Calculus:-

Differential calculus

• Differentiation
• Gradients
• Limits
• Derived function
• Notation

First principles

• First principles
• x^n
• ax^n
• Derivatives of sums
• (x + a)^n
• (ax + b)^n
• The chain rule
• The product rule
• The quotient rule
• Derived trig functions

Differention - examples

• x^n
• ax^n
• Derivatives of sums
• (x + a)^n
• (ax + b)^n
• The chain rule
• The product rule
• The quotient rule
• Trig functions
• seca coseca cota
• Logs and exponentials
• Higher derivatives
• Rectilinear motion
• Table of derived functions

Sketching functions and tangents

• Tangents- gradients
• Tangents- equations
• Increasing / decreasing functions
• Stationary points
• finding stationary points
• maxima and minima
• using 2nd derivative (ad higher)
• closed intervals
• critical points (ad higher)
• curve sketching
• graphing derived functions

Differential Equations

• Differential equations
• First-order differential equations
• Second-order differential equations
• Applications
• Applications of Differential equations
• Rectilinear motion
• Higher derivatives

Further differentiation

• Extrema of functions
• Approximating roots

Integration

• Integral calculus
• indefinite integrals
• basic rules of integration
• indefinite integral of (ax+b)^n
• infinite integrals (discontinuities)
• indefinite integrals - trig functions
• indefinite integrals - exponentials & logarithmic functions
• Integration by substitution

Integration and graphs

• Areas of graphs
• Newton's equations of motion
• areas under curves
• lower bound
• upper bound
• area function
• integration and the area function
• definite integrals
• fundamental theorem of calculus
• areas enclosed by graph and x-axis
• area between curve and the y-axis
• area between two graphs
• Formula for area between two graphs

Further Integration

• e^x, 1/x, sec²x
• Volumes of revolution
• Displacement, velocity & acceleration
• Inverse trig functions
• Integration of rational functions
• Integration by parts