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Title: Mathematical Physics Reference
Description: These notes cover formulae and brief description of many topics of mathematical physics/engineering at the level it is taught in undergraduate courses. The topics included are: basic trigonometry, differential and integral calculus, differential equations, vector calculus, complex analysis, coordinate transformations, Fourier analysis, Matrices and determinants, Stats and Probability etc.
Description: These notes cover formulae and brief description of many topics of mathematical physics/engineering at the level it is taught in undergraduate courses. The topics included are: basic trigonometry, differential and integral calculus, differential equations, vector calculus, complex analysis, coordinate transformations, Fourier analysis, Matrices and determinants, Stats and Probability etc.
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Reference Text for Mathematical Physics
Deepanshu Bisht
Contents
1 Some Common Standard Math Formulas
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2
3
2 Some less used formulae
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5
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3 Partial Derivatives
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6
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4 Differential Equations
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10
5 Complex Analysis
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14
6 Vector Calculus
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7 Coordinate Systems
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8 Binomial theorem, Permutation and Combinations
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9 Matrices and Determinants
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24
10 Limits and Series
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11 Standard Functions
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12 Everything Fourier
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13 Stats and Probability
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About the document
This document is a go-to reference in need of mathematical formulae/equations and associated notes
which are directly or indirectly useful in doing physics
...
Chapter 1
Some Common Standard Math
Formulas
1
...
1
...
1)
(1
...
3)
sin(a + b) = sin(a) cos(b) + cos(a)sin(b)
(1
...
5)
cos(a + b) = cos(a) cos(b) − sin(a) sin(b)
(1
...
7)
tan(a + b) =
tan(a) + tan(b)
1 − tan(a) tan(b)
(1
...
9)
sin(2a) = 2 sin(a) cos(a)
(1
...
11)
(1
...
13)
(1
...
15)
(1
...
17)
(1
...
1
...
2
(1
...
20)
(1
...
22)
(1
...
24)
Derivatives
d
(sin x) = cos x
dx
d
(cos x) = − sin x
dx
d
(tan x) = sec2 x
dx
d
(cot x) = −cosec2 x
dx
d
(sec x) = sec x tan x
dx
(1
...
26)
(1
...
28)
(1
...
30)
d
1
(sin−1 x) = √
dx
1 − x2
(1
...
32)
d
1
(tan−1 x) =
dx
1 + x2
d
−1
(cot−1 x) =
dx
1 + x2
1
d
(sec−1 x) = √
dx
x x2 − 1
d
−1
(cosec−1 x) = √
dx
x x2 − 1
d x
(e ) = ex
dx
d
1
(log|x|) =
dx
x
x
d
a
= ax
dx loga
2
(1
...
34)
(1
...
36)
(1
...
38)
(1
...
3
Integrals
Note: Evaluating the integral by changing the variables through substitution is all well and good
until
...
That is, x = f −1 (t) is a multi-valued function
...
40)
0
If for this integral we make the substitution sin x = t, both upper and lower limits become zero and
integral turns out to be 0
...
This happens cause x = sin−1 (t)
is multivalued
...
For the substitution cos x = t this doesnt happen since cos x doesnt repeat in 0 ≤ x ≤ π
1
...
1
Algebraic
ˆ
xn dx =
xn+1
+c
n+1
(1
...
3
...
42)
px + q
A
B
=
+
(x − a)2
x − a (x − a)2
(1
...
44)
px2 + qx + r
A
Bx + C
=
+ 2
2
(x − a)(x + bx + c)
x − a x + bx + c
(1
...
46)
ln|x|dx = xln|x| − x + c
(1
...
48)
(1
...
50)
(1
...
52)
(1
...
3
...
54)
cot x dx = ln| sin x| + c
(1
...
56)
cosec x dx = ln|cosec x − cot x| + c
(1
...
58)
cot2 xdx = −cot x − x + c
(1
...
60)
(1
...
62)
(1
...
64)
(1
...
66)
(1
...
3
Title: Mathematical Physics Reference
Description: These notes cover formulae and brief description of many topics of mathematical physics/engineering at the level it is taught in undergraduate courses. The topics included are: basic trigonometry, differential and integral calculus, differential equations, vector calculus, complex analysis, coordinate transformations, Fourier analysis, Matrices and determinants, Stats and Probability etc.
Description: These notes cover formulae and brief description of many topics of mathematical physics/engineering at the level it is taught in undergraduate courses. The topics included are: basic trigonometry, differential and integral calculus, differential equations, vector calculus, complex analysis, coordinate transformations, Fourier analysis, Matrices and determinants, Stats and Probability etc.