What are some introductory notes on integration?

In summary, there was a conversation about notes on integration and receiving feedback. The notes were created using LaTeX and inkscape, with the intention of being a free and helpful resource for students. There was a suggestion to use a different symbol for the dummy variable in the integral and a typo was pointed out. Overall, the notes were praised for their quality and usefulness.
  • #1
hunt_mat
Homework Helper
1,782
32
For fun, I wrote some notes on integration which should provide a good solid introduction to the subject. They are not analysis notes but more of a first introduction to integration.

Any (constructive) comments or suggestions are always welcome.

Mat
 

Attachments

  • integration.pdf
    414.3 KB · Views: 642
Mathematics news on Phys.org
  • #2
I just did a quick browse, but this is great, I had read calculus for dummies as my first introduction to the subject and this is of equal if not better quality. Plus its free! thanks alot, this is great!
 
  • #3
Looks great! If you don't mind me asking, what programs did you use to make this...(i.e. for getting a nice math font, pictures, etc).
 
  • #4
I am hoping to do some tutoring on the side and it helps if you have your own set of notes for things.

I used LaTeX to do the equations and things and I used inkscape for the pictures.
 
  • #5
At P.5, the symbols for the upper and lower integral at eq. (11) and (13) are just the normal integral sign. Apart from that, I don't see any problems. Good work!
 
  • #6
Cheers.
 
  • #7
I have been compiling a sets of notes in certain things on my website: http://hyperkahler.co.uk/maths-tuition/learning-materials/
 
Last edited by a moderator:
  • #8
shape function:

it is to find the field variables at any point which is in terms of nodes
field variables are=displacements,rotations,e.t.c
 
  • #9
I think this is really good, both as a reference to integration methods and as theory. One thing I could think of is to be careful about [itex] \int _a ^x f(x) dx [/itex], to have a different symbol for the dummy variable.
 
  • #10
I make this explicit at the bottom of page 5, I see one typo with I haven't done this but I have used a different letter in other integrals.
 
  • #11
Thanks!
 

1. What is integration?

Integration is a mathematical concept that involves finding the area under a curve. It is a fundamental tool in calculus and is used to solve various problems, such as finding the distance traveled by an object or the volume of a 3D shape.

2. How is integration different from differentiation?

Differentiation and integration are inverse operations. While differentiation finds the slope of a curve at a specific point, integration finds the area under the curve. In other words, differentiation is about finding the rate of change, while integration is about finding the total change.

3. What are the different types of integration?

There are two main types of integration: indefinite and definite. Indefinite integration involves finding the general antiderivative of a function, while definite integration involves evaluating the area under a curve between two specific points. Other types of integration include improper integration, multiple integration, and line integration.

4. What are the basic integration rules?

The basic integration rules include the power rule, which states that the integral of x^n is (x^(n+1))/(n+1), and the constant multiple rule, which states that the integral of c*f(x) is c times the integral of f(x). Other important rules include the sum and difference rules, the substitution rule, and the integration by parts rule.

5. How is integration used in real life?

Integration is used in various fields, including physics, engineering, and economics. It is used to calculate areas, volumes, and rates of change, making it an essential tool for solving real-world problems. For example, integration is used to calculate the trajectory of a projectile, the volume of a tank, and the profit of a business.

Similar threads

Replies
9
Views
1K
  • Sticky
  • Science and Math Textbooks
Replies
10
Views
5K
Replies
4
Views
380
  • Science and Math Textbooks
Replies
2
Views
1K
Replies
21
Views
789
  • General Math
Replies
7
Views
2K
  • STEM Academic Advising
Replies
11
Views
633
Replies
13
Views
2K
  • Sticky
  • Science and Math Textbooks
Replies
27
Views
3K
Replies
1
Views
2K
Back
Top