Whether you’re a student, educator, or professional engineer, this guide is designed to illuminate the path ahead of engineering mathematics and provide you with the tools you need to succeed to be a mathematical engineer guru.
Engineering Mathematics is the cornerstone of innovation in engineering. It’s the silent force that drives the gears of progress, turning complex problems into elegant solutions. Our tutorial series is more than just a set of instructions; it’s a beacon for those who aspire to excel in the engineering field.
The Roadmap Overview to Mastery
Our roadmap is tailored to guide you through the fundamental concepts, all the way to the advanced topics that will challenge your intellect and enhance your problem-solving skills.
1. The Fundamentals
We begin with the basics: algebra, geometry, and trigonometry. These are the building blocks that form the foundation of all engineering feats. You’ll learn how to manipulate equations, understand geometric principles, and navigate the unit circle with ease.
2. The Heart of Engineering: Calculus
Calculus is where the magic happens. From derivatives to integrals, we’ll explore how calculus is applied in real-world engineering scenarios. You’ll discover the beauty of limits and the power of the infinite series.
3. Diving into Differential Equations
Differential equations are the language of dynamic systems. We’ll demystify these equations and show you how they model everything from electrical circuits to fluid dynamics.
4. The Digital Frontier: Discrete Mathematics.
In our digital age, discrete mathematics has become increasingly important. We’ll cover topics like graph theory, combinatorics, and Boolean algebra, which are essential for computer engineering and algorithm design.
5. The Final Frontier: Advanced Topics
For those who dare, we venture into the realms of complex analysis, tensor calculus, and partial differential equations. These topics are the final pieces of the puzzle, unlocking the secrets of advanced engineering challenges.
Complete Engineering Mathematics Tutorials.
These tutorials are subdivided into two sections and engineering mathematics branches. They include, Discrete Mathematics & Engineering Mathematics:
1.Discrete Mathematics
- Propositional and First Order Logic
- Set Theory
- Combinatorics
- Probability
- Graph Theory
2. Engineering Mathematics:
- Linear Algebra
- Calculus
- Statistics and Numerical Methods
- Quick Links
Discrete Mathematics
1. 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
2. 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
3. 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
4. Probability :
- Mathematics | Probability
- Conditional Probability
- Bayes’s Formula for Conditional probability
- Prosecutor’s Fallacy
- Random Variables
5. 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
1. 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
>> Quiz on Linear Algebra
2. 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
3. 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
4. Quick Links :
- ‘Quizzes’ on Engineering Mathematics !
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Conclusion
Engineering Mathematics is a vast and vibrant field, filled with challenges and rewards. Our tutorials are crafted to ensure that you not only understand the concepts but also appreciate their applications and beauty. So, gear up and get ready to conquer the mathematical mountains that lie ahead!
Remember, this is just the beginning. Stay curious, stay determined, and let the power of mathematics fuel your engineering dreams.
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