
Bruce P.
Udemy student
excellent course
John L.
Udemy student
Great awesome
Sam
Udemy student
She does a great job presenting theory
Ali A.
Udemy student
I needed some help in the calc 3 and this course is the ultimate
highly recommended
highly recommended
Matteo M.
Udemy student
It is a well-planned and detail-oriented class.
IMO, the best set of math courses available on the Internet.
The Professor is keen to transmit the concepts to the audience through this well-organised, structured, detailed and logical course.
IMO, the best set of math courses available on the Internet.
The Professor is keen to transmit the concepts to the audience through this well-organised, structured, detailed and logical course.
Abraham M.
Udemy student
I'll purchase EVERY course of this teacher. She is the teacher you need for learning Calculus.
Anonymized User
Udemy student
Overall an amazing course, definitely would recommend it to anyone trying to learn multi variable calculus such as myself. Very well structured, and self studying multivariable calculus was made so much easier with this course as this was my first transition from khan academy to Udemy, being 15yrs old and being done all the prerequisites to this course coming in to it was outstanding. Cannot say much more, just simply amazing!
P.S this is on my dad's business account.
P.S this is on my dad's business account.
Rajarshi M.
Udemy student
beyond amazing , this will do a better job than uni , pair it up with problems sets you are more than golden
Keivan S.
Udemy student
Hania's "Calculus 3 (multivariable calculus), Part 1 of 2" and "Part 2 of 2" courses are simply outstanding! Her deep knowledge of the subject and her ability to explain complex concepts with clarity and precision are remarkable. The courses are well-structured, with a perfect balance of theory and practical examples. Hania patiently solves each problem step-by-step, ensuring that students grasp the underlying principles thoroughly. The additional resources, such as detailed slides and notes, are incredibly useful for reinforcing the material. Highly recommended for anyone aiming to master this subject!
Roman
Udemy student
Great course with fundamental and consistent explanations of main topics of multivariable calculus. Hania, thanks a lot for your work - it was really useful and helpful!
Walter S.
Udemy student
Trust me, it is worth it, your mathematical maturity will be improved.
Bård K.
Udemy student
I have purchased both part 1 and part 2, and strongly recommend it if you do not like the way your university is teaching the subject, or if you want to get complete understanding of the subject, in WAY less time. This is probably the best investment I have made in my time in University! Hania is the best!
Ravi B.
Udemy student
Amazing!
Anvarbek A.
Udemy student
very comprehensive course for people who want to learn calculus 3 in detail 👌
CARLOS G.
Udemy student
the clases are clear. I am able to understand the complex subjects of this course
Mark J.
Udemy student
Very good. It is above expectations thus far. Instead of just providing a pdf with questions and answers, the lecturer patiently solves every problem. Very good way to learn.
Luís G.
Udemy student
It's an excellent course and one that, in my opinion, is at the top of its field. It is structured in a very professional, exhaustive way and at the same time is presented in a very pleasant way. The course offers everything; very explicit and explanatory theoretical presentation, very enlightening examples and presented in a detailed way. All of this is accompanied by pdfs of the presentation slides and notes on how to solve the exercises. It was a great pleasure for me to revisit these subjects, in this way, more than 40 years after my first encounter with them. It is undoubtedly the best course I have attended both electronically and in person to date. I therefore intend to use the author's various courses in my cycle of refreshing my knowledge of mathematics.
Deepa R.
Udemy student
Really well explained. I am visiting Maths after 30 years, so this chapter was very nicely understood and explained.
Venelin S.
Udemy student
Excellent presentation. Very clear explanation. Very well structured and systemized. It helps me to sort out all my previous knowledge. I am enjoying the course.
Robert G.
Udemy student
This is the 3rd course I have completed on Udemy and by far the best.
Prof. Uscka-Wehlou is easy to understand, provides many slides and graphics so that you really don't require the text. Also, the Prof. solves many examples without cutting any corners, ie. full explanations.
I would recommend this course and any others of this quality.
Prof. Uscka-Wehlou is easy to understand, provides many slides and graphics so that you really don't require the text. Also, the Prof. solves many examples without cutting any corners, ie. full explanations.
I would recommend this course and any others of this quality.
Chawn N.
Udemy student
Really helpful, east to understand, and exciting course for calc 3 up until midterms! Thanks
Omar S.
Udemy student
In the beginning of the course, i found that there was a lake of explanation and illustation of fundamental bases of linear algebra and all thier uses in multivariable calculus and how the link was made between two branches of mathwhich is a crucial point to well-understanding the multivariable functions, and in this part of course i would rpopose the first two chapters of vector calculus book for Susan Colley. But for the rest of what i have finished, i found the course is quite detailles and the instructor gives alot of example and uses all means like online software to illustrate shaps and figures. For me, one of the most and well-explained aprt of this this course was the module of Quadric surfaces
Joaquin G.
Udemy student
oh yeah !
Miguel G.
Udemy student
The best course that I have been able to find on the Internet about Calculus. Thank you very much Hania, for me you are the best teacher in this subject and in this format, and I'm so sorry I don't have enough time to work all these huge and magnificent contents as much as I would like. Greetings and good luck for everyone.
Gray M.
Udemy student
Hania is an absolute legend. She is on a mission to make high quality mathematics education accessible to those that want it <3
Alok K.
Udemy student
This course has been truly amazing with very clear explanations and examples of complex topics in Multivariable Calculus Part 1. I would highly recommend this to anyone interested in learning this subject.
mohamed Y.
Udemy student
best course ever the professor really knows what she is teaching ,,and i really love the way she explains the theory and the proof of each topic ,,because the why is most important in learning than the how,, i hope you make a linear algebra course on udemy the same way as this course ,,,thank u so much and god bless u
Josefana R.
Udemy student
Hania always gives the best courses.
Kin L.
Udemy student
Really thorough expanation! I have finally found a course that would not rush into the main topic straightaway, but spend some time on bridging new concepts with our past math learnings. The course is well arrange, I love the way you teach the basics. Apart from the topics like linear alegbra and calculus, I think you can make some courses about mathematical statistics or skills and concept of problem solving and proofs. Thank you.
Thomas P.
Udemy student
nearly perfect
Daniel S.
Udemy student
There are at least a couple of other multi-variable calculus courses at Udemy, but this one promises to be thorough and enriching. A couple of other courses I sampled consisted of perfunctory solutions of very simple exercises and no theory, and they are sadly diminished in comparison to this one, obviously a labor of love on the part of the instructor.
Kim N.
Udemy student
Great course and great teacher!
This is a rare course for math enthusiasts. Hania made hard concepts simple.
Your course encourages me to move on the next chapters of math.
Thank you very much!
This is a rare course for math enthusiasts. Hania made hard concepts simple.
Your course encourages me to move on the next chapters of math.
Thank you very much!
Bruno P.
Udemy student
Crystal clear!
Yuanqi J.
Udemy student
perfect over udemy
James B.
Udemy student
Dr. Uscka-Wehlou is the best. If you thinking about it, but are unsure, do yourself a favor and take this course, and all of her other courses.
Adil H.
Udemy student
Before taking this course i thought that i know most of the stuff in multivariable calculus but after taking this course how much ignorant i was of this beautiful math.
Alami F.
Udemy student
Les supports et les explications sont très claires. Juste un grand merci.Machine translation: The materials and explanations are very clear. Just a big thank you.
Yhasreen A.
Udemy student
clean clear presentation
John K.
Udemy student
Good pace
Benji S.
Udemy student
Wonderful teacher of both application and theory. I actually switched from another Udemy Cal 3 course to this one because I required a deeper understanding of the behind-the-scenes mechanisms. She has delivered in spectacular fashion.
Chamila G.
Udemy student
This course is amazingly structured , with very good explanations with lots of diagrams(sure your are going to understand things really well with those diagrams and Geogebra explanations)
The Professor is Solving problems (lot) on her ipad and walk you through every detail while she is solving the problems.This is pretty helpful to me.
The Professor is Solving problems (lot) on her ipad and walk you through every detail while she is solving the problems.This is pretty helpful to me.
David L.
Udemy student
I think this course is great. Top quality production, engagingly delivered in a comfortable setting that is perfectly matched to the content.
Almir B.
Udemy student
This course gave me the tools to better understand physics and engineering. Thanks Hania to putted your knowledge and teaching skills in it.
Cristobal M.
Udemy student
excelente
Murat F.
Udemy student
Great course with very thorough explanations and proofs. I was lacking lots of fundamental concepts about Calc 3, which is very important for many more advanced topics, like machine learning, optimization, signals and systems, etc. and now I feel more confident.
Professor Hania is very kind, knowledgeable and answers every question. I took all of her courses, and look forward to her future lectures.
Professor Hania is very kind, knowledgeable and answers every question. I took all of her courses, and look forward to her future lectures.
Bernard X.
Udemy student
Que ce soit pour le plaisir ou par nécessité, je pense que vous aurez beaucoup de plaisir à suivre ce cours.Machine translation: Whether you're taking this course for fun or out of necessity, I think you'll really enjoy it.
Serdar K.
Udemy student
This course is clear, gives a lot of additional background information about the subjects and great organization of videos that makes it really easy to follow.
Scott M.
Udemy student
This is a University quality / level course. I hope that any struggling undergrad mathematics student, who has a lecturer that is not making this subject clear and easy to understand, finds this course. It will do more than just get them through their assignments and tests, it will give them an excellent understanding of Calculus 3
Frank C.
Udemy student
Great and concise explanations Clear pronounciation. Good documentation with the course.
Amlan D.
Udemy student
Brilliant
Frederick S.
Udemy student
Absolutely the best course I've ever taken. Hope Prof Hania continues to make more. (Courses on ODE's and PDE's would be great). Fred S.
Sergio F.
Udemy student
Very good explanation about the content of this course.
Bobby Z.
Udemy student
Very detailed explanations! The professor replies to any questions very quickly. Overall very good experience! 10/10 would recommend
Estevan K.
Udemy student
This class is structured really really well and I hope it will help me pass my calculus class with an A.
Wan Y.
Udemy student
Excellent materials and coverage Slow moving, because of detailed-oriented. Nothing is left behind Completeness rather than speed of coverage. Patience is needed though, just like learning any serious subjects. Thank you for sharing with the world.
Nawid R.
Udemy student
Amazing course and great professor.
Afua D.
Udemy student
The professor is exceptional !
Ali T.
Udemy student
Hi, this is a great course and I'm really liking it. Can you please upload some exams like maybe previous exams for this course at your university. Thank you again for this great effort you put in teaching people around the world.
Somesh C.
Udemy student
I want to really thank you for creating this marvelous course!! The content is explained so well!
Christopher C.
Udemy student
Excellent course! I have found some of the other calc 3 courses helpful for quick referencing specific topics, but this is far and away the best comprehensive course I've found to take alongside my credit calculus 3 course. Organization, explanations and visuals are excellent. Highly recommended!
Ruchi P.
Udemy student
Very comprehensive
Mithun M.
Udemy student
Thank you for such a nice course, excited for part2.
Jesaya S.
Udemy student
Excellent pedagogy - very hard to find such lecture from where I come from.
Hopefully, Hania can produce more high-quality lectures on other mathematics topic in the near future, such as Calculus IV, Linear Algebra, Mathematical Physics, and so on.
Hopefully, Hania can produce more high-quality lectures on other mathematics topic in the near future, such as Calculus IV, Linear Algebra, Mathematical Physics, and so on.
Humberto R.
Udemy student
I just want to congratulate her for the AMAZING effort. WONDERFUL course. Detailed explained. If you want to progressively learn this topic that is applicable to other areas, this is your choice. I cannot wait for the second part of this course.
She is an extremely conscious, empathetic, and humanitarian expert in teaching.
She is an extremely conscious, empathetic, and humanitarian expert in teaching.
Gerd B.
Lecturer
This course will be inspiring for anyone studying calculus of several variables. It is pedagogically and technically well planned and elaborated at every level. The vivid presentations are elegant, clear and well-structured. Accompanying slides contain all the essential and necessary information combined with illustrative figures - crucial and central for the course. Still the slides are not overloaded. Great job!
As a former mathematics lecturer with long experience of teaching calculus of several variables I can strongly recommend this course to students interested in understanding and mastering calculus of several variables.
As a former mathematics lecturer with long experience of teaching calculus of several variables I can strongly recommend this course to students interested in understanding and mastering calculus of several variables.
Wanda W.
Lecturer
This course introduces a variety of topics in Calculus. The total number and duration of the lectures is impressive and everybody can find the knowledge they were looking for, but watching such a huge amount of lectures takes a lot of time, which is a drawback for impatient students. Luckily, there is a detailed list of all the topics and problems which can help you cherry pick for exactly what you need. Moreover, the course in not expensive, and you really get value for your money. Lectures (by a real university teacher) are taught in beautiful and clear English, with perfect illustrations in presentations. You get to see a lot of digital means in the teaching: surfaces in 3D change their shape with change of parameters x, y and z; formulas are perfectly explained and problems are solved by the teacher in her own handwriting, which gives you almost a classroom experience. I have completed the course and I highly recommend it to all who want to study Calculus 3. The second part of Calculus 3 is even better! I have also completed Calculus 1 and 2 by these instructors.
Shiva S.
Mathematician
I have worked as Lecturer in mathematics, and taught similar courses at university level. I have watched some of the videos but not all of them. Hania has introductions which can help understanding what you expect to learn and know, not just at the beginning but even during the course for different subjects. Whenever it is possible, she uses geometrical description to help understanding the concepts, and she explains things in a simple way that you understand them without being scared of their complexity.
Richard B.
Lecturer
No, I was not taking this course. I have been teaching introductory several real variables many times and to varying audience, and it then only is natural to want to know how others do it. The subject is necessarily technical, so one either may hide the details by quickly getting abstract, or else must handle the technicalities directly, a formidable task. Hania is doing the latter, and she is doing it thoroughly. Nothing is swept under the carpet. There is a wealth of examples and graphical illustrations. The prerequisites are largely explained too, slowly and methodically. The student is left no choice but to follow, step by step, learning complicated things without even noticing. Well done, Hania!
Andrzej P.
Udemy student
This course is perfect for people who would like to gain a good and thorough understanding of calculus. The lectures provide great explanations of a wide variety of subjects, with many pictures to illustrate what the covered concepts mean. There are plenty of expertly chosen and well explained exercises to choose from which show the most important techniques in calculus in an easy to follow manner.
Christer K.
Lecturer
Hania Uscka-Wehlou has presented several absolutely excellent courses, in particular on analysis in several real variables. Every single element of these courses is of utmost quality. In particular, the listing of the various parts is very clear and easy to follow. Hania gives a very clear introduction to each of the courses and what a student can expect in the coming course, and how to go further. This is just the beginning. Then all the following lectures are just wonderful. It is a pure pleasure to follow each and every one of them. Of course she gets five stars---but with the reservation that it is according to my expectations, having followed her remarkable development since 2003.