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
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of 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
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: 4 minutes
Population growth, Bacterial colony growth, Surface area, Newton’s laws of cooling, Radioactive decay
Maharashtra State Board: Class 12
Key Points: Applications of Differential Equation
1. Population Growth
-
Rate of change of population ∝ population
-
\[\frac{\mathrm{dP}}{\mathrm{dt}}=\mathrm{kP}\]
Growth increases with time
2. Radioactive Decay
-
Rate of decay ∝ of the amount present
-
\[\frac{\mathrm{d}x}{\mathrm{d}t}=-\mathrm{k}x\]
Negative sign → quantity decreases
3. Newton’s Law of Cooling
-
Rate of cooling ∝ temperature difference
-
\[\frac{\mathrm{d}\theta}{\mathrm{d}t}=-k\left(\theta-\theta_{0}\right)\]
θ = body temp, θ₀ = surrounding temp
Shaalaa.com | Applications of Differential Equations
to track your progress
