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BT-102 · Mathematics I/Official Syllabus

Mathematics I (BT-102) - Official Syllabus

1
Unit 1

Calculus

  • Rolle’s theorem
  • Mean Value theorems
  • Expansion of functions by Mc. Laurin’s and Taylor’s for one variable
  • Taylor’s theorem for function of two variables
  • Partial Differentiation
  • Maxima & Minima (two and three variables)
  • Method of Lagranges Multipliers
2
Unit 2

Calculus

  • Definite Integral as a limit of a sum and Its application in summation of series
  • Beta and Gamma functions and their properties
  • Applications of definite integrals to evaluate surface areas and volumes of revolutions
  • Multiple Integral
  • Change the order of the integration
  • Applications of multiple integral for calculating area and volumes of the curves
3
Unit 3

Sequences and series

  • Convergence of sequence and series
  • tests for convergence
  • Power series
  • Taylor's series
  • series for exponential, trigonometric and logarithm functions
  • Fourier series: Half range sine and cosine series
  • Parseval’s theorem
4
Unit 4

Vector Spaces

  • Vector Space
  • Vector Sub Space
  • Linear Combination of Vectors
  • Linearly Dependent
  • Linearly Independent
  • Basis of a Vector Space
  • Linear Transformations
5
Unit 5

Matrices

  • Rank of a Matrix
  • Solution of Simultaneous Linear Equations by Elementary Transformation
  • Consistency of Equation
  • Eigen Values and Eigen Vectors
  • Diagonalization of Matrices
  • Cayley-Hamilton theorem and its applications to find inverse

Reference Books

  • Higher Engineering Mathematics — Ramana B.V. — Tata McGraw Hill New Delhi — 11th Reprint
  • Linear Algebra: A Modern Introduction — D. Poole — Brooks/Cole — 2nd Edition
  • A text book of Engineering Mathematics — N.P. Bali, Manish Goyal — Laxmi Publications — Reprint
  • Higher Engineering Mathematics — B.S. Grewal — Khanna Publishers — 36th Edition
  • Calculus and Analytic geometry — G.B. Thomas, R.L. Finney — Pearson — 9th Edition
  • Advanced Engineering Mathematics — Erwin kreyszig — John Wiley & Sons — 9th Edition
  • Engineering Mathematics for first year — Veerarajan T. — Tata McGraw-Hill, New Delhi
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