MATHEMATICS-VOLUME 2 · 12th TN - English Medium
8 chapters · 125 topics
Chapter 1: Chapter
- . . Early Developments
- Learning Objectives
- . . Derivative as slope
- . . Derivative as rate of change
- . . Related rates
- EXERCISE .
- . . Equations of Tangent and Normal
- . . Angle between two curves
- . Mean Value Theorem
- . . Rolle’s Theorem
- . . Lagrange’s Mean Value Theorem
- . . Applications
- . Series Expansions
- . . A Limit Process
- . . Indeterminate forms
- . . Indeterminate forms , ∞ and ∞
- . . Monotonicity of functions
- . . Absolute maxima and minima
- . . Relative Extrema on an Interval
- . . Extrema using First Derivative Test
- . . Concavity, Convexity, and Points of Inflection
- . . Extrema using Second Derivative Test
- . Applications in Optimization
- x x
- . . Symmetry
- . . Asymptotes
- . Sketching of Curves
- SUMMARY
- ) be a critical point of function f x
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- Motivation
Chapter 2: Chapter
- . . Linear Approximation
- . . Errors: Absolute Error, Relative Error, and Percentage Error
- EXERCISE .
- Properties of Differentials
- . Functions of Several Variables
- . . Recall of Limit and Continuity of Functions of One Variable
- . Limit and Continuity of Functions of Two Variables
- . Linear Approximation and Differential of a function of several variables
- . . Function of Function Rule
- . . Homogeneous Functions and Euler’s Theorem
- SUMMARY
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Chapter 3: Chapter
- . .Introduction
- Learning Objectives
- . . Riemann Integral
- When x =
- . Evaluation of a Bounded Plane Area by Integration
- . . Area of the region bounded between two curves
- ) is x
- EXERCISE .
- . Volume of a solid obtained by revolving area about an axis
- ] into n segments by x x
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- Motivation and Early Developments
Chapter 5: Chapter 5
Chapter 7: Chapter
- . Differential Equation, Order, and Degree
- EXERCISE .
- . Classification of Differential Equations
- . . Formation of Differential equations from Physical Situations
- . . Formation of Differential Equations from Geometrical Problems
- . Solution of Ordinary Differential Equations
- . . Variables Separable Method
- . . Substitution Method
- . . Homogeneous Form or Homogeneous Differential Equation
- . First Order Linear Differential Equations
- . Applications of First Order Ordinary Differential Equations
- . . Population growth
- . . . Radioactive decay
- . . . Newton’s Law of cooling/warming
- . . Mixture problems
- SUMMARY
- or Scan the QR Code
- Probability Distributions
- Learning Objectives
Chapter 8: Chapter
- . Random Variable
- { ω , ω , ω ,... ω k } is
- Section
- EXERCISE .
- . Types of Random Variable
- . . Discrete random variables
- . . Probability Mass Function
- . . Cumulative Distribution Function or Distribution Function
- . . Cumulative Distribution Function from Probability Mass function
- . . Probability Mass Function from Cumulative Distribution Function
- . Continuous Distributions
- . . Probability density function
- . . Distribution function from Probability density function
- EXERCISE11.
- . Mathematical Expectation
- . . Variance
- ( using Gamma integral for positive integer n , x e
- . Theoretical Distributions: Some Special Discrete Distributions
- . . The One point distribution
- . . The Bernoulli distribution
- . . The Binomial Distribution
- SUMMARY
- or Scan the QR Code
Chapter 9: Chapter
- . Introduction
- Discrete Mathematics
- Learning Objectives
- . . Definitions
- . . Some more properties of a binary operation
- ) ∉ . Other properties need not be checked as it is not
- . . Some binary operations on Boolean Matrices
- . . Modular Arithmetic
- . Mathematical Logic
- . . Statement and its truth value
- . . Compound Statements, Logical Connectives, and Truth Tables
- Logical Connectives and their Truth Tables
- . . Tautology, Contradiction, and Contingency
- . . Duality
- . . Logical Equivalence
- (ii) p ∧ 𝕋 ≡ p and p ∧ 𝔽 ≡ 𝔽
- EXERCISE .
- SUMMARY
- (i) p ∨ 𝕋 ≡ 𝕋 and p ∨ 𝔽 ≡ p
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- (iii) y = − , y =
- f x ( )
- Application of Differential Calculus
- BOOKS FOR REFERENCE
- Text Book Development Team - Class