Statistics
Introduction Statistics is a branch of mathematics which gives us the tools to deal with large quantities of data and
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Rules of Probability
There are six rules of probability using which the probability of any compound event involving arbitrary events A and B,
Read MoreAxioms of Probability
Consider an experiment whose sample space is S. For each event E of the sample space S, we assume that
Read MoreProbability Fundamentals
Definitions Sample Space and Event: Consider an experiment whose outcome is not predictable with certainty. Such an experiment is called
Read MoreDefinite Integrals
If ∫ab f(x)dx = [F(x)]ab = F(b) – F(a) is called the definite integral of f(x) between the limits of
Read MoreApplications of Integration
We study three areas where applications of integration is applied 1. Areas of curves 2. Length of curves 3. Volumes
Read MoreApplications of Derivatives
There are two areas where derivatives are used 1. Increasing and Decreasing Functions 2. Maxima and Minima Relative maxima and
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Soil Mechanics and Foundation Engineering
Civil Engineering Soil Mechanics and Foundation Engineering: Complete Guide for Civil Engineering Students What is Soil Mechanics? Soil is defined
Read MoreViscosity in fluid Mechanics
What is Viscosity in fluid mechanics? Viscosity is the property of fluids by virtue of which they offer resistance to
Read MoreMean Value Theorems
Rolle’s Theorem If a function f (x) is such that: f (x) is continuous in the closed interval a ≤
Read MoreRelationship between Differentiability and Continuity
Theorem: If a function is differentiable at any point, then it is necessarily continuous at that point; proof of this
Read MoreDifferentiability
Derivative at a point: Let I denote the open interval (a, b) in R, and let x₀ ∈ I. Then
Read MoreContinuity
Definition of Continuity A function f(x) is defined for x = a is said to be continuous at x =
Read MoreInverse of Matrix
Inverse of Matrix The inverse of a matrix A, exists if A is non-singular (i.e., ⏐A⏐ ≠ 0) and is
Read MoreProperties of Determinants
The value of a determinants does not change when rows and columns are interchanged. i.e., ⏐AT⏐= ⏐A⏐ If any row
Read MoreDeterminants
Definition of Determinants: Let a11, a12, a21, a22 be any four numbers. The symbol represents the number a11a22 – a12a21 and
Read MoreClassification of Complex Matrices
Complex matrices can be classified into the following three types based on the relationship between Aθ and A. Hermitian Matrix
Read MoreClassification of Real Matrices
Real matrices can be classified into the following three types based on the relationship between AT and A. 1. Symmetric
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