Calculus:-
A system of rules used for the evaluation and analysis of functions
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
- Tangents- gradients
- Tangents- equations
- Increasing / decreasing functions
- Stationary points
- finding stationary points
- maxima and minima
- using 2nd derivative
- closed intervals
- critical points
- curve sketching
- graphing derived functions
- Differential equations
- First-order differential equations
- Second-order differential equations
- Applications
- Applications of Differential equations
- Rectilinear motion
- Higher derivatives
Further differentiation
- 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
- Deriving Newton's equations of motion
- 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
© Alexander Forrest