Chairperson : Prof. Neeru Department Coordinator : Prof Vinay Kanwar Courses Leader : Prof. Vinay Kanwar B.A. SEMESTER – I, MATHEMATICS PAPER : III, TRIGONOMETRY AND MATRICES Introductory Letter (i) Syllabus (ii) CONTENTS L. No. Title Author Page No. 1. De Moivre’s Theorem Dr. G.S. Sandhu 1 2. Applications of De Moivre’s Theorem Dr. G.S. Sandhu 25 3. Elementary Functions of a Complex Number Dr. G.S. Sandhu 53 4. Summation of Series Dr. G.S. Sandhu 77 5. Hermitian & Skew-Hermitian matrices Dr. G.S. Sandhu 105 6. Rank of a Matrix Dr. G.S. Sandhu 120 7. System of Linear Equations Dr. G.S. Sandhu 151 8. Eigen Values & Eigen Vectors of a Matrix Dr. G.S. Sandhu 174 Vetter : Prof. Vinay Canwar E-Mail of Department -
[email protected] Contact No. of Department - 0172-2534330
(i) Introductory Letter Dear Student, We congratulate you on joining USOL and hope you will enjoy your association with our Institute. It will be our endeavor to make this association meaningful and a great learning experience. As you know you are now in the first semester of BA Mathematics, you are encouraged to solve exercises of this book as well as from other standard text books at your own instead of finding solutions from the help books. This block of lessons deals with Trigonometry and Matrices. You will find in this block of lessons a detailed discussion on all the topics and their applications. The exercises given at the end of each lesson deal with the topics discussed in the text and are sufficient for practice and for examination point of view. Please go through them very carefully. If you have any difficulties do not hesitate to write to us or visit us personally. Yours sincerely Deptt. of Mathematics
(ii) Paper III: TRIGONOMETRY AND MATRICES Max. Marks : 30 Time : 3 Hours Note: 1. The syllabus has been split into two Units: Unit-I and Unit-II. Four questions will be set from each Unit. 2. A student will be asked to attempt five questions selecting at least two questions from each Unit. Each question will carry 6 marks. 3. The teaching time shall be five periods (45 minutes each) per paper per week including tutorial. 4. If internal assessment is to be conducted in the form of written examinations, then there will be only one written examination in a Semester Unit-I D’Moivre’s theorem, application of D’Moivre’s theorem including primitive nth roots of unity. Expansions ofsin n , cos n , sinn , cosn (n∈N). The exponential, logarithmic, direct and inverse circular andhyperbolic functions of a complex variable.Summation of series including Gregory Series. Unit-II Hermitian and skew-hermitian matrices, linear dependence of row and column vectors, row rank, column rankand rank of a matrix and their equivalence. Theorems on consistency of a system of linear equations (bothhomogeneous and non-homogeneous).Eigen-values, eigen-vectors and characteristic equation of a matrix,Cayley-Hamilton theorem and its use in finding inverse of a matrix.Diagonalization. References: 1. K.B. Datta :Matrix and Linear Algebra, Prentice Hall of India Pvt. Ltd., New Delhi, 2000. 2. S. R. Knight and H.S. Hall :Higher Algebra, H.M. Publications, 1994. 3. R.S. Verma and K.S. Shukla :Text Book on Trigonometry, Pothishala Pvt. Ltd., Allahabad. 4. Shanti Narayan and P.K. Mittal :A Text Book of Matrices, S. Chand & Co., New Delhi, RevisedEdition, 2007
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