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Calculus:-
A system of rules used for the evaluation and analysis of functions
Amazon : Calculus
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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
closed intervals
critical points
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
Formulae for differentiation
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
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
e
x
, 1/x, sec
2
x
Volumes of revolution
Displacement, velocity & acceleration
Inverse trig functions
Integration of rational functions
Integration by parts
Standard integrals
© Alexander Forrest