Differential - Applications - Explanation

• Differential - Definition and explanation
• Differential - Applications - Small errors

• Derivative - Application - Rate of change - Average
• Derivative - Application - Motion of a particle
• Derivative - Application - Freely falling body
• Derivative - Application - Angular velocity

• Tangent to a Curve at a Point
• Tangent - Geometrical interpretation
• Tangent and normal - Equations
• Tangent and normal - Length
• Tangent - Angle between two curves

• Subtangent and subnormal - Examples
• Subtangent and subnormal - Lengths

Intermediate value theorems

• Rolle's theorem - Statement and proof

• Lagrange's mean value theorem - Statement and proof

• Taylor's and Maclaurin's Theorem - Statement and proof

• Indeterminate forms - L'Hospital's Rule

Partial derivatives

• Partial derivatives - Examples
• Partial derivatives - Higher orders
• Partial derivatives - Chain rule
• Homogeneous functions

Curve Tracing

• Curve Tracing - Symmetry
• Curve Tracing - Special points
• Curve Tracing - Range of values
• Curve Tracing - Extension of curve
• Curve Tracing - Turning points
Curve Tracing - Bending of the curves

Monotonic functions

• Increasing functions
• Decreasing functions

Maxima and minima

• Maximum and minimum - Function value - Absolute
• Maxima and minima - Local
• Function value - Local extreme - Test
• Maxima and minima - Closed interval
• Maxima and minima - Point of inflection

Definite integral - Applications - Areas and volumes

• Area - Bounded regions - Two curves
• Area - Bounded regions - Curve, x-axis and ordinates
• Area - Circle
• Area - Ellipse
• Area - Bounded regions - Parabola and its latus rectum
• Length of the curve and Surface area of a solid
• Simpson's rule and Trapezoidal rule

• Volume - Computation

Polyhedra and networks

• Incidence and degree
• Types of graphs
• Theorems on graphs
• Paths and cycles
• Connected graphs and components
• Bridges
• Trees