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College Mathematics 2 – (XII Grade)
Matrices and Transformations
The Derivative
Applications of Differentiation
Matrices
Square Matrices
Equality of Matrices
Transpose of a Matrix
Addition of Matrices
Null of Zero Matrices
Subtraction of Matrices
Multiplication of a Matrix by a Scalar
Multiplication of Matrices
Unit or Identity Matrices
Inverse of a Square Matrix and Determinants
Transformations
Reflections
Rotations
Stretching Transformations
Shear Transformations
Inverse Transformations
General Linear
Transformations
Gradient and Derivative
The Derivative of xn
Differentiation of Sum, Difference, Product and Quotient
Differentiation of Trigonometrical Functions
The Chain Rule
Implicit Differentiation
Parametric Representation
Exponential Functions
Logarithmic Functions
Differentiation of Exponential and Logarithmic Functions
Inverse Trigonometric Functions
Higher Derivatives
Rates of Change
Velocity and Acceleration
Maxima and Minima
Maximization and imization Problems
Inflexion Points
Graph Sketching
Small Increments
The Indefinite Integral
The Definite Integral
Polar Coordinates, de Moivre's Theorem and Power Series
Introduction
Definition of Indefinite Integral
Significance of the Constant C
Basic Properties of Indefinite Integral
Method of Substitution
Integration by Parts
Partial Fractions
Introduction
Definite Integral as the Limit of a Sum
Computation of Definite Integrals
Plane Areas
Mean Value of a Function
Volumes
Trapezium Rule
Polar Coordinates
Gradient of Tangent
Curve Sketching
Area
Exponential Function and Some of its Properties
Euler's Formula and de Moivre's Theorem
Higher Order Differentiation
Power Series Expansion
MacLaurin's Theorem
Taylor's Theorem
Differential Equations
Solutions of Algebraic Equations
Probability
Introduction
Law of Growth and Decay
Separable Equations
Solution Curves
Linear Equations
Second Order Linear Equations
Simple Harmonic Motion
Inhomogeneous Equations
Other Types of Second Order
Differential Equations
Introduction
Location of Roots
Estimates of Roots and Their Error
Linear Interpolation
The Newton-Raphson Method
Random Experiments and Events
Relative Frequency and Probability of an Event
Finite Sample Spaces and Equally Likely Outcomes
Conditional Probability and Independence
Total Probability Theorem and Bayers' Theorem
Random Variables
Some Important Classes of Distribution
Statistical Inference
Random Variables
Distribution Function and Expectation of a Random Variable
Bivariate Random Variables
Uniform Distribution (Discrete Type)
Binomial Distribution
Poisson Distribution
Rectangular Distribution
Normal Distribution
Central Limit Theorem
Presentation of Observed Data
Sample Characteristics I
Sample Characteristics II
Point and Interval Estimations
Test of Hypotheses
Kinematics
Dynamics
Statics
Displacement
Velocity
Acceleration
Units
One-Dimensional Motions
Uniform Motion
Uniformly Accelerated Motion
General Case
Simple Harmonic Motion
Two-Dimensional Motions
Motion with Constant
elerationv
Projectile Motion
Circular Motion
Uniform Circular Motion
Relative Velocity
Uniform Relative Motion
Force
The Law of Inertia
Linear Momentum
Newton's Second Law of Motions
Friction
Elastic Force
Gravitation
Motion of Planets
Conservation of Linear Momentum
Newton's Third Law
Connected bodes
Impulse
Work
Power
Kinetic Energy
Potential Energy
Conservation of Mechanical Energy
Collision of Two Particles
Equilibrium of a Particle
Centre of Mass
Moment
Equilibrium of a Rigid body
Stability of a Position of Equilibrium
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