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# BCA Semester-IVth - Mathematics-III Syllabus

Here you will find the syllabus of fifth subject in BCA Semester-IVth, which is Mathematics-III.

Important - The syllabus may vary from college to college.

## Mathematics-III Units

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

1. Complex Variables
2. Sequences, Series, and Convergence
3. Vector Calculus
4. Fourier Series
5. Ordinary Differential Equations of First Order
6. Ordinary Differential Equations of Second Order

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

## Unit-I Syllabus - Complex Variables

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

## Unit-II Syllabus - Sequence, Series and Convergence

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)

## Unit-III Syllabus - Vector Calculus

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
• Directional Derivatives
• Divergence and Curl and their Physical Meaning

## Unit-IV Syllabus - Fourier Series

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

## Unit-V Syllabus - Ordinary Differential Equations of First Order

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

## Unit-VI Syllabus - Ordinary Differential Equations of Second Order

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

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