**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 Batches

### Course Curriculum

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 |

### Course Reviews

**3467 STUDENTS ENROLLED**

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