# Calculus

Calculus is that branch of Mathematics that deals with the study of change in the value of a function as the points in the domain change.

### 1. Functions and Graphs

- Intervals
- Constants and Variables
- Functions
- Types of Functions
- Quadratic Inequations

### 2. Limits and Continuity

### 3. Differentiation

- Concept of Differentiation
- Derivative of a Function
- Product Rule For Differentiation
- Quotient Rule For Differentiation
- Derivatives of Composite Function

### 4. Applications of Differential Calculus

- Derivative As Rate Measure
- Tangents and Normals: Derivative As Measure Of Slope
- Rolle’s Theorem
- Lagrange Mean Value Theorem (LMVT)
- Indeterminate Forms: L'Hospital's Rule
- Increasing and Decreasing Functions
- Maximum and Minimum Values
- Concavity, Convexity and Points of Inflection
- Differentials: Errors and Approximation
- Curve Tracing

### 5. Integral Calculus & Applications

- Integration
- Integrals of Linear Functions of x
- Integration by Partial Fractions
- Integration by Substitution
- Integration by Parts
- Standard Integral Forms
- Definite Integrals
- Properties of Definite Integrals
- Reduction Formulae For Integration
- Area of Bounded Regions