# 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,
• 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).