#### MA6151 ENGINEERING MATHEMATICS – I  SYLLABUS (REGULATION 2013) AFFILIATED TO ANNA UNIVERSITY (SEMESTER 1)

##### UNIT I: MATRICES

(MA6151) Eigen values and Eigen vectors of a real matrix – Characteristic equation – Properties of eigenvalues and eigen vectors. – Statement and applications of Cayley-Hamilton Theorem. – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.

##### UNIT II: SEQUENCES AND SERIES

Sequences: Definition and examples – Series. Types and Convergence – Series of positive terms – Tests of convergence. Comparison test, Integral test and D’Alembert’s ratio test. – Alternating series – Leibnitz’s test – Series of positive and negative terms – Absolute and conditional convergence.

##### UNIT III: APPLICATIONS OF DIFFERENTIAL CALCULUS

Curvature in Cartesian co-ordinates – Centre and radius of curvature. – Circle of curvature – Evolutes – Envelopes – Evolute as envelope of normals.

##### UNIT IV: DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES

Limits and Continuity – Partial derivatives – Total derivative – Differentiation of implicit functions – Jacobian and properties: – Taylor’s series for functions of two variables – Maxima and minima of functions of two variables – Lagrange’s method of undetermined multipliers.

##### UNIT V: MULTIPLE INTEGRALS

Double integrals in cartesian and polar coordinates. – Change of order of integration – Area enclosed by plane curves – Change of variables in double integrals – Area of a curved surface – Triple integrals – Volume of Solids.

### Course Curriculum

 IMPORTANT QUESTION MA6151 MATHEMATICS 1 FREE 00:00:00 QUESTION BANK – MA6151 ENGINEERING MATHEMATICS 1 FREE 00:00:00 Unit 1 Introduction to Matrices FREE 00:05:00 Chapter 1 Introduction FREE 00:07:00 Type 1 problem 1 FREE 00:10:00 Type 2- problem 2 FREE 00:15:00 Type 2 problem 3 FREE 00:15:00 Type 3 problem 4 00:15:00 Type 4 problem 5 00:10:00 Chapter 2 and properties 00:15:00 Problem based on properties 00:15:00 Chapter 3 – Cayley – Hamilton theorem FREE 00:05:00 Chapter 3 problem 2 00:10:00 chapter 4 00:10:00 Chapter 4 problem 1 00:10:00 unit 1 chapter 4 problem 2 00:10:00 Chapter 5 00:10:00 Nature of a quadratic form 00:10:00 Chapter 5 problem 3 00:10:00 Index of a quadratic form 00:10:00 Chapter 5 problem 4 00:10:00 Chapter 5 Problem 5 00:15:00 Chapter 5 problem 6 00:15:00 Unit 2 Unit 2 Introduction 00:10:00 Chapter 1 definitions 00:10:00 Convergent sequence definition and Problems 00:10:00 Monotonic sequence and bounded sequence- definition 00:10:00 series or infinite series – definitions 00:05:00 Properties of infinite series and problems 00:10:00 Chapter 2 theorems and problems 00:10:00 Chapter 2 comparison test – theorems 00:05:00 Type 1 problem 1-4 00:15:00 Type-2 problem 1-4 00:15:00 Chapter 3 Integral test – statement 00:05:00 Chapter 3 problems 1-5 00:15:00 Chapter 4 -D’Alembert ratio test and problems 1-4 00:15:00 Chapter 4 , problems 5-8 00:15:00 Chapter 5- alternating series, problem 1-3 00:15:00 Chapter 5 , problem 4 – 7 00:15:00 Chapter 6- introduction , problem 1-3 00:15:00 Chapter 6 , problem 4-6 00:15:00 Unit 3 chapter 1 definition and formula 00:10:00 chapter 1, problem 1-5 00:15:00 Chapter 1 Problem 6-8 00:15:00 Chapter 1 , problem 9-11 00:15:00 Chapter 1, problem 12 00:10:00 Chapter 1, problem 13 00:10:00 Chapter 1, problem 14 00:10:00 Chapter 2 , problem 1-2 00:10:00 Chapter 2 , problem 3-5 00:10:00 Chapter 3, definition and problem 1 00:10:00 chapter 3, problem 2-5 00:10:00 Chapter 4, definition and properties 00:10:00 unit 3 Chapter 4 , problem 2 00:05:00 Chapter 4, problem 3 00:05:00 Chapter 4, problem 4 00:10:00 Chapter 4, problem 5 00:10:00 Chapter 4, problem 6 00:10:00 Chapter 4, problem 7 00:10:00 Chapter 4, problem 8 00:10:00 Chapter 5 , problem 1-2 00:10:00 chapter 5 problem 3-5 00:10:00 Two parameters – problem 1-4 00:10:00 unit 3 Chapter 6 introduction , problem 1-2 00:15:00 Unit 4 unit 4 – chapter 1 – Introduction, problem 1-4 00:10:00 unit 4-Partial derivatives- introduction , problems 1-4 00:15:00 Unit 4 – Euler theorem , problem 1-4 00:15:00 Unit 4, chapter 2 , problem 1-2 00:10:00 Unit 4 . composite function of two variable , problem 1-3 00:10:00 Unit 4 , composite function, problem 4-7 00:15:00 unit 4 , differentiation of implicit function, problem 1-3 00:10:00 Unit 4, Chapter 3 , Jacobians , problem 1-4 00:15:00 Unit 4 , chapter 3 , problem 5-8 00:10:00 Unit 4, chapter 4 -Taylor’s series ,problem 1-3 00:15:00 Unit 4, chapter 4, problem 4-7 00:15:00 Chapter 5 , maxima and minima , problem 1-2 00:10:00 Chapter 5 , problem 3-5 00:10:00 unit 4 , chapter 6 , Lagrange’s method , problem 1-2 00:10:00 Unit 4 , chapter 6 , problem 3-6 00:15:00 Unit 5 Introduction to multiple integrals 00:05:00 Unit 5 , chapter 1 introduction and problem 1-2 00:10:00 unit 5 , chapter 1 , problem 3-8 00:10:00 Unit 5, chapter 1 , 8-marks , problem 1-4 00:15:00 Unit 5, chapter 2, Introduction and problem 1-4 00:15:00 Unit 5, chapter 2, and problem 5-8 00:15:00 Unit 5 , chapter 3 , introduction and problem 1-2 00:15:00 Unit 5 , chapter 3, problem 3-5 00:15:00 Unit 5 , chapter 4 , introduction and problem 1-3 00:15:00 Unit 5 , chapter 4, problem 4-6 00:15:00 Unit 5, chapter 4, problem 7-9 00:10:00 Unit 5 , chapter 5, triple integrals , problem 1-4 00:15:00 Unit 5 , chapter 5, problem 5-8 00:15:00 unit 5, chapter 5, problems 9-11 00:15:00

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1. ### good

5

very useful

2. ### Good, But not worth !!!

3

Explanation is very speeded.
Not to understand clearly.
Lower amount of sums solved.

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