Mathematics

Calculus – Application of Integrals (Area between Curves)

by ComputingNotes
References: Integrals can be used to calculate many things such as area between curves, volumes and surfaces of solids, length of curves etc. Areas between Curves: In calculus, we define the exact area under a curve not by measuring it directly, but by slicing it into rectangles, adding them up, and then making the slices ... Read More

Probability – Introduction

by ComputingNotes
Book Probability by Jim Pitman, Springer The main concepts of probability theory include: These three concepts form the fundamental framework of probability theory. They describe the structure of any random process, from a simple coin toss to complex risk modeling. Outcome Space (Sample Space) The outcome space (often denoted by the Greek letter Omega, Ω, ... Read More

Linear Algebra – Gaussian Elimination

by ComputingNotes
Book: Introduction to Linear Algebra, Johnson et al. Third Edition Gaussian Elimination is a method in linear algebra used to solve systems of linear equations.It systematically transforms a system of equations into a simpler form so the solutions become easy to find. It works by manipulating the augmented matrix of the system using basic row ... Read More

Rank of Matrix

by ComputingNotes
The Rank of a Matrix is a fundamental concept in linear algebra that tells you how much “information” or “dimensionality” a matrix preserves. At its core, the rank represents the number of linearly independent rows or columns in a matrix. It is the dimension of the vector space generated by its columns (or rows). https://www.mathsisfun.com/algebra/matrix-rank.html ... Read More

Calculus – Integration

by ComputingNotes
Book Calculus by Thomas/Finney, 9th Edition, Page 275 Differential Calculus to Integral Calculus. This is where we stop asking “how fast is it changing?” and start asking “how much have we accumulated?” Indefinite Integrals The chapter kicks off with a simple question: If I give you the answer (the derivative), can you tell me the ... Read More

Calculus – Linearization and Differentials

by ComputingNotes
Book Calculus by Thomas/Finney, 9th Edition, Page 248 Linearization: Approximating functions https://math.stackexchange.com/questions/1385936/approximating-sqrt1-frac1n-by-1-frac12n#:~:text=The%20function%20f(%20x)=%20%E2%88%9A%201+%20x,%E2%88%9A%201+%20x%20for%20x%20%E2%89%A5%200. Differentials Differential Estimate of Change:In calculus, estimating change with differentials is a method from calculus used to approximate how much a function’s output changes when the input changes by a small amount. Instead of calculating the exact change (which can be difficult and ... Read More

Calculus – Optimization

by ComputingNotes
Book Calculus by Thomas/Finney, 9th Edition, Page 233 Example problem: Find 2 positive numbers whose sum is 20 and their product is as large as possible.

Calculus – Application of Derivatives

by ComputingNotes
Book calculus by Thomas/Finney, 9th Edition, Page 189 Derivatives can be used to analyze the behaviour of functions and solve practical optimization problems. Max-Min Theorem relates to existence of max and min value for a function $f4$ that is continous at every point of closed interval I. Absoluted maxima and minima on a closed interval ... Read More
error: