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### CSIR-NET Physics and GATE physics: Fourier Series

CSIR-NET Physics and GATE physics: Fourier Series: Fourier series is an expansion of a periodic function of period $2\pi$ which is representation of a function in a series of sine or cosine...

### Mathematics revision sheet for class 11 and class 12 physics

Differentiation
We have two quantities x and y such that  where  is some function of x.We may be interested in finding followings things
1.
2. Maximum and Minimum values of y.It can be find with the method of Maxima and Minima
is the called the derivative of y w.r.t to x
It is defined as
Some commonly known functions and their derivatives are:-
Some important and useful rules for finding derivatives of composite functions
1.  where c is constant
2.  where a and b are function of x
3.
4.
5.
6.
Maximum and Minimum values of y
Step 1:
fine the derivative of y w.r.t x
Step2:
Equate
Solve the equation to find out the values of x
Step3:
find the second derivative of y w.r.t x and calculate the values of
for the values of x from step2
if  then the value of x corresponds to mimina of y then  can be find out by putting this value of x
if  then the value of x corresponds to maxima of y then  can be find out by putting this value of x
Integration
It reads as integration of function f(x) w.r.t. x within the limits from x=a to x=b.
Integration of some important functions are
Useful rules for integration are
Trigonometry
Properties of trigonometric functions
1. Pythagorean identity
2. Periodic function
3.Even-Odd Identities
4. Quotient identities

5. Co-function identities

6. Sum difference formulas

7. Double angle formulas

8. Product to sum formulas

9. Power reducing formulas

10. reciprocal identities
Binomial Theorem

From the binomial formula, if we let a = 1 and b = x, we can also obtain the binomial series which is valid for any real number n if |x| < 1.
(1+x)^n=1+nx+\frac{n(n-1)}{2!}x^2+\frac{n(n-1)(n-2)}{3!}x^3+………..
Geometric Series
where q is not equal to 0, q is the common ratio and a is a scale factor.Formula for the sum of the first n numbers of geometric progression

Infinite geometric series where |q| < 1
If |q| < 1 then , when n -> infinity So the sum S of such a infinite geometric progression is:
which is valid only for |x|
Arithmetic Progression
The sum S of the first n values of a finite sequence is given by the formula: