PURE AND APPLIED > CALCULUS
Calculus used to derive Kepler's Laws.
Calculus, arguably the single-handedly most important field of mathematics that is needed to explain the physical science. From the time of it's conceptualization, it has been used thoroughly to explain a vast amount of other topics - mechanics, satistics, analysis, probability and even concepts in physics and chemistry.
Calculus is split into two main families namely differentiation and integration, both of which are generally reversal processes of each other. Together, they seek to facilitate or at least give a mathematical treatment to moving objects, hence, anything that deals with variable quantities will most likely involve calculus.
This subject has an exceeding breath and width. On a single aspect of calculus, you can go on to talk about definite integral, areas, rate of changes, derivative of the nth degree and the aspects can range from single-variable, multi-variable, differential equations, the list goes on. In GMath, we'll do things a little different. I would like to focus on those rare but equally important and interesting parts of calculus. Hope you enjoy it.
Gottfried Wihelm Leibniz
Fundamental Theorem of Calculus
Statistics
Analysis
Probability
Thermodynamics
Calculus used to derive Kepler's Laws.
Calculus is split into two main families namely differentiation and integration, both of which are generally reversal processes of each other. Together, they seek to facilitate or at least give a mathematical treatment to moving objects, hence, anything that deals with variable quantities will most likely involve calculus.
This subject has an exceeding breath and width. On a single aspect of calculus, you can go on to talk about definite integral, areas, rate of changes, derivative of the nth degree and the aspects can range from single-variable, multi-variable, differential equations, the list goes on. In GMath, we'll do things a little different. I would like to focus on those rare but equally important and interesting parts of calculus. Hope you enjoy it.
CONCEPT CONTENTS
> DIFFERENTIATING BY FIRST PRINCIPLES
> CHAIN RULE
> FUNDAMENTAL THEOREM OF CALCULUS
> INTEGRATING BY PARTS
> HYPERBOLIC FUNCTIONS
> DERIVATIVES OF HYPERBOLIC FUNCTIONS
> THE CATENARY
> WALLIS'S PRODUCT
> LEIBNIZ'S QUEST FOR PI
> IN SEARCH FOR THE ORBIT
> KEPLER'S LAWS PRELIMINARIES
> KEPLER'S SECOND LAW
> KEPLER'S FIRST LAW
> KEPLER'S THIRD LAW
Notable Mathematicians
Sir Issac Newton Gottfried Wihelm Leibniz
Important Theorems
Differentiation by First Principles Fundamental Theorem of Calculus
Applications
MechanicsStatistics
Analysis
Probability
Thermodynamics
