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

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

This course/subject is divided into total of 5 units as given below:

- Determinants
- Limits and Continuity
- Differentiation
- Integration
- Vector Algebra

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 determinants:

- Definition
- Minors
- Cofactors
- Properties of Determinants
- Matrices
- Definition
- Types of Matrices
- Matrix Addition
- Matrix Subtraction
- Matrix Multiplication
- Scalar Multiplication
- Adjoint
- Inverse
- Cramer's Rule
- Rank of Matrix Dependence of Vectors
- Eigen Vectors of a Matrix
- Calley-Hamilton Theorem (without proof)

Here are the list of topics that comes under the syllabus of unit-II, that is limits and continuity:

- Limit at a Point
- Properties of Limit
- Computation of Limits of Various Types of Functions
- Continuity at a Point
- Continuity Over an Interval
- Intermediate Value Theorem
- Type of Discontinuities

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

- Derivative
- Derivatives of Sum
- Differences
- Product and Quotients
- Chain Rule
- Derivatives of Composite
- Functions
- Logarithmic Differentiation
- Rolle's Theorem
- Mean Value Theorem
- Expansion of Functions (Maclaurin's and Taylor's)
- Indeterminate Forms
- L' Hospitals Rule
- Maxima and Minima
- Curve Tracing
- Successive Differentiation and Liebnitz Theorem

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

- Integral as Limit of Sum
- Fundamental Theorem of Calculus (without proof)
- Indefinite Integrals
- Methods of Integration
- Substitution
- By Parts
- Partial Fractions
- Reduction Formulae for Trigonometric Functions
- Definition of Gamma and Beta Functions

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

- Definition of a vector in 2 and 3 Dimensions
- Double and Triple Scalar and Vector Product and physical interpretation of area and volume