#### MA8151 – ENGINEERING MATHEMATICS – I SYLLABUS (REGULATION 2017) AFFILIATED TO ANNA UNIVERSITY (SEMESTER 1)

##### UNIT I DIFFERENTIAL CALCULUS

Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules. Maxima and Minima of functions of one variable (ma8151).

##### UNIT II FUNCTIONS OF SEVERAL VARIABLES

Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians. Partial differentiation of implicit functions – Taylor’s series for functions of two variables. Maxima and minima of functions of two variables – Lagrange’s method of
undetermined multipliers.

##### UNIT III INTEGRAL CALCULUS

Definite and Indefinite integrals – Substitution rule – Techniques of Integration – Integration by parts. Trigonometric integrals. Trigonometric substitutions, Integration of rational functions by partial fraction, Integration of irrational functions – Improper integrals.

#### UNIT IV MULTIPLE INTEGRALS

Double integrals – Change of order of integration – Double integrals in polar coordinates. Area enclosed by plane curves. Triple integrals – Volume of solids – Change of variables in double and triple integrals.

##### UNIT V DIFFERENTIAL EQUATIONS

Higher order linear differential equations with constant coefficients – Method of variation of parameters. Homogenous equation of Euler’s and Legendre’s type – System of simultaneous linear differential equations with constant coefficients – Method of undetermined coefficients.

### Course Curriculum

 MA8151 QUESTION PAPER 00:00:00 UNIT 1 MA8151 UNIT1 INTRODUCTION FREE 00:00:00 MA8151 UNIT1 CHAPTER1 REPRESENTATION OF FUNCTION FREE 00:00:00 MA8151 UNIT1 CHAPTER1 GRAPH OF FUNCTION PROBLEM1,2 FREE 00:00:00 MA8151 UNIT1 CHAPTER1 TYPES OF FUNCTION FREE 00:00:00 MA8151 UNIT1 CHAPTER1 FUNCTIONS PROBLEM1,2,3 00:00:00 MA8151 UNIT1 CHAPTER2 LIMITS OF FUNCTION PROBLEM 1,2,3 00:00:00 MA8151 UNIT1 CHAPTER2 LIMITS OF FUNCTION PROBLEM4,5 INFINITE LIMITS PROBLEM6,7,8 00:00:00 MA8151 UNIT1 CHAPTER2 INFINITE LIMITS PROBLEM9,10,11,12 00:00:00 MA8151 UNIT1 CHAPTER3 CONTINUITY OF A FUNCTION PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER3 REMOVABLE DISCONTINUITY PROBLEM2 00:00:00 MA8151 UNIT1 CHAPTER4 DERIVATIVES FORMULAS, PRODUCT RULE , QUOTIENT RULE THEOREM PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER4 PROBLEM2,3 00:00:00 MA8151 UNIT1 CHAPTER4 PROBLEM4,5 00:00:00 MA8151 UNIT1 CHAPTER4 BASED ON DERIVATIVES PROBLEM1,2,3 00:00:00 MA8151 UNIT1 CHAPTER4 PRODUCT RULE FOR DIFFERENTIATION PROBLEM1,2,3,4,5,6 00:00:00 MA8151 UNIT1 CHAPTER4 QUOTIENT RULE FOR DIFFERENTIATION PROBLEM1,2,3 00:00:00 MA8151 UNIT1 CHAPTER4 QUOTIENT RULE FOR DIFFERENTIATION PROBLEM4,5 CHAIN RULE PROBLEM1,2,3 00:00:00 MA8151 UNIT1 CHAPTER4 DERIVATIVES OF INVERSE FUNCTION PROBLEM1,2,3 00:00:00 MA8151 UNIT1 CHAPTER4 LOGARITHMIC DIFFERENTIATION PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER4 LOGARITHMIC FUNCTION PROBLEM2,3 00:00:00 MA8151 UNIT1 CHAPTER4 DIFFERENTIATION OF PARAMETRIC FUNCTION PROBLEM1,2 00:00:00 MA8151 UNIT1 CHAPTER4 DIFFERENTIATION OF PARAMETRIC FUNCTION PROBLEM3,4 IMPLICIT FUNCTION PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER4 IMPLICIT FUNCTION PROBLEM2,3,4 00:00:00 MA8151 UNIT1 CHAPTER4 IMPLICIT FUNCTION PROBLEM5,6 00:00:00 MA8151 UNIT1 CHAPTER4 IMPLICIT FUNCTION PROBLEM7,8 00:00:00 MA8151 UNIT1 CHAPTER4 IMPLICIT FUNCTION PROBLEM9 , HYPERBOLIC FUNCTION HIGHER DERIVATIVES PROBLEM1,2,3 00:00:00 MA8151 UNIT1 CHAPTER4 HYPERBOLIC FUNCTION HIGHER DERIVATIVES PROBLEM4,5,6 00:00:00 MA8151 UNIT1 CHAPTER4 HYPERBOLIC FUNCTION HIGHER DERIVATIVES PROBLEM7,8 00:00:00 MA8151 UNIT1 CHAPTER4 HYPERBOLIC FUNCTION HIGHER DERIVATIVES PROBLEM9 00:00:00 MA8151 UNIT1 CHAPTER4 HYPERBOLIC FUNCTION HIGHER DERIVATIVES PROBLEM10 00:00:00 MA8151 UNIT1 CHAPTER5 MAXIMA &MINIMA OF FUNCTION OF ONE VARIABLE, FERMAT THEOREM PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER5 FERMAT THEOREM PROBLEM2 00:00:00 MA8151 UNIT1 CHAPTER5 SECOND DERIVATIVE TEST FOR MAXIMA &MINIMA PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER5 SECOND DERIVATIVE TEST FOR MAXIMA &MINIMA PROBLEM2 00:00:00 MA8151 UNIT1 CHAPTER5 SECOND DERIVATIVE TEST FOR MAXIMA &MINIMA PROBLEM3,4 00:00:00 MA8151 UNIT1 CHAPTER5 SECOND DERIVATIVE TEST FOR MAXIMA &MINIMA PROBLEM5,6 00:00:00 MA8151 UNIT1 CHAPTER5 SECOND DERIVATIVE TEST FOR MAXIMA &MINIMA PROBLEM7,8 00:00:00 MA8151 UNIT1 CHAPTER5 SECOND DERIVATIVE TEST FOR MAXIMA &MINIMA PROBLEM9 00:00:00 MA8151 UNIT1 CHAPTER5 INCREASE & DECREASE FUNCTIONS PROBLEM1 00:00:00 MA8151 UNIT1 CHAPTER5 INCREASE & DECREASE FUNCTIONS PROBLEM2 00:00:00 MA8151 UNIT1 CHAPTER5 CONCAVITY TEST INFLECTION POINT PROBLEM1 00:00:00 UNIT 2 - FUNCTIONS OF SEVERAL VARIABLES MA8151 – unit 2 – chapter 1 – Introduction, problem 1-4 00:10:00 MA8151 – unit 2-Partial derivatives- introduction , problems 1-4 00:15:00 MA8151 – Unit 2 – Euler theorem , problem 1-4 00:15:00 MA8151 – Unit 2, chapter 2 , problem 1-2 00:10:00 MA8151 – Unit 2 , composite function of two variable , problem 1-3 00:10:00 MA8151 – Unit 2 , composite function, problem 4-7 00:15:00 MA8151 – Unit 2 , differentiation of implicit function, problem 1-3 00:10:00 MA8151 – Unit 2 , Chapter 3 , Jacobians , problem 1-4 00:15:00 MA8151 – Unit 2 , chapter 3 , problem 5-8 00:10:00 MA8151 – Unit 2 , chapter 4 -Taylor’s series ,problem 1-3 00:15:00 MA8151 – Unit 2 , chapter 4, problem 4-7 00:15:00 MA8151 – Unit 2 , Chapter 5 , maxima and minima , problem 1-2 00:10:00 MA8151 – Unit 2 ,Chapter 5 , problem 3-5 00:10:00 MA8151 – Unit 2 , chapter 6 , Lagrange’s method , problem 1-2 00:10:00 MA8151 – Unit 2 , chapter 6 , problem 3-6 00:15:00 UNIT3 MA8151 UNIT3 INTRODUCTION 00:00:00 MA8151 UNIT3 CHAPTER1 INDEFINITE INTEGRAL INTRODUCTION 00:00:00 MA8151 UNIT3 CHAPTER1 INDEFINITE INTEGRAL PROBLEM1 & FORMULAS 00:00:00 MA8151 UNIT3 CHAPTER2 INTEGRATION BY SUBSTITUTION RULES PROBLEM1 00:00:00 MA8151 UNIT3 CHAPTER2 INTEGRATION BY SUBSTITUTION RULES PROBLEM2,3,4,5 00:00:00 MA8151 UNIT3 CHAPTER2 INTEGRATION BY PARTS PROBLEM1,2,3,4 00:00:00 MA8151 UNIT3 CHAPTER2 INTEGRATION BY PARTS PROBLEM5,6 00:00:00 MA8151 UNIT3 CHAPTER2 INTEGRATION BY PARTS PROBLEM7,8 00:00:00 MA8151 UNIT3 CHAPTER2 INTEGRATION BY PARTS PROBLEM9,10 00:00:00 MA8151 UNIT3 CHAPTER3 TRIGONOMETRIC INTEGRALS PROBLEM1 00:00:00 MA8151 UNIT3 CHAPTER3 TRIGONOMETRIC INTEGRALS PROBLEM2 00:00:00 MA8151 UNIT3 CHAPTER3 PROPERTIES OF DEFINITE INTEGRALS PROBLEM3 00:00:00 MA8151 UNIT3 CHAPTER3 PROPERTIES OF DEFINITE INTEGRALS PROBLEM4 & SUBSTITUTION METHOD PROBLEM1 00:00:00 MA8151 UNIT3 CHAPTER3 SUBSTITUTION METHOD PROBLEM2 00:00:00 MA8151 UNIT3 CHAPTER3 REDUCTION FORMULA PROBLEM3 00:00:00 MA8151 UNIT3 CHAPTER3 EVALUATION OF INTEGRALS USING TRIGONOMETRIC SUBSTITUTION PROBLEM1,2 00:00:00 MA8151 UNIT3 CHAPTER3 EVALUATION OF INTEGRALS USING TRIGONOMETRIC SUBSTITUTION PROBLEM3,4 00:00:00 MA8151 UNIT3 CHAPTER3 EVALUATION OF INTEGRALS USING TRIGONOMETRIC SUBSTITUTION PROBLEM5,6,7 00:00:00 MA8151 UNIT3 CHAPTER3 EVALUATION OF INTEGRALS USING TRIGONOMETRIC SUBSTITUTION PROBLEM8,9 00:00:00 MA8151 UNIT3 CHAPTER4 INTEGRATION OF RATIONAL FUNCTION BY PARTIAL FRACTION PROBLEM1 00:00:00 MA8151 UNIT3 CHAPTER4 INTEGRATION OF RATIONAL FUNCTION BY PARTIAL FRACTION PROBLEM2 00:00:00 MA8151 UNIT3 CHAPTER4 INTEGRATION OF RATIONAL FUNCTION BY PARTIAL FRACTION PROBLEM3 00:00:00 MA8151 UNIT3 CHAPTER4 INTEGRATION OF RATIONAL FUNCTION BY PARTIAL FRACTION PROBLEM4 00:00:00 MA8151 UNIT3 CHAPTER4 PROBLEM5 00:00:00 MA8151 UNIT3 CHAPTER4 PROBLEM6 00:00:00 MA8151 UNIT3 CHAPTER4 PROBLEM7 00:00:00 MA8151 UNIT3 CHAPTER5 INTEGRATION OF IRRATIONAL FUNCTION PROBLEM1,2 00:00:00 MA8151 UNIT3 CHAPTER5 INTEGRATION OF IRRATIONAL FUNCTION PROBLEM3,4 00:00:00 MA8151 UNIT3 CHAPTER5 INTEGRATION OF IRRATIONAL FUNCTION PROBLEM5 00:00:00 MA8151 UNIT3 CHAPTER5 INTEGRATION OF IRRATIONAL FUNCTION PROBLEM6,7 00:00:00 MA8151 UNIT3 CHAPTER6 IMPROPER INTEGRALS DEFINITION PROBLEM1,2,3 00:00:00 MA8151 UNIT3 CHAPTER6 IMPROPER INTEGRALS DEFINITION PROBLEM4,5 00:00:00 MA8151 UNIT3 CHAPTER6 COMPARISON TEST FOR IMPROPER INTEGRAL, THEOREM & PROBLEM1,2,3 00:00:00 UNIT 4 - MULTIPLE INTEGRALS MA8151 – unit 4- Introduction to multiple integrals 00:05:00 MA8151 – unit 4, chapter 1 introduction and problem 1-2 00:10:00 MA8151 – unit 4, chapter 1 , problem 3-8 00:10:00 MA8151 – unit 4, chapter 1 , 8-marks , problem 1-4 00:15:00 MA8151 – unit 4, chapter 2, Introduction and problem 1-4 00:15:00 MA8151 – unit 4, chapter 2, and problem 5-8 00:15:00 MA8151 – unit 4 , chapter 3 , introduction and problem 1-2 00:15:00 MA8151 – unit 4, chapter 3, problem 3-5 00:15:00 MA8151 unit 4 , chapter 4 , introduction and problem 1-3 00:15:00 MA8151 unit 4, chapter 4, problem 4-6 00:15:00 MA8151 unit 4, chapter 4, problem 7-9 00:10:00 MA8151 unit 4, chapter 5, triple integrals , problem 1-4 00:15:00 MA8151 unit 4, chapter 5, problem 5-8 00:15:00 MA8151 unit 4, chapter 5, problems 9-11 00:15:00 UNIT 5 DIFFERENTIAL EQUATIONS MA8151 – UNIT 5 – Introduction 00:00:00 MA8151 – UNIT 5 -Higher order differential equation with constant co efficients 00:00:00 MA8151 – Unit 5- Type 1 00:00:00 MA8151 – Unit 5-Type 2 00:00:00 MA8151 – Unit 5- Type 3 00:00:00 MA8151 – Unit 5- Type 4 00:00:00 MA8151 – Unit 5- Type 5 00:00:00 MA8151 – Unit 5- Type 6 00:00:00 MA8151 – Unit 5- Method of variation of parameter 00:00:00 MA8151 – Unit 5- Homogeneous equation of Euler type Cauchy’s type 00:00:00 MA8151 – Unit 5- Homogeneous equation of legendre’s type 00:00:00 MA8151 – Unit 5- Simultaneous first order linear differential equation with constant co efficient 00:00:00 MA8151 – Unit 5- Conclusion 00:00:00

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