Calculus 2, part 1 of 2: Integrals with applications
A total of 56 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 the contents of the four Precalculus courses and Calculus 1, part 1 and 2 to comfortably follow along in 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 2, 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.
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Course Objectives & Outcomes for part 1
How to solve problems concerning integrals of real-valued functions of 1 variable (illustrated with 419 solved problems) and why these methods work.
Integration by parts as the Product Rule in reverse with many examples of its applications.
Integration of rational functions with help of partial fraction decomposition.
Direct and inverse substitutions; various types of trigonometric substitutions.
Euler’s substitutions.
Riemann integral (definite integral): its definition and geometrical interpretation in terms of area.
Oscillatory sums; Cauchy criterion of (Riemann) integrability.
Proof of uniform continuity of continuous functions on a closed bounded interval.
Integration by inspection: Riemann integrals of odd (or: even) functions over compact and symmetric-to-zero intervals.
Fundamental Theorem of Calculus (FTC) in two parts, with a proof.
Application of FTC for computing derivatives of functions defined with help of Riemann integrals with variable (one or both) limits of integration.
The Mean-Value Theorem for integrals with proof and with a geometrical interpretation; the concept of a mean value of a function on an interval.
Applications of Riemann integrals: rotational volume.
Applications of Riemann integrals: curve length.
Improper integrals of the second kind (integration of unbounded functions).
The concept of antiderivative / primitive function / indefinite integral of a function, and computing such integrals in a process reverse to differentiation.
Integration by substitution as the Chain Rule in reverse with many examples of its applications.
Various types of trigonometric integrals and how to handle them correctly.
The tangent half-angle substitution (universal trigonometric substitution).
Triangle substitutions.
An example of a function that is not Riemann integrable (the characteristic function of the set Q, restricted to [0,1]).
Sequential characterisation of (Riemann) integrability.
Integrability of continuous functions on closed intervals.
Integration by inspection: evaluating some definite integrals with help of areas known from geometry.
Applications of Fundamental Theorem of Calculus in Calc 2 and Calc3.
Application of FTC for computing limits of sequences that can be interpreted as Riemann sums for some integrable functions.
Applications of Riemann integrals: (signed) area between graphs of functions and the x-axis, area between curves defined by two continuous functions.
Applications of Riemann integrals: rotational area.
Improper integrals of the first kind (integration over an unbounded interval).
Comparison criteria for determining whether an improper integral is convergent or not.
Reviews (15)
Fernando L.
Udemy student
Excellent! 🥳
Vasanth G.
Udemy student
I have completed 4 parts of Precalculus and 3 parts of calculus so far, really enjoying it!
Francisco O.
Udemy student
This first part of calculus 2 is really depth, we cover many integrals techniques. Furthermore it is also balanced with practical exercises, there also interplay between the theory and practice. What can I say and excellent course
Pierpaolo D.
Udemy student
Yet again, another amazing course by Prof. Uscka. Everything is clearly explained, outlining all the logical steps and proofs. The course is full of solved exercises and extra material to practice further.
Ilir S.
Udemy student
Yet another masterpiece by Hania! Can't wait to move to the second part.
Kipkoech D.
Udemy student
i like the way in which you make calc 2 seem easy and understandable.. i hope to use the concepts and tricks learnt in this course to ease my college calculus 2 class next semester..
Hamid A.
Udemy student
Yes it was good so far and your language is clear and beautiful thank you mam
Bernard X.
Udemy student
parfait merciMachine translation: Perfect, thank you
Zacharias T.
Udemy student
Nice course
Josa191
Udemy student
I listened to 50% of the lecture and that's enough for me to write a review, but of course I will listen to the end 🙂
I have to admit that I am glad that I enrolled in the integral course and it exceeded my expectations. Much more than I expected! I will write in several installments what I recognized in that course:
1.) Every time I ask questions, Dr. Hania really tries to answer every question and never leaves a blank. Not only does she answer questions, but she answers in detail in the fine print. She explains very well and with quality, and she kept emphasizing that if I didn't understand the answer, I could ask again. I can say that I am delighted with it 🙂
2.) I noticed when she solves the integral examples and she really tries and is very patient and I can't believe that she solves every problem to the end with detailed steps. Other professors would write, for example, a+2b+c+3a = .... ( solve it yourself ) = ( the solution is given by the professor ). I have never seen so many examples in my life from the easiest all the way to the most difficult in all steps. She explains very patiently and calmly. I have never seen such teaching skills.
3.) In general, lectures on integrals have been adapted to first teach indefinite integrals in order to adopt the rules, and then everything else is easy to learn for definite integrals and improper integrals. A very good method because it well thought out that first the indefinite integral is learned as a kind of basic base for learning how to integrate and then build on the definite integral. Very good learning system!
4.) I liked how she gave examples from real life, I like good stories, tricks, anecdotes and applications of integrals in real life. It makes math more beautiful
5.) Dr. Hania is very humble, she accepts her mistake in a humble way. That is something wonderful! It is normal for us humans to make mistakes and she gladly accepts that. That's a huge plus.
6.) She always answers questions to e-mails quickly, I have never experienced such a thing where she would be happy to answer e-mails
7.) I looked at other math programs on Udemy, none of them are as professional as this one from Dr. Hania. I have experience in assessing mathematical expertise and can recognize when it is high quality, good and professional
8.) It can be seen that she has good pedagogy in education and has a very good approach to students so that they do not panic. She knows how to introduce control and peace in solving tasks
9.) She has a very neat handwriting when solving tasks and she really tries and makes sure that it is neat and legible
And finally, I definitely RECOMMEND everyone to enroll in this course to those who struggle with integration.
Given that English is my third foreign language, apologies for any grammatical or spelling mistakes in writing.
I have to admit that I am glad that I enrolled in the integral course and it exceeded my expectations. Much more than I expected! I will write in several installments what I recognized in that course:
1.) Every time I ask questions, Dr. Hania really tries to answer every question and never leaves a blank. Not only does she answer questions, but she answers in detail in the fine print. She explains very well and with quality, and she kept emphasizing that if I didn't understand the answer, I could ask again. I can say that I am delighted with it 🙂
2.) I noticed when she solves the integral examples and she really tries and is very patient and I can't believe that she solves every problem to the end with detailed steps. Other professors would write, for example, a+2b+c+3a = .... ( solve it yourself ) = ( the solution is given by the professor ). I have never seen so many examples in my life from the easiest all the way to the most difficult in all steps. She explains very patiently and calmly. I have never seen such teaching skills.
3.) In general, lectures on integrals have been adapted to first teach indefinite integrals in order to adopt the rules, and then everything else is easy to learn for definite integrals and improper integrals. A very good method because it well thought out that first the indefinite integral is learned as a kind of basic base for learning how to integrate and then build on the definite integral. Very good learning system!
4.) I liked how she gave examples from real life, I like good stories, tricks, anecdotes and applications of integrals in real life. It makes math more beautiful
5.) Dr. Hania is very humble, she accepts her mistake in a humble way. That is something wonderful! It is normal for us humans to make mistakes and she gladly accepts that. That's a huge plus.
6.) She always answers questions to e-mails quickly, I have never experienced such a thing where she would be happy to answer e-mails
7.) I looked at other math programs on Udemy, none of them are as professional as this one from Dr. Hania. I have experience in assessing mathematical expertise and can recognize when it is high quality, good and professional
8.) It can be seen that she has good pedagogy in education and has a very good approach to students so that they do not panic. She knows how to introduce control and peace in solving tasks
9.) She has a very neat handwriting when solving tasks and she really tries and makes sure that it is neat and legible
And finally, I definitely RECOMMEND everyone to enroll in this course to those who struggle with integration.
Given that English is my third foreign language, apologies for any grammatical or spelling mistakes in writing.
Yusuf E.
Udemy student
explanation is very simple but effective and very graphical slides.
Frederick S.
Udemy student
Yet another superb course. A bargain at any price, but with the discount coupon from Dr. Wehlou's website, this is an incredible value for the money. The production quality, graphics, and sound are all just so good. The subject material has been carefully organized and is expertly taught. I learned some new integration techniques and this course had the best explanation of the fundamental theorem of calculus I've ever seen. Can't wait until the next course comes out.
Wanda W.
Udemy student
Lecture is well presented and easy to understand. This is my 15th course by Hania and Martin that I've completed and I can recommend all of them.
Richard B.
Lecturer
This is the technical core of the thing come to be called Calculus, to the uninitiated surely a dark maize. But Hania shines the light for the wary wanderer, always showing the next turn, always leading the way. With the fog of doubt gone, the devil of detail quickly gets conquered, and the menacing jungle turns flower garden, every plant in due place. This said, the task in question is more like bike riding than flower picking, practice is paramount, and it then only is for the biker to be to bravely, thoroughly, patiently and conscientiously, endure the pain and the pleasure from each day honestly performing dozens and dozens of the zillion expertly crafted exercises.
Andrzej P.
Udemy student
Great course. I love how many optional details are included, in case the students want to understand the topics in more depth. Also, there are so many solved exercises!