Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
- Elementry Transformations
- Adjoint and Inverse of a Matrix
- Application of Matrices
- Overview of Matrices
Trigonometric Functions
- Trigonometric Equations and Their Solutions
- Solutions of Triangle>Polar Co-Ordinates
- Solving a Triangle>Solving a Triangle
- Basics of Inverse Trigonometric Functions
- Graphs of Inverse Trigonometric Functions
- Domain, Range & Principal Value
- Properties of Inverse Trigonometric Functions > Self-adjusting Property
- Overview of Trigonometric Functions
- Properties of Inverse Trigonometric Functions > Reciprocal Property
- Properties of Inverse Trigonometric Functions > Complementary Property
- Properties of Inverse Trigonometric Functions > Addition & Subtraction Formula for Inverse Tangent
- Properties of Inverse Trigonometric Functions > Double-angle Property
- Properties of Inverse Trigonometric Functions > Triple-angle Property
- Properties of Inverse Trigonometric Functions > Addition–Subtraction Formula for Inverse Sine & Cosine
- Properties of Inverse Trigonometric Functions > Negative Argument Property
Pair of Straight Lines
Vectors
- Overview of Vectors
- Basic Concepts of Vector Algebra
- Types of Vectors in Algebra
- Algebra of Vectors > Scalar Multiplication
- Algebra of Vectors > Addition & Subtraction of Two Vectors
- Collinearity and Coplanarity of Vectors
- Vectors in Coordinate Geometry
- Components of Vector in Algebra
- Vector Joining Two Points in Algebra
- Section Formula in Vector Algebra
- Product of Two Vectors > Scalar (Dot) Product
- Product of Two Vectors > Vector (Cross) Product
- Direction Ratios, Direction Cosine & Direction Angles in Vector
- Scalar Triple Product
- Vector Triple Product
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivatives of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Trigonometric Function
- Logarithmic Differentiation
- Differentiation of Implicit Functions
- Derivatives of Functions in Parametric Forms
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
- Basic Concepts of Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Forms of Solving Differential Equations> Homogeneous Differential Equations
- Forms of Solving Differential Equations>Linear Differential Equations
- Applications of Differential Equation
- Solution of a Differential Equation
- Overview of Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
Estimated time: 1 minutes
Maharashtra State Board: Class 12
Key Points: Higher Order Derivatives
- If y = f(x), then \[\frac{dy}{dx}\] = f′(x) is called the first-order derivative.
- The derivative of the first derivative is called the second-order derivative:
\[\frac{d^2y}{dx^2}\] = f″(x) - Higher order derivatives are written as:
fⁿ(x) or \[\frac{d^ny}{dx^n}\]
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