Calculus is the most important part of higher school mathematics as it includes differentiation, integration, and differential equations. Calculus finds its application in solving different types of mathematical problems. Calculus is the study of the impact of change in independent variables on the function. Calculus forms the basis for advanced mathematics and also plays a valuable role in modern physics and science. This article will help you prepare yourself for GATE exam by providing calculus tips and tricks for GATE ECE, GATE Calculus GATE questions with solutions, best books to study calculus, calculus notes for GATE ECE, Calculus notes for computer science, Calculus study material for GATE ECE, and calculus syllabus for GATE.
Important Topics of Calculus for GATE ECE
Here are some of the important topics of calculus for GATE ECE
Topics  Meaning 
Basic Calculus  Basic calculus is based on the concepts of limits and continuity and involves understanding of integration and differentiation. It forms the basis for differential calculus and integral calculus. 
Differential Calculus  Differential calculus studies the rate of change of one quantity with respect to some other variable or quantity. To find the solution to the problem, derivatives are used. It involves studying the limits of the problem to obtain solutions. 
Limits  Limit is expressed as the closeness of one value to some other value or term. It is represented as Limit x f(x) = A where x is approaching c. 
Derivatives  It is the rate of change of one quantity with respect to some other quantity and represented as Limit x f(x+h)f(x)/h = A where x is approaching h. The process of finding the derivatives of a function is called differentiation. 
Continuity  A function is referred to as continuous at a point x = a, if it satisfies 3 conditions:  f(a) is defined
 Limit x f(x) where x is approaching a exists
 Limit x f(x) where x is approaching a = Limit x f(x) where x is approaching +a = f(a)

Integral Calculus  It is the study of integration and integrals. It is used in mathematics to solve 2 purposes:  Find the area under the curve
 To find f from f'. It means finding the function back from its derivative.

Integration  It is completely the opposite of the differentiation function. Differentiation means dividing a whole into smaller pieces while integration means collecting the smaller pieces to form a whole. 
Definite Integral  It is integral which has specific boundaries or limits within which the function is solved. Both lower and upper limits are specified in the definite integral. 
Indefinite Integral  There are no specific limits or boundaries for the function. Both upper and lower limits are not specified in indefinite integral. So, constant c is used along with the equation. 
Tips to Solve Calculus Questions for GATE
 Learn the standard formulae especially related to trigonometry.
 Understand the nature of the function before solving the problem. It could be a maxima function, minimal function, odd function, and an even function etc.
 Practice more for integration as people find this topic confusing and difficult. Practice all the methods of solving problems using integration.
 Graph problems whenever possible as it will help you understand the problem better without doing any calculations. It is also very useful while finding the area under the curve.
Importance of Calculus in GATE ECE
 Calculus is always a part of the syllabus for any competitive examination. The majority of competitive examinations have questions from calculus.
 Calculus questions find its use in solving different types of mathematical problems in Physics and Chemistry.
 A number of questions are directly asked from differential and integral calculus while some questions are from the subtopics such as limits, derivatives, differential equations, and continuity.
 Every year JEE and GATE examination do have at least 1 or 2 questions from topics calculus while the NDA examination has more than 15 questions from different topics of calculus.
 Calculus MCQs are common in GATE ECE papers as well as for other GATE exams as well.
Most Recommended Books for Calculus for GATE ECE
Following are the most recommended books to practice calculus:
Book  Author 
Essential Calculus Skills Practice  Chris McMullen 
Calculus for Dummies  Mark Ryan 
Calculus  James Stewart 
Why Study Calculus from BYJU'S Exam Prep?
Studying with BYJU'S Exam Prep allows you to interact and compete with each other at all India level with the help of GATE Calculus practice tests, GATE ECE online MCQ, and daily quizzes. BYJU'S Exam Prep provides you with a platform to study through highquality preparation material and scan through previous year's examinations and mock papers. You will get access to verified and highquality study preparation material and that will boost your confidence with the help of GATE ECE mock question papers and regular live lessons to clarify your doubts and queries with field experts. It provides you with calculus quizzes, calculus notes for GATE ECE, calculus MCQ pdf, calculus online tests, calculus syllabus for GATE, calculus notes for computer science and calculus questions and answers pdf to prepare for examinations.
Frequently Asked Questions (FAQs)
Q. How are calculus questions asked in exams?
Some questions are asked directly in the form of an equation and some are asked in the form of subtopics like limits and continuity.
Q. Which is the best method of studying calculus?
Always start with basic questions that are available in NCERT and then try solving complex questions. After that, you can use any of the aboverecommended above recommended books to practice calculus.
Q. How are calculus questions weightage divided in competitive exams?
Questions come from both integral and differential calculus. GATE and JEE examination every year have at least 1 question from both the topics while the NDA exam every year includes at least 7 questions from differential calculus and 3 questions from integral calculus.
Q. Is calculus part of the syllabus for all competitive examinations?
Yes, all competitive exams that have a mathematical section include questions from calculus and subtopics. Few examinations which include calculus in the syllabus are:
 GATE ECE
 JEE Advanced
 JEE Mains
 UPSC IES
 CAT and other MBA Entrance exams
Q. What are the most recommended books to prepare for calculus for GATE ECE?
There are many books available in the market to prepare for calculus but the most recommended books by experts are Class 11th and 12th NCERT, RD Sharma, and Calculus for Dummies.