Basic Mathematics Applied in Physics

(SHORT NOTES)

 BINOMIAL APPROXIMATION 

If x << 1, then (1 + x)n ≈ 1 + nx & (1 – x)n ≈ 1 – nx

 LOGARITHM

 log mn = log m + log n

 log m/n = log m – log n

 log mn = n log m

 loge m = 2.303 log10m

 log 2 = 0.3010

 COMPONENDO AND DIVIDENDO LAW 

If p a pq ab then q b pq ab + + = = − −

 ARITHMETIC PROGRESSION-AP FORMULA

 a, a + d, a + 2d, a + 3d, …, a + (n – 1)d,

 here d = common difference

 Sum of n terms Sn = n 2 [2a + (n – 1)d]

GEOMETRICAL PROGRESSION-GP FORMULA

 a, ar, ar2 , … here, r = common ratio 

Sum of n terms Sn = n a(1 r ) 1 r − − 

Sum of ∞ terms S∞ = a 1 r − 

TRIGONOMETRY

 • 2p radian = 360°

 ⇒ 1 rad = 57.3° 

• cosec q = 1/ sin θ

 • sec q = 1/ cos θ

 • cot q = 1/ tan θ

 • sin^2 q + cos^2 q = 1 

• 1 + tan^2 q = sec^2 q 

• 1 + cot^2 q = cosec^2 q

 • sin (A ± B) = sin A cos B ± cos A sin B 

• cos (A ± B) = cos A cos B ∓ sin A sin B 

• tan (A ± B) = tan A tan B/ 1 tan A± tan B 

 • sin 2A = 2 sin A cos A 

• cos 2A = cos^2 A – sin^2 A = 1 – 2 sin^2 A = 2 cos^2 A – 1

 • tan 2A = 2  tan A /1 -tan^2 A

Approximation for small q 

• sin q ≈ q • cos q ≈ 1 

• tan q ≈ q ≈ sin q 

Formulae for Calculation of Area

 • Area of a square = (side)2

 • Area of rectangle = length × breadth

 • Area of a triangle = 1/2 × base × height

 • Area of a trapezoid = 1/2 × (distance between parallel sides) × (sum of parallel sides)

 • Area enclosed by a circle = pi r^2 (r = radius)

 • Surface area of a sphere = 4pi r^2 (r = radius)

 • Area of a parallelogram = base × height

 • Area of curved surface of cylinder = 2pi rl (r = radius and l = length)

 • Area of whole surface of cylinder = 2pi r (r + l) (l = length)

 • Area of ellipse = pi ab (a & b are semi major and semi minor axis repsectively)

. • Surface area of a cube = 6(side)2 Volume of Geometrical Figures

 • Volume of a sphere = 4/ 3 pi r^3 (r = radius)

 • Volume of a cylinder = pi r^2 l (r = radius and l = length)

 • Volume of a cone = 1/ 3 pi r^2 h (r = radius and h = height