# How to Study Engineering Maths for GATE?

Hello Readers,

In this post, we will discuss Engineering Maths and how to prepare it for GATE exam. Engineering Maths is very much relevant to the GATE exam as the weightage given to this subject is consistent over the years whereas other subjects may not be that consistent. Every year you can find the weight-age of this subject to be 12 to 15 Marks. The importance of this subject not only lies in its weightage but also its concepts which are useful for other subjects as well. Never think of Engineering Maths as a separate subject but rather a tool to understand the engineering subjects. Without a good command in Engineering Maths, an engineer is not complete as the only difference between Engineering and Medical is Maths so you as an engineer need to be good at it.

**Linear Algebra**- This chapter starts with the basic concept of Matrices and Determinants which you have already encountered in Class 12th. These are basic concepts and can be referred from any 12th standard book. This topic is very trivial but is very helpful for other subjects as well which involves matrices.
- The application of Matrices comes in the Solution of Linear Equations in which you can understand Cramer’s Rule and the conditions for a unique solution, no solution, and infinite solutions.
- The next topic that needs to be studied is the concept of Eigenvalue and Eigenvectors as there have been many problems in the past from this topic. One must also remember the 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 unnecessary for GATE and are asked very rarely.

**Calculus**- This chapter has mainly three parts: Differential Calculus, Integral Calculus, and Vector Calculus. This is the widest topic and the most important one as it has applications in almost all the subjects.
- Differential calculus starts from the basic concept of derivative and the properties of the derivative such as Product Rule, Quotient Rule etc. Then we have to prepare the applications of derivative such as Increasing and Decreasing Functions, Maxima and Minima. Also, we have to understand the concept of Partial Derivative for multi-variable functions. Multi-variable functions are new as compared to the 12th standard course, so we should study about the optimization of multi-variable functions.
- The next part is Integral Calculus which starts from the basic concept of Indefinite Integration and some common integration pairs such as trigonometric functions. Then comes the concept of Definite Integral in which you have to study about the properties of the definite integral. There are some special functions that you need to study about such as Gamma Function, Beta Function etc. You also have to study about multi-integrals such as Double and Triple Integral and how to change the variables and order of integral using Jacobian Matrix.
- The last part of this chapter is Vector Calculus which will be new for all. This topic will start with the basics of vector analysis such as Addition and Subtraction of vectors, Dot and Cross Product, Scalar and Vector Triple Product. Then we start with the concept of Differential Operator (nabla) and we study differential operations such as Gradient, Divergence, and Curl.
- The next part of this topic includes vector integrals like Line Integral, Surface Integral, and Volume Integral. Also, the vector integral theorems such as Green’s Theorem, Stoke’s Theorem and Gauss Theorem and you must remember all properties to solve the problems faster like divergence of the curl is always zero, believe me, that these properties do come-in handy in the exam.

**Differential Equations**- This chapter is not very difficult because even if you don’t remember how to solve a Differential Equation you can always verify the options by fitting them into the Differential Equation.
- This chapter starts with the solution of First-Order Differential Equations using the methods such as Variable Separation Method, Exact Differential Equation, Homogenous Differential Equation, Linear Differential Equation. But at the same time, you should be careful with some special types of Differential Equations such as Bernoulli’s Equation, Euler-Cauchy Equation.
- Then we move to the concept of Higher Order Differential Equations where we study the concept of Complimentary Function and the Particular Integral. We should understand how to derive the Complimentary Function using Method of Differential Operator. Also how to calculate the Particular Integral for various functions. One method is important here which is Method of Variation of Parameters using Wronskian Matrix.
- ME and CE students should also prepare Partial Differential Equations well which is not asked in other streams but is important for ME and CE GATE Aspirants.

**Complex Functions**- This is the simplest chapter in GATE course and this will begin with the basic information about Complex Numbers.
- Then you have to study about the complex functions which operate on the complex number and give another complex number as output. The important thing is to judge whether a complex function is analytic or not. It is achieved using Cauchy-Riemann Equations.
- Then we have to understand the different types of singularities present like Isolated Singular Point, Essential Singular Point, Removable Singular Point.
- The next topic is the concept of Complex Integral in which we understand the method of Cauchy’s Integral Formula and the Cauchy residue theorem and these concepts are important for GATE.
- The last topic is Complex Power Series in which we understand the method of computing the Radius of convergence of power series using ratio test and root test.

**Probability and Random Variable**- This is the most troubling topic for any engineer because it is mostly based on mental aptitude rather than the method involved. So this topic can only be improved by practice and do not get demotivated if you are unable to solve problems from this topic because it will take time.
- In this chapter, you will first start with basics of Probability where you study about Total Probability Theorem, Conditional Probability, and Baye’s Theorem. Then you have to study concepts such as Probability Density Function (PDF) and Cumulative Distribution Function (CDF). These topics generally help in Random Variable.
- Statistics is a small topic which is included in this unit and the concepts of Mean, Median, Mode and Standard Deviation should be studied.
- The last topic is Random Variable in which you have to study about Discrete Random Variables such as Binomial Distribution, Poisson’s Distribution and some Continuous Random Variable like Uniform Distribution, Exponential Distribution, Gaussian Distribution. You have to understand the method of computation of Expectation, Standard Deviation and Variance of a Random Variable.

**Numerical Methods**- Two things are important in this section one is the equation solving by methods like Newton-Raphson and Bisection Method and other is the Numerical Integration technique by methods like Trapezoidal Rule and Simpson’s rule. So do mug up the formulas for each of these methods and be careful about how will you use Virtual Calculator to solve problems based on Numerical Techniques.

**Transform Theory**- This topic can also be covered in Signals and Systems by EE and ECE Aspirants and is not included in ME and CE GATE course.
- Under this topic, you have to study three transforms, Fourier Transform, Laplace Transform and Z-Transform.
- In each of the transform, you have to understand the method of computation of Transform and some of the common properties of each of the Transforms.

So basically the key to tackling such a large subject is to narrow down the course content to the most relevant topics and cut-out the unnecessary topics otherwise your workload will increase but not your performance.

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