In this article, we will discuss the importance of Gate engineering mathematics, and share your necessary tips and tricks for engineering mathematics preparation. Engineering mathematics is an important part of Gate syllabus, and it constitutes almost 15 marks of each gate engineering stream paper. So, this part is absolutely important in scoring good marks and getting a good Gate ranks in your exam. Gate engineering mathematics is a subject which is part of first-year basic sciences (mathematics) course in every engineering college. Most of this syllabus is covered in first 2 semesters, although some syllabus is also covered in second years too. It is important to note that it is more of an extension of Class 11-12 mathematics, so your JEE mathematics notes will come in handy in preparation of basics. So the key to preparing for such subjects is to keep short notes handy with you or maybe you can have a sort of Formula Sheet so that you can look up to a concept whenever you need it.

# Engineering mathematics for Gate exam – Topic wise analysis

Gate engineering mathematics is broadly classified into 7-8 main topics. We have shared the detailed description of these mathematics topics below. We have also shared you required tips and tricks for preparation of engineering mathematics topics.

### Linear Algebra (All Engineering streams)

#### Important topics in Linear Algebra

- Eigenvalues and vectors
- Matrix Algebra
- System of linear equation
- Finding ranks and determinants of matrices

While studying for linear algebra in engineering mathematics, give much attention to the matrix (properties, solving them) and eigenvalue problems. Most of the questions come from these 2 sections in this part. You should remember shortcuts and important properties of eigenvalues like the relation between eigenvalues of two matrices which are inverse of each other and other similar properties. No need to get involved in the basis vectors and span of basis vectors to form an n-dimensional space as those concepts are absolutely unnecessary for GATE.

#### Sample questions on Linear Algebra

- Rank and determinant of a matrix
- A solution for a given set of linear equations
- Creating a matrix with given eigenvalues and eigenvector
- Symmetrical matrix and finding properties of eigenvalues

### Calculus (All engineering streams)

#### Important topics in calculus

- Limit
- Maxima and Minima
- Vector Analysis
- Gradient, divergence, and curl
- Differential calculus
- Integral calculus
- Vector calculus

Calculus can be basically divided into three categories:

- Differential Calculus: It covers basic concepts of Limits, Derivative, and application of derivatives such as Increasing, Decreasing function and Maxima and Minima problems.
- Integral Calculus: It covers indefinite and definite integral and the properties of definite integrals. Also, you need to be very well versed with the concepts of multiple integrals like Double and Triple Integral and also Line, Surface, and Volume Integrals.
- Vector Calculus: It covers Gradient, Divergence and Curl and Vector Integral Theorems (Green’s, Gauss’s and Stokes Theorem) and there are lot many properties of each concept and you must remember all those to solve the problems faster like divergence of curl is always zero, believe me, that these properties do come in handy in the exam.

#### Sample questions in calculus

- Find the divergence in the given vector field
- Questions on limit, continuity, and differentiation
- Finding maxima and minima of the given equation

### Differential equations (For all engineering streams)

#### Important topics in differential equations

- Cauchy’s and Euler equation
- Bernoulli’s Equation
- First order linear and non-linear equation

There are not many concepts in the differential equations as you can always check the solution by satisfying each option in the differential equation given in the problem statement but at the same time do remember some special differential equations like Bernoulli’s Equation and Euler Differential Equation. Also, in the latest years questions based on the existence of solution and uniqueness theorem have been seen so they also need to be prepared.

#### Sample questions in differential equations

- Given an equation, solve it

### Complex Analysis (All engineering streams except CS)

#### Important topics in complex analysis

- Taylor series
- Cauchy and Riemann equations
- Residue Method of Integration

It is the smallest topic among all topics from Engineering Mathematics and the only important concepts are Cauchy-Riemann Equations for Analytic Functions and Residue Method of Integration and rest of the topics are not necessary for GATE.

#### Sample questions on complex analysis

- Integration of a given complex function in the clockwise and anti-clockwise direction

### Numerical methods (All engineering streams except CS)

#### Important topics in numerical methods

- Newton-Raphson method
- Integration by trapezoidal and Simpson’s rules
- Trapezoidal Rule
- Bisection Method

Numerical methods course is part of most engineering streams (except CS). In this part, you need to understand different formulas and rules and use a calculator to arrive at the given answer for the problem.

#### Sample questions on numerical methods

- Find the value of a given equation using trapezoidal and Simpson’s rules
- Find the value of a given equation using the Newton-Raphson method

### Transform theory (for Gate ECE and EE streams)

#### Important topics in transform theory

- Laplace transform
- Fourier series
- Z transform

Transform theory is for electrical and electronics engineering streams only (EE and ECE). This syllabus is part of communication courses (especially signal and system, communication devices) during the first 4 semesters of their respective engineering course. Students can refer to signal and system book by Oppenheim and Wilsky to cover the syllabus of this part. But make sure to read only the relevant part of a book, a lot of the chapters in the book are not covered. So basically you have to narrow down the course content to the most relevant topics and leave the unnecessary topics otherwise your workload will increase but not your performance.

#### Sample questions on transform theory

- Find the Laplace transform and inverse Laplace transform of the given function

### Probability and statistics (all engineering streams)

#### Important topics in probability and statistics

- Conditional probability
- Joint probability
- Bayes theorem
- Uniform, normal and exponential distribution
- Covariance and correlation
- Probability distribution

#### Sample questions on probability and statistics

- Coin based problems
- Dice based problems
- Probability using distribution
- Circular arrangement

### Discrete mathematics (for computer science CS)

#### Important topics in discrete mathematics

- Relations and functions
- Graph connectivity and coloring
- Mathematics logic
- Set theory
- Permutation and Combination
- Boolean algebra
- Predicates and quantifiers
- Hasse diagram
- Partial order and lattices
- Binary tree

Discrete Mathematics is only asked for computer science stream, and you are expected to have knowledge of basic computer science subject (elementary level) along with data structure. Often this is a high scoring topic, as most of the chapters like Set theory, logic, Trees and graphs, Permutation and combination are well covered during computer science stream, and some of these in class 11-12 JEE exam preparation as well. But, it does require a lot of practice and understanding different rules.

#### Sample questions in discrete mathematics

- Finding the first order logic sentence of a given statement with predicates
- Find the number of edges, vertices components in the connected or disconnected graph
- Shortest time and path to traverse a graph
- Shortest time to add, remove a node in the tree

## Important books for preparation of gate engineering mathematics

B.S Grewal – Higher engineering mathematics

## Preparation tips for gate engineering mathematics

In our opinion, for a beginner who is studying 2-3 hours daily, it will take 3-4 weeks to completely finish Gate engineering mathematics subject and acquire confidence. Practice is the most important. It is important to follow one source of material, following too many sources will only consume time and won’t yield many results.

Take all the concepts one by one, and start making notes on important equations and formulas. Solve previous year Gate engineering mathematics paper, first taking help from your notes and then without them. Try to do as many practice exercises as you can.

## Conclusion

In this article, we have shared tips and tricks to study engineering mathematics for Gate exam. We hope that this article will help you in your gate engineering mathematics preparation. If you have any doubt, you can comment in the discussion thread below. We will be glad to assist you in your gate preparation.

All the best!

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