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.

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. PDNF and PCNF
5. Predicates and Quantifiers
6. Predicates and Quantifiers Rules
7. Theorems on Nested Quantifiers
8. Rules of Inference

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. Set Theory Symbols
4. Subsets & Supersets
5. Power Set
6. Properties of Power Set
7. Set Theory Formulas
8. Inclusion-Exclusion
9. Introduction to Proofs
10. Sequence, Series, and Summations
11. Introduction to Relations
12. Representing Relations
13. Representing Relations in Matrices and Graphs
14. Closure of Relations
15. Partial Orders and Lattices
16. Hasse Diagrams
17. Equivalence Relations on a finite set
18. Total number of Possible Functions
19. Classes of Functions
20. Generating Functions
21. Groups
22. Rings, Integral Domains and Fields
23. Independent Sets, Covering and Matching

>> 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. Combinatorics Basics
2. PnC and Binomial Coefficients
3. Generalized PnC- [Set 1] & [Set 2]
4. Corollaries of Binomial Theorem
5. Pigeon Hole Principle
6. Sum of squares of even and odd natural numbers
7. Finding the nth term of any Polynomial Sequence
8. Types of Recurrence Relations

>> Combination and Permutation Practice Questions | Set 1 | Set 2

Probability :

Learn key probability concepts including conditional probability, Bayes's formula, random variables.

1. Probability
2. Conditional Probability
3. Bayes’s Formula
4. Random Variables

Graph Theory :

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

1. Graph Theory Basics
2. Graph Types
3. Walks, Trails, Paths, Cycles, and Circuits in Graph
4. Graph Isomorphisms and Connectivity
5. Euler and Hamiltonian Paths
6. Planar Graphs and Graph Coloring
7. Matching
8. Graph Measurements
9. Betweenness Centrality
10. 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. System of Linear Equations
5. LU Decomposition of a System of Linear Equations
6. Doolittle Algorithm: LU Decomposition
7. Eigen Values and Eigen Vectors

>> Quiz on Linear Algebra

Calculus :

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

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

Statistics and Numerical Methods :

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

1. Scales of Measurement
2. Univariate, Bivariate, and Multivariate Data
3. Mean, Variance, and Standard Deviation
4. Covariance and Correlation
5. Law of Total Probability
6. Binomial Distribution
7. Hypergeometric Distribution Model
8. Probability Poisson Distribution
9. Uniform Distribution
10. Exponential Distribution
11. Normal Distribution
12. Homogeneous Poisson Process
13. Nonhomogeneous Poisson Processes
14. Renewal processes in Probability
15. Newton’s Divided Difference Interpolation Formula

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