[Download] Applied Mathematics 1 by Hari Arora and A. Sachdev book for Polytechnic. Applied Mathematics by hari Arora full book PDF download. Download Applied Mathematics 1 for Polytechnic by Dr. Hari Arora and A. Sachdev. Applied Mathematics by Dr. Hari Arora download in pdf for free. Dr. hari Arora's Applied Mathematics.

Applied Mathematics 1 by Dr. Hari Arora and A. Sachdev

Download Applied Mathematics 1 for Polytechnic by Dr. Hari Arora and A. Sachdev. Applied Mathematics by Dr. Hari Arora download in pdf for free. Dr. hari Arora's Applied Mathematics.

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In Book Detail Contants/Syllabus

1. Coordinate Geometry

• Point: Cartesian coordinates, polar coordinates and their conversion to Cartesian coordinates and vice versa (In two dimensions only).
• Distance between two points. Internal and External division formulae.
• Area of a triangle when its vertices are given conditions of collinearity of points. To find the coordinates of centroid, incentre of a triangle given the vertices using the formula. Simple problems on locus.
• Straight line: Equation of straight line in various standard forms. Intersection of two straight lines, angle between two lines.
• Perpendicular distance formula
• Circle: General equation of a circle and its characteristics. To find the equation of a circle given (i) Center and radius (ii) Three points on it (iii) Co-ordinates of end points of a diameter.
• Concise: Definition of conic section. Standard equation of parabola. Equation of parabola given its focus and directrix. Given the equation of a parabola, determination of its locus, vertex, axis, directrix and latus rectum.
• Ellipse and hyperbola (standard equations without proof), writing equations given the directrix, focus and eccentricity; given the equation determination of focus, directrix, latus rectum, axes, eccentricity and vertex.

2. Vector Algebra

• Concept of a vector, vector in polar and cartesian systems. Expressing a polar vector in terms of cartesian unit vectors and vice versa. Representation of a point by a vector.
• Arithmetic operations on vectors addition, subtraction. Multiplication of a vector by a scalar, scalar product of two vectors and vector product of two vectors. Application of a point by a vector. Application in Mechanics and Electro-magnetism.

3. Matrices and Determinant

• Determinant and its evaluation, minor, co-factor, matrix and its simplification. Matrix multiplication, inverse matrix. Solution of simultaneous equations containing upto 3 unknowns only.

4. Differential Calculus

• Function and Limits:
• Concept of a function, its value and limit.
• Evaluation of limits in case of four standard limits.

Differentiation:

• Definition, its physical meaning as rate measure and its geometrical meaning as slope.
• Differentiation from first principles of xn, ax, log x, sin x, cos x, tan x
• Differentiation of sum product and quotient of functions
• Differentiation of sec x, cosec x, cot x and of inverse t-ratios
• Differentiation of implicit functions and parametric equations.
• Logarithmic differentiation

Applications of Differentiation: Errors, maximum and minimum, tangent and normal.

5. Integral Calculus

(a) Indefinite Integrals: Integration as inverse process of differentiation. Simple integration by substitution, by parts and by partial fraction.

• Definite Integrals: Evaluation of definite integrals (simple problems) evaluation of Application: area bounded by a curve and axes. Volume of solid formed by revolution of an area about axis.

(b) Differential Equation: Solution of differential equation of first order and first degree.

• (i) Homogeneous differential equation.
• (ii) Linear differential equation.