Engineering Mathematics Tutorials
Last Updated :
28 Dec, 2024
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Engineering mathematics is a vital component of the engineering discipline, offering the analytical tools and techniques necessary for solving complex problems across various fields. Whether you're designing a bridge, optimizing a manufacturing process, or developing algorithms for computer systems, a solid understanding of mathematical principles is crucial.
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Table of Content
Discrete Mathematics
Propositional and First Order Logic :
- Introduction to Propositional Logic
- Introduction to Propositional Logic | Set 2
- Propositional Equivalences
- Predicates and Quantifiers
- Predicates and Quantifiers | Set 2
- Some theorems on Nested Quantifiers
- Rules of Inference
- PDNF and PCNF in Discrete Mathematics
Set Theory :
- Introduction
- Set Operations
- Inclusion-Exclusion and its various Applications
- Power Set and its Properties
- Partial Orders and Lattices
- Groups
- Introduction and types of Relations
- Discrete Mathematics | Representing Relations
- Relations | Representations in Matrices and Graphs
- Closure of Relations and Equivalence Relations
- Number of possible Equivalence Relations on a finite set
- Classes (Injective, surjective, Bijective) of Functions
- Total number of possible functions
- Generating Functions | Introduction and Prerequisites
- Generating Functions – Set 2
- Sequence, Series and Summations
- Independent Sets, Covering and Matching
- Introduction to Proofs
- Hasse Diagrams
- Introduction to Mojette transform
- Rings, Integral domains and Fields
>> Quiz on Set Theory and Algebra
Combinatorics :
- Pigeon Hole Principle
- Combinatorics Basics
- PnC and Binomial Coefficients
- Generalized PnC Set 1
- Generalized PnC Set 2
- Corollaries of Binomial Theorem
- Number of triangles in a plane if no more than two points are collinear
- Sum of squares of even and odd natural numbers
- Finding nth term of any Polynomial Sequence
- Discrete Mathematics | Types of Recurrence Relations – Set 2
>> Combination and Permutation Practice Questions | Set 1
>> Problem on permutations and combinations | Set 2
Probability :
- Mathematics | Probability
- Conditional Probability
- Bayes’s Formula for Conditional probability
- Prosecutor’s Fallacy
- Random Variables
Graph Theory :
- Graph Theory Basics – Set 1
- Graph Theory Basics – Set 2
- Graph Types and Applications
- Euler and Hamiltonian Paths
- Planar Graphs and Graph Coloring
- Graph Isomorphisms and Connectivity
- Matching (graph theory)
- Betweenness Centrality (Centrality Measure)
- Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph
- Graph measurements: length, distance, diameter, eccentricity, radius, center
- Relationship between number of nodes and height of binary tree
>> Graph theory practice questions
Engineering Mathematics
Linear Algebra :
- Matrix Introduction
- Different Operations on Matrices
- Representations of Matrices and Graphs in Relations
- Eigen Values and Eigen Vectors
- System of Linear Equations
- LU Decomposition of a System of Linear Equations
- Doolittle Algorithm : LU Decomposition
Calculus :
- Limits, Continuity and Differentiability
- Cauchy’s Mean Value Theorem
- Lagrange’s Mean Value Theorem
- Rolle’s Mean Value Theorem
- Unimodal functions and Bimodal functions
- Surface Area and Volume of Hexagonal Prism
- Inverse functions and composition of functions
- Indefinite Integrals
Statistics and Numerical Methods :
- Mean, Variance and Standard Deviation
- Newton’s Divided Difference Interpolation Formula
- Law of total probability
- Probability Distributions Set 1 (Uniform Distribution)
- Probability Distributions Set 2 (Exponential Distribution)
- Probability Distributions Set 3 (Normal Distribution)
- Probability Distributions Set 4 (Binomial Distribution)
- Probability Distributions Set 5 (Poisson Distribution)
- Homogeneous Poisson Process
- Nonhomogeneous Poisson Processes
- Renewal processes in probability
- Mathematics | Covariance and Correlation
- Scales of Measurement
- Univariate, Bivariate and Multivariate data and its analysis
- Hypergeometric Distribution model
