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BCA Syllabus Mathematics-III 2nd Year Notes Pdf

Learn about the Mathematics-III BCA Syllabus notes. Discover advanced calculus, numerical techniques, and insightful knowledge to succeed in your academics. Improve your mathematical skills to succeed in school.

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Unit-I: Complex Variables (Mathematics-III)

  • Complex Number System,
  • Algebra of Complex Numbers,
  • Polar Form, Power and Roots,
  • Functions of Complex Variables,
  • Elementary Functions,
  • Inverse Trigonometric Functions. 

Unit-II: Sequence, Series and Convergence (Mathematics-III)

  • Sequence,
  • Finite and Infinite Sequences,
  • Monotonic Sequence,
  • Bounded Sequence,
  • Limit of a Sequence,
  • Convergence of a Sequence, Series,
  • Partial Sums, Convergent Series,
  • Theorems on Convergence of Series (Statement, Alternating Series, Conditional Convergent),
  • Leibnitz Test,
  • Limit Comparison Test,
  • Ratio Test,
  • Cauchy’s Root Test,
  • Convergence of Binomial and Logarithmic Series,
  • Raabe’s Test,
  • Logarithmic Test,
  • Cauchy’s Integral Test (Without Proof).

Unit-III: Vector Calculus (Mathematics-III)

  • Differentiation of Vectors,
  • Scalar and Vector Fields,
  • Gradient,
  • Directional Derivatives,
  • Divergence and Curl and their Physical Meaning. 

Unit-IV: Fourier Series (Mathematics-III)

  • Periodic Functions,
  • Fourier Series,
  • Fourier Series of Even and Odd Functions.
  • Half Range Series.

Unit-V: Ordinary Differential Equations of First Order (Mathematics-III)

  • Variable separable Method,
  • Homogeneous Differential Equations.
  • Exact Differential Equations,
  • Linear Differential Equations,
  • Bernoutli’s Differential Equations,
  • Differential Equations of First Order and First Degree by Integrating Factor.

Unit-VI: Ordinary Differential Equations of Second Order (Mathematics-III)

  • Homogeneous Differential Equations with Constant Coefficients,
  • Cases of Complex Roots and Repeated Roots,
  • Differential Operator.
  • Solutions by Methods of Direct Formulae for Particular Integrals,
  • Solutions by Undetermined Coefficients.
  • Cauchy Differential Equations (Only Real and Distinct Roots),
  • Operators Methods for Finding Particular Integrals (Direct Formulae). 

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