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Here you will find the syllabus of fifth subject in BCA Semester-IV^{th},
which is Mathematics-III.

**Important** - The syllabus may vary from college to college.

This course/subject is divided into total of 6 units as given below:

- Complex Variables
- Sequences, Series, and Convergence
- Vector Calculus
- Fourier Series
- Ordinary Differential Equations of First Order
- Ordinary Differential Equations of Second Order

Now let's expand the above listed units with its syllabus.

Here are the list of topics that comes under the syllabus of unit-I, that is complex variables:

- Complex Number System
- Algebra of Complex Numbers
- Polar Form
- Powers and Roots
- Functions of Complex Variables
- Elementary Functions
- Inverse Trigonometric Function

Here are the list of topics that comes under the syllabus of unit-II, that is sequence, series, and convergence:

- 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)

Here are the list of topics that comes under the syllabus of unit-III, that is vector calculus:

- Differentiation of Vectors
- Scalar and Vector Fields
- Gradient
- Directional Derivatives
- Divergence and Curl and their Physical Meaning

Here are the list of topics that comes under the syllabus of unit-IV, that is fourier series:

- Periodic Functions
- Fourier series
- Fourier Series of Even and Odd Functions
- Half Range Series

Here are the list of topics that comes under the syllabus of unit-V, that is ordinary differential equations of first order:

- Variable Separable Method
- Homogeneous Differential Equations
- Exact Differential Equations
- Linear Differential Equations
- Bernoulli's Differential Equations
- Differential Equations of First Order and First Degree by Integrating Factor

Here are the list of topics that comes under the syllabus of unit-VI, that is ordinary differential equations of second order:

- Homogenous Differential Equations with Constant Coefficients
- Cases of Complex Roots and Repeated Roots
- Differential Operator
- Solutions by Methods of Direct Formulae for Particular Integrals
- Solution by Undetermined Coefficients
- Cauchy Differential Equations
- Operator Method for Finding Particular Integrals