23UMATC13 Algebra & Trigonometry Syllabus:

23UMATC13 Algebra & Trigonometry Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives

  • Basic ideas on the Theory of Equations, Matrices and Number Theory.
  • Knowledge to find expansions of trigonometry functions, solve theoretical and applied problems.

Unit I:

Reciprocal Equations-Standard form–Increasing or decreasing the roots of a given equation- Removal of terms, Approximate solutions of roots of polynomials by Horner’s method – related problems.

Unit II:

Summation of Series: Binomial– Exponential –Logarithmic series (Theorems without proof) – Approximations – related problems.

Unit III:

Characteristic equation – Eigen values and Eigen Vectors-Similar matrices – Cayley – Hamilton Theorem (Statement only) – Finding powers of square matrix, Inverse of a square matrix up to order 3, Diagonalization of square matrices – related problems.

Unit IV:

Expansions of sinnθ, cosnθ in powers of sinθ, cosθ – Expansion of tannθ in terms of tan θ, Expansions of cosnθ, sinnθ, cosmθsinnθ –Expansions of tan(θ1+θ2+,…,+θn)-Expansions of sinθ, cosθ and tanθ in terms of θ – related problems.

Unit V:

Hyperbolic functions – Relation between circular and hyperbolic functions Inverse hyperbolic functions, Logarithm of complex quantities, Summation of trigonometric series – related problems.

Recommended Text Book

  • T. K. Manickavasagam Pillay, T. Natarajan and K. S. Ganapathy, Algebra Volume I, S. Viswanathan (Printers & Publishers) Pvt. Ltd., Reprint 2011 (Unit I ). UNIT I: Chapter-VI: Sec (16-19;30) UNIT II: Chapter-III and IV
  • T. K. Manickavasagam Pillay, T. Natarajan and K. S. Ganapathy, Algebra Volume II, S. Viswanathan (Printers & Publishers) Pvt. Ltd., Reprint 2011 (Unit I ). UNIT III: Chapter-II
  • S. Narayanan, T. K. Manickavasagam Pillay, Trigonometry, S. Viswanathan (Printers and Publishers) Pvt. Ltd., Reprint 2009 UNIT IV: Chapter- 3: Sec(1-5) UNIT V: Chapter- 3: Sec(2-2.3; 5-5.5)
  • S. Narayanan, R. Hanumantha Rao, T.K. Manicavachagom Pillay and Dr. P. Kandaswamy, Ancillary Mathematics, Volume-I, S. Viswanathan (Printers & Publishers) Pvt. Ltd., 2009.
  • S.Arumugam & others, Trigonometry and Fourier series, New Gamma Publications -1999

Books for Reference

  • S. Burnstine and A.W. Panton, Theory of equations
  • David C. Lay, Linear Algebra and its Applications, 3rd Ed., Pearson Education Asia, Indian Reprint, 2007
  • B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, 2005
  • V. Durell and A. Robson, Advanced Trigonometry, Courier Corporation, 2003
  • Stewart, L. Redlin, and S. Watson, Algebra and Trigonometry, Cengage Learning, 2012.
  • Calculus and Analytical Geometry, G.B. Thomas and R. L. Finny, Pearson Publication, 9th Edition, 2010.