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CALCULUS AND DIFFERENTIAL EQUATIONS IS THE SUBJECT IN WHICH STUDENTS HAVE TO STUDY MAINLY TWO MODULES: DIFFERENTIAL CALCULUS AND INTEGRAL CALCULUS. SOME BASIC TOPICS OF THE SUBJECTS THEY HAVE ALREADY STUDIED IN H.S.C LIKE LIMIT, CONTINUITY, DIFFERENTIABILITY, APPLICATIONS OF DIFFERENTIATION, & INTEGRATION. IT IS IMPORTANT TO STUDY OTHER ADVANCED MODULES LIKE SUCCESSIVE DIFFERENTIATION, FUNCTIONS OF TWO VARIABLE & THEIR APPLICATIONS, REDUCTION FORMULA, BETA GAMMA FUNCTIONS, DOUBLE INTEGRATION, TRIPLE INTEGRATION’S AND THEIR APPLICATIONS, WHICH ARE PART OF THE COURSE OF CALCULUS AND DIFFERENTIAL EQUATIONS. HERE STUDENT HAVE TO LEARN THREE IMPORTANT TOPICS OF INTEGRAL CALCULUS: REDUCTION FORMULA, IMPROPER INTEGRAL’S LIKE GAMMA FUNCTION, BETA FUNCTION, ERROR FUNCTION, AND EVALUATION OF AREA AND VOLUME BY DOUBLE AND TRIPLE INTEGRATION’S. THE CONCEPT OF PARTIAL DIFFERENTIATION, DOUBLE AND TRIPLE INTEGRATION’S ARE NEW FOR THE STUDENTS OF B. TECH. SEMESTER – 2. IN FIRST YEAR B.TECH THIS SYLLABUS IS INTRODUCED SO THAT THE ENGINEERING STUDENTS DEVELOP THEIR ANALYTICAL AND LOGICAL THINKING MORE SHARPLY WITH KNOWLEDGE AND THE 2ND STAGE IDEAS OF CALCULUS.