# Mathematics

Maths related to High School Mathematics, Madhyamik Mathematics, Engineering Mathematics, and Graduation level Mathematics

### Integral calculus

Integral calculus : Integration as a reverse process of differentiation, indefinite integral of standard functions.
Integration by parts. Integration by substitution and partial fraction.

### Differential calculus

Differential calculus : Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and of functions defined parametrically. Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only).

### Co-ordinate Geometry: Circle

Circle : Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y may represent a circle. Equation of a circle in terms of endpoints of a diameter . Parametric equation of a circle. Intersection of a line with a circle.

### Co-ordinate Geometry: Conics

Conics : Definition, Directrix, Focus and Eccentricity, classification based on eccentricity.

### Co-ordinate Geometry: Parabola

Parabola :Standard equation. Reduction of the form x = ay²+by+c or y = ax²+bx+c to the standard form y² = 4ax or x² = 4ay respectively. Elementary properties and parametric equation of a parabola.

### Co-ordinate Geometry: Ellipse and Hyperbola

Ellipse and Hyperbola : Reduction to standard form of general equation of second degree when xy term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with respect to a conic.

### Co-ordinate Geometry: Straight line

Straight line : Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and parallelism of two lines. Distance of a point from a line. Distance between two parallel lines.

### Basic Ideas of Co-ordinate Geometry

Co-ordinate Geometry

### Trigonometry

Trigonometry

Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions. Co-ordinate geometry of two dimensions

### Probability

Probability : Classical definition, addition rule, conditional probability and Bayes’ theorem, independence, multiplication rule.