Applications of Matrices and Determinants
Chapter 1: Applications of Matrices and Determinants
“The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.” - Felix Klein
1.1 Introduction
Matrices are very important and …
Complex Numbers
Chapter 2: Complex Numbers
“Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being.” — Gottfried Leibniz
Many mathematicians contributed to the full development of complex …
Theory of Equations
Chapter 3: heory of Equations
“It seems that if one is working from the point of view of getting beauty in one’s equation, and if one has really a sound insight, one is on a sure line of progress.” - Paul Dirac
3.1 Introduction …
Inverse Trigonometric Functions
Chapter 4: Inverse Trigonometric Functions
4.1 Introduction
In everyday life, indirect measurement is used to obtain solutions to problems that are impossible to solve using measurement tools. Trigonometry helps us to find measurements like heights …
Two Dimensional Analytical Geometry-II
Chapter 5: Two Dimensional Analytical Geometry-II
5.1 Introduction
Analytical Geometry of two dimension is used to describe geometric objects such as point, line, circle, parabola, ellipse, and hyperbola using Cartesian coordinate system. Two …
Applications of Vector Algebra
Chapter 6: Applications of Vector Algebra
“Mathematics is the science of the connection of magnitudes. Magnitude is anything that can be put equal or unequal to another thing. Two things are equal when in every assertion each may be replaced …
Applications of Differential Calculus
Chapter 7: Applications of Differential Calculus
“Nothing takes place in the world whose meaning is not that of some maximum or minimum”
- Leonhard Euler
7.1 Introduction
7.1.1 Early Developments
The primary objective of differential …
Differentials and Partial Derivatives
Chapter 8: Differentials and Partial Derivatives
“He who hasn’t tasted bitter things hasn’t earned sweet things” - Gottfried Wilhelm Leibniz
8.1 Introduction
Motivation
In real life we have to deal with many functions. Many …
Applications of Integration
Chapter 9: Applications of Integration
“Give me a place to stand and I will move the earth” - Archimedes
9.1. Introduction
One of the earliest mathematicians who made wonderful discoveries to compute the areas and volumes of geometrical …
Ordinary Differential Equations
Chapter 10: Ordinary Differential Equations
“Mathematics is the most beautiful and most powerful creation of the human spirit”
- Stefan Banach
10.1 Introduction Motivation and Early Developments
Just we look at some real life situations …
Probability Distributions
Chapter 11: Probability Distributions
Laplace (1749-1827)
The history of random variables and how they evolved into mapping from sample space to real numbers was a subject of interest. The modern interpretation certainly occurred after the invention …
Discrete Mathematics
Chapter 12: Discrete Mathematics
Young man, in mathematics you don’t understand things. You just get used to them. — John von Neumann
12.1 Introduction
Mathematics can be broadly classified into two categories: Continuous Mathematics - It is …