Complete BASIC MATHEMATICS For Physics NEET 2024 | PART 1 | Basic Maths for Physics |Free

 

Complete BASIC MATHEMATICS For Physics NEET 2024 | PART 1 | Basic Maths for Physics | 

Foreign, I hope you all are doing well. Welcome to Vedanta NEET English channel. In this lecture, we will cover the basics of mathematics for physics, which is often a challenge for biology students. We will focus on algebra, fractions, and finding roots.

Algebra

• In algebra, we use operations like multiplication and division.
• For example, if we multiply a with b and divide it by c, we can write it as a*b/c.
• If we have a fraction like a/b/c/d, we convert it into multiplication by taking the reciprocal of the denominator. So, a/b/c/d becomes a*d/b*c.

Fractions

We also need to know how to find fractions. For example, if we have ax + bx, we can factor out x to get x(a+b). Similarly, x^2 - y^2 can be written as (x+y)(x-y). These are the basic forms of fractions we need to be familiar with.

Finding Roots

In physics, we often come across problems where we need to find the roots of an equation. Let's take an example of finding the roots of x^2 - 2x - 15 = 0.

We can use two methods to find the roots:

1. Common method: By factoring the equation, we can rewrite it as (x+3)(x-5) = 0. So, the roots are x = -3 and x = 5.
2. Formula method: We can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. For example, if we have the equation 10x^2 - 27x + 5 = 0, we can directly substitute the values of a, b, and c into the formula to find the roots.

By using these methods, we can easily find the roots of equations.

Quadratic Equations

To find the roots of a quadratic equation, you can use the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

The roots are usually named as alpha (α) and beta (β).

For example, if you have the equation ax^2 + bx + c = 0, the roots can be found using:

• α = (-b + √(b^2 - 4ac)) / 2a
• β = (-b - √(b^2 - 4ac)) / 2a

You can also check the values of α and β using the formulas:

• α + β = -b / a
• α * β = c / a

Make sure to substitute the correct values of a, b, and c into the formulas.

Multiplying Powers

When multiplying powers with the same base, you can add the exponents:

x^m * x^n = x^(m+n)

If the bases are different, the exponents cannot be added or subtracted.

For example, (x^m)/(x^n) = x^(m-n).

You can also apply these rules to more complex expressions:

• (x^m * y^m) = (xy)^m
• (x^m)/(y^m) = (x/y)^m

Logarithmic Functions

There are two types of logarithms: ln (natural log) and log (base 10).

The natural log, ln, is the logarithm with base e.

The logarithm with base 10 is written as log.

You can convert ln to log by multiplying it with 2.303, and vice versa.

Some important formulas to remember:

• ln(e) = 1
• log(1/x) = -log(x)
• log(x^n) = n * log(x)
• log(x * y) = log(x) + log(y)
• log(x/y) = log(x) - log(y)

When dealing with logarithms, there are various formulas that can be applied. For example, the formula for log(1/x) to the base e can be written as -log(x) to the base e. These formulas also apply to logarithms with base 10.

Arithmetic progression is a sequence of numbers arranged in increasing order with a constant difference between them. For example, the sequence 2, 4, 6, 8, 10 follows this rule. The formulas for arithmetic progression include the nth term formula: an = a0 + (n-1)d, and the sum of arithmetic progression formula: Sn = n/2(a0 + an).

Geometric progression is a sequence of numbers where each successive term is obtained by multiplying the previous term by a constant ratio. For example, the sequence 1, 1/3, 1/9, 1/27 follows this rule. The formulas for geometric progression include the sum of n terms formula: Sn = a(1 - r^n) / (1 - r), and the sum of infinite terms formula: Sn = a / (1 - r).

For both arithmetic and geometric progressions, it is important to remember the given formulas and the conditions for their application. By using these formulas, you can easily find the nth term or sum of a series.

To illustrate, let's consider an example:

Given the series 10, 13, 16, ..., we can see that it follows the conditions for arithmetic progression. To find the sum of the series, we can use the formula Sn = n/2(a0 + an). In this case, a0 = 10 and an = 16. Plugging these values into the formula, we get Sn = 7/2(10 + 16) = 35.

Similarly, for a geometric progression example, let's consider the series 1, 1/3, 1/9, .... It follows the conditions for geometric progression. To find the sum of the infinite terms, we can use the formula Sn = a / (1 - r). In this case, a = 1 and r = 1/3. Plugging these values into the formula, we get Sn = 1 / (1 - 1/3) = 3/2.

Trigonometry Formulas

Trigonometry deals with angles, specifically the angle theta (θ). The relationship between the arc length (l), radius (r), and angle (θ) is given by the formula l = rθ or θ = l/r.

To convert degrees to radians, multiply by π/180. For example, 180 degrees is equal to π radians, 90 degrees is equal to π/2 radians, 45 degrees is equal to π/4 radians, and so on.

Trigonometric functions are sine (sin), cosine (cos), and tangent (tan). The formulas for these functions are:

• Sine (sin) = opposite/hypotenuse
• Cosine (cos) = adjacent/hypotenuse
• Tangent (tan) = opposite/adjacent

The reciprocal functions are cosecant (csc), secant (sec), and cotangent (cot). These are found by taking the reciprocal of the sine, cosine, and tangent functions, respectively.

In a Cartesian coordinate system, there are four quadrants. In quadrant one, all functions are positive. In quadrant two, only sine is positive. In quadrant three, only tangent is positive. In quadrant four, only cosine is positive.

Remember the mnemonic "All Silver Tea Cups" or "Add Sugar to Coffee" to recall which functions are positive in each quadrant.

270 minus theta comes into third quadrant, 360 plus theta comes into first quadrant, 360 minus theta comes into fourth quadrant. So, the basic knowledge you need is that sine becomes cos and cos becomes sine. Understanding these quadrants will help you remember the formulas easily.

Remembering the values of sine and cosine for different angles is important. But I will also provide you with a shortcut method to find values for angles like 37 degrees and 53 degrees.

Let's take an example of finding the value of sine 15 degrees. You can use the formula sine (90 + theta) = cos theta or sine (180 - theta) = sine theta. In this case, sine (90 + 45) = cos 45 = 1/√2 or sine (180 - 45) = sine 45 = 1/√2.

There are also some basic trigonometric identities that you need to memorize, like sine^2 theta + cos^2 theta = 1, cosec^2 theta = 1 + cot^2 theta, and sec^2 theta = 1 + tan^2 theta.

These are the essentials of trigonometry that will help you in solving problems.