**Table Of Contents**

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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