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BT-202 · Mathematics II/Official Syllabus

Mathematics II (BT-202) - Official Syllabus

1
Unit 1

Ordinary Differential Equations I

  • Differential Equations of First Order and First Degree (Leibnitz linear, Bernoulli’s, Exact)
  • Differential Equations of First Order and Higher Degree
  • Higher order differential equations with constants coefficients
  • Homogeneous Linear Differential equations
  • Simultaneous Differential Equations
2
Unit 2

Ordinary differential Equations II

  • Second order linear differential equations with variable coefficients
  • Method of variation of parameters
  • Power series solutions
  • Legendre polynomials
  • Bessel functions of the first kind and their properties
3
Unit 3

Partial Differential Equations

  • Formulation of Partial Differential equations
  • Linear and Non-Linear Partial Differential Equations
  • Homogeneous Linear Partial Differential Equations with Constants Coefficients
4
Unit 4

Functions of Complex Variable

  • Functions of Complex Variables: Analytic Functions
  • Harmonic Conjugate
  • Cauchy-Riemann Equations (without proof)
  • Line Integral
  • Cauchy-Goursat theorem (without proof)
  • Cauchy Integral formula (without proof)
  • Singular Points
  • Poles & Residues
  • Residue Theorem
  • Application of Residues theorem for Evaluation of Real Integral (Unit Circle)
5
Unit 5

Vector Calculus

  • Differentiation of Vectors
  • Scalar and vector point function
  • Gradient
  • Geometrical meaning of gradient
  • Directional Derivative
  • Divergence and Curl
  • Line Integral, Surface Integral and Volume Integral
  • Gauss Divergence, Stokes and Green theorems

Reference Books

  • Calculus and Analytic geometry — G.B. Thomas, R.L. Finney — Pearson — 9th Edition
  • Advanced Engineering Mathematics — Erwin kreyszig — John Wiley & Sons — 9th Edition
  • Elementary Differential Equations and Boundary Value Problems — W. E. Boyce, R. C. DiPrima — Wiley India — 9th Edn.
  • Differential Equations — S. L. Ross — Wiley India — 3rd Ed.
  • An Introduction to Ordinary Differential Equations — E. A. Coddington — Prentice Hall India — 1995
  • Ordinary Differential Equations — E. L. Ince — Dover Publications — 1958
  • Complex Variables and Applications — J. W. Brown, R. V. Churchill — McGraw Hill — 7th Ed.
  • A text book of Engineering Mathematics — N.P. Bali, Manish Goyal — Laxmi Publications
  • Higher Engineering Mathematics — B.S. Grewal — Khanna Publishers — 36th Edition
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