Engineering Mathematics Tutorials

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.

Discrete Mathematics

Propositional and First Order Logic :

This section covers the basics of propositional and first-order logic, including logical equivalences, predicates, quantifiers, and rules of inference, helping you understand their applications and key concepts.

1. Introduction to Propositional Logic
2. Propositions Laws and Algebra
3. Propositional Equivalences
4. Predicates and Quantifiers
5. Predicates and Quantifiers Rules
6. Theorems on Nested Quantifiers
7. Rules of Inference
8. PDNF and PCNF in Discrete Mathematics

Set Theory :

This section introduces key concepts in set theory and algebra, including set operations, relations, functions, generating functions, and various algebraic structures, focusing on their properties and applications.

1. Sets in Maths
2. Representation of Sets:
3. Subsets & Supersets
4. Power Set
5. Set Theory Symbols
6. Set Theory Formulas
7. Rings, Integral domains and Fields
8. Introduction to Mojette transform
9. Hasse Diagrams
10. Introduction to Proofs
11. Independent Sets, Covering and Matching
12. Sequence, Series and Summations
13. Generating Functions | Introduction and Prerequisites
14. Total number of possible functions
15. Classes (Injective, surjective, Bijective) of Functions
16. Number of possible Equivalence Relations on a finite set
17. Closure of Relations and Equivalence Relations
18. Relations | Representations in Matrices and Graphs
19. Discrete Mathematics | Representing Relations
20. Introduction and types of Relations
21. Groups
22. Partial Orders and Lattices
23. Power Set and its Properties
24. Inclusion-Exclusion and its various Applications

>> Quiz on Set Theory and Algebra

Combinatorics :

This section covers essential combinatorics concepts, including the pigeonhole principle, permutations, combinations, binomial coefficients, recurrence relations, and problem-solving techniques.

1. Pigeon Hole Principle
2. Combinatorics Basics
3. PnC and Binomial Coefficients
4. Generalized PnC Set 1
5. Generalized PnC Set 2
6. Corollaries of Binomial Theorem
7. Number of triangles in a plane if no more than two points are collinear
8. Sum of squares of even and odd natural numbers
9. Finding the nth term of any Polynomial Sequence
10. Discrete Mathematics | Types of Recurrence Relations – Set 2

>> Combination and Permutation Practice Questions | Set 1
>> Problem on permutations and combinations | Set 2

Probability :

Learn key probability concepts including conditional probability, Bayes's formula, random variables, and the prosecutor's fallacy.

1. Mathematics | Probability
2. Conditional Probability
3. Bayes’s Formula for Conditional probability
4. Prosecutor’s Fallacy
5. Random Variables

Graph Theory :

Understand basic graph theory, types of graphs, Euler/Hamiltonian paths, graph coloring, and centrality measures.

1. Graph Theory Basics – Set 1
2. Graph Theory Basics – Set 2
3. Graph Types and Applications
4. Euler and Hamiltonian Paths
5. Planar Graphs and Graph Coloring
6. Graph Isomorphisms and Connectivity
7. Matching (graph theory)
8. Betweenness Centrality (Centrality Measure)
9. Mathematics | Walks, Trails, Paths, Cycles, and Circuits in Graph
10. Graph measurements: length, distance, diameter, eccentricity, radius, center
11. Relationship between number of nodes and height of binary tree

>> Graph theory practice questions

Linear Algebra :

Explore matrix operations, eigenvalues/eigenvectors, linear equations, and LU decomposition.

1. Matrix Introduction
2. Different Operations on Matrices
3. Representations of Matrices and Graphs in Relations
4. Eigen Values and Eigen Vectors
5. System of Linear Equations
6. LU Decomposition of a System of Linear Equations
7. Doolittle Algorithm: LU Decomposition

>> Quiz on Linear Algebra

Calculus :

Cover limits, continuity, differentiation, mean value theorems, and integration techniques.

1. Limits, Continuity, and Differentiability
2. Cauchy’s Mean Value Theorem
3. Lagrange’s Mean Value Theorem
4. Rolle’s Mean Value Theorem
5. Unimodal functions and Bimodal functions
6. Surface Area and Volume of Hexagonal Prism
7. Inverse functions and composition of functions
8. Indefinite Integrals

Statistics and Numerical Methods :

Learn about mean, variance, standard deviation, probability distributions, interpolation, and statistical analysis methods.

1. Mean, Variance, and Standard Deviation
2. Newton’s Divided Difference Interpolation Formula
3. Law of total probability
4. Probability Distributions Set 1 (Uniform Distribution)
5. Probability Distributions Set 2 (Exponential Distribution)
6. Probability Distributions Set 3 (Normal Distribution)
7. Probability Distributions Set 4 (Binomial Distribution)
8. Probability Distributions Set 5 (Poisson Distribution)
9. Homogeneous Poisson Process
10. Nonhomogeneous Poisson Processes
11. Renewal processes in probability
12. Mathematics | Covariance and Correlation
13. Scales of Measurement
14. Univariate, Bivariate, and Multivariate data and its analysis
15. Hypergeometric Distribution model

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