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BCA Mathematics Syllabus: 2024 Comprehensive Guide

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Kamaldeep

27 June, 2024

BCA Mathematics Syllabus: 2024 Comprehensive Guide

If you are pursuing a BCA or planning to apply for a BCA degree in maths, understanding the BCA mathematics syllabus is essential for your academic performance and future employment. The BCA Mathematics syllabus aims to provide you with the fundamental mathematical ideas and methods that support information technology and computers. You will study a variety of mathematical topics throughout your BCA program, which will improve your ability to solve problems and think analytically and logically. These abilities are essential for creating effective algorithms, analysing data, and comprehending intricate computational theories. You will be well-equipped to handle the mathematical difficulties you will face in the fast-paced world of computer applications if you can complete the BCA Mathematics syllabus. Read the blog to know about the detailed semester-wise BCA mathematics syllabus.

Overview Of The BCA Mathematics Course

BCA’s full form is a Bachelor of Computer Applications. It is a 2-year undergraduate degree. If you have completed 10+2 from a recognised college, you can pursue BCA. It is a degree in the field of computer science. There are various specialisations offered in the BCA course. Taking mathematics in a BCA course improves your logical thinking when learning computer languages. This is just a topic to assist you in becoming more logical; it is not a major topic.

BCA Mathematics 1st Year Syllabus

There are 2 semesters in BCA 1st year. The subjects are listed below.

Semester 1 Semester 2
Fundamentals of IT & Computers Financial Accounting & Management
C Programming C Programming Advanced Concepts
Digital Electronics & Computer Organization Organisational Behaviour
Basic Mathematics-I Basic Mathematics-II
Business Communication Operating System & Fundamentals

BCA Mathematics 2nd Year Syllabus

BCA Mathematics’s second year begins with Computer programming languages after mathematics in the first year, which served as a foundation for the following semesters.

Semester 3 Semester 4
Computer Organization and Architecture Python Programming
Java Programming Software Engineering
Data Communication & Protocols Data Mining & Visualization
Operating Systems Introduction to Network Security
Artificial Intelligence for Problem Solving Python Programming Lab
Java Programming Lab Data Mining and Visualization Lab
Operating System Lab

BCA Mathematics 3rd Year Syllabus

Semester 5 Semester 6
Mobile Application Development Wireless Communication
Machine Learning Unix and Shell Programming
Cloud Computing & Applications Big Data
Machine Learning Lab Machine Learning Lab
Aptitude and Technical Development Unix and Shell Programming Lab
Elective-I Project

BCA Mathematics 1st Semester Syllabus: Detailed

Mathematics constitutes an important part of the BCA syllabus. The Mathematics syllabus for your first semester of the Bachelor of Computer Applications (BCA) programme will give you a solid foundation in fundamental mathematical ideas essential to your computer science studies and applications.

1. Discrete Mathematics BCA Syllabus

Set Theory:

  • Understanding sets, subsets, power sets, and operations on sets.

  • Venn diagrams and their applications.

  • Cartesian products and relations.

Logic and Propositional Calculus:

  • Introduction to logic, propositions, and logical operators.

  • Truth tables, tautologies, and contradictions.

  • Logical equivalence, implications, and rules of inference.

Functions and Relations:

  • Definition and types of functions (one-to-one, onto, inverse functions).

  • Composition of functions and binary relations.

  • Equivalence relations and partial orderings.

2. Calculus

Limits and Continuity:

  • Concept of limits, techniques for finding limits.

  • Continuity and types of discontinuities.

Differentiation:

  • Basic rules of differentiation, product and quotient rules.

  • Chain rule, implicit differentiation, and higher-order derivatives.

  • Applications of differentiation: tangents and normals, maxima and minima, and rate of change problems.

Integration:

  • Fundamental theorems of integration.

  • Techniques of integration: substitution, integration by parts, partial fractions.

  • Definite integrals and applications to areas and volumes.

3. Algebra

Matrix Algebra:

  • Introduction to matrices, types of matrices, and matrix operations.

  • Determinants, properties of determinants, and Cramer’s rule.

  • The inverse of a matrix, rank of a matrix, and solutions of linear systems using matrices.

Complex Numbers:

  • Definition and operations on complex numbers.

  • Polar form, exponential form, and powers and roots of complex numbers.

  • Applications of complex numbers in solving equations.

4. Linear Algebra

Vector Spaces:

  • Definition and examples of vector spaces.

  • Subspaces, linear independence, basis, and dimension.

Linear Transformations:

  • Definition and properties of linear transformations.

  • Matrix representation of linear transformations and change of basis.

Eigenvalues and Eigenvectors:

  • Definition and calculation of eigenvalues and eigenvectors.

  • Diagonalisation of matrices and applications to differential equations.

5. Probability and Statistics

Probability Theory:

  • Basic concepts of probability, conditional probability, and Bayes’ theorem.

  • Random variables, probability distributions, and expected value.

Descriptive Statistics:

  • Measures of central tendency (mean, median, mode).

  • Measures of dispersion (range, variance, standard deviation).

  • Correlation and regression analysis.

6. Graph Theory

Graphs and Their Properties:

  • Introduction to graphs, types of graphs, and graph terminology.

  • Eulerian and Hamiltonian paths and circuits.

  • Graph colouring, planar graphs, and applications of graph theory in computer science.

BCA Mathematics 2nd Semester Syllabus

The BCA mathematics syllabus degree expands on the ideas covered in the first semester and covers increasingly complex subjects. This syllabus aims to improve your critical thinking, reasoning, and problem-solving skills, essential for your computer science and applications coursework. The following is a detailed explanation of the subjects usually included in the BCA Mathematics 2nd Semester syllabus:

1. Unit -I Sets

Sets:

  • The basic concept of sets: a collection of distinct objects.

  • Notation and representation of sets.

Subsets:

  • Definition of subsets: A set A is a subset of set B if every element of A is also an element of B.

  • Proper and improper subsets.

Equal Sets:

  • Definition: Two sets are equal if they have exactly the same elements.

Universal Sets:

  • Definition: A set that contains all the objects under consideration, usually denoted by U.

Finite and Infinite Sets:

  • Finite sets: Sets with a limited number of elements.

  • Infinite sets: Sets with an unlimited or an infinite number of elements.

Operations on Sets:

  • Union: The set containing all elements from both sets.

  • Intersection: The set containing only the elements common to both sets.

  • Complement: The set of all elements in the universal set that are not in the given set.

Cartesian Product:

  • Definition: The set of all ordered pairs (a, b) where a is in set A and b is in set B.

  • Representation and properties.

Cardinality of Set:

  • Definition: The number of elements in a set.

  • The cardinality of finite sets and the concept of cardinality for infinite sets.

Simple Applications:

  • Practical examples and problems involving the use of sets and their operations.

2. Unit-II Relations & Functions

Properties of Relations:

  • Reflexive, symmetric, transitive, and antisymmetric properties.

Equivalence Relation:

  • Definition and examples: A reflexive, symmetric, and transitive relation.

Partial Order Relation:

  • Definition and properties: A reflexive, antisymmetric, and transitive relation.

Functions:

  • Domain and Range: The set of a function’s possible inputs (domain) and outputs (range).

  • Types of Functions:

  • Onto (surjective) functions: Every element of the range is mapped to by some domain element.

  • Into functions: The domain does not map every element of the range.

  • One-to-one (injective) functions: Every element of the domain maps to a unique element in the range.

Composite and Inverse Functions:

  • Composite Function: Combining two functions where the output of one function becomes the input of the other.

  • Inverse Function: A function that reverses the mapping of the original function.

Introduction to Trigonometric, Logarithmic, and Exponential Functions:

  • Basic properties and applications of trigonometric functions (sine, cosine, tangent, etc.).

  • Properties and uses of logarithmic and exponential functions in solving equations.

3. Unit-III Partial Order Relations & Lattices

Partial Order Sets (Posets)

  • Representation and properties of partially ordered sets.

  • Hasse diagram: A graphical representation of a partial order set.

Chains, Maximal and Minimal Points:

  • Chains: Totally ordered subsets.

  • Maximal Point: No other element in the poset is greater.

  • Minimal Point: No other element in the poset is lesser.

Greatest Lower Bound (glb) and Least Upper Bound (lub):

  • Definitions and examples in posets.

Lattices and Algebraic Systems:

  • Lattices: Posets where every pair of elements has a glb and lub.

  • Principle of Duality: Properties and operations in lattice theory.

Basic Properties of Lattices:

  • Sublattices: A subset of a lattice that is itself a lattice.

  • Distributive and Complemented Lattices: Definitions and characteristics.

4. Unit-IV Functions Of Several Variables

Partial Differentiation:

  • Differentiation concerning one variable while holding others constant.

  • Applications in finding tangent planes and optimisation problems.

Change of Variables:

  • Transformation of variables in multivariable functions.

Chain Rule:

  • Differentiation of composite functions involving several variables.

Extrema of Functions of Two Variables:

  • Finding local maxima, minima, and saddle points using second-order partial derivatives.

  • Lagrange multipliers for constrained optimisation.

Euler’s Theorem:

  • Applications in homogeneous functions and their properties.

5. Unit -V 3D Coordinate Geometry

Coordinates in Space:

  • Representation of points in 3-dimensional space.

  • Direction Cosines: Cosines of angles between a vector and coordinate axes.

Angle Between Two Lines:

  • Calculating the angle between two lines in space.

Projection of Join of Two Points on a Plane:

  • Finding the projection of a line segment onto a plane.

Equations of Planes and Straight Lines:

  • Formulating equations for planes and lines in space.

  • Conditions for a line to lie on a plane and for two lines to be coplanar.

Shortest Distance Between Two Lines:

  • Methods to calculate the shortest distance between skew lines.

Equations of Sphere and Tangent Plane:

  • Deriving the equation of a sphere.

  • Finding the equation of the tangent plane to a sphere at a given point.

6. Unit-VI Multiple Integration

Double Integral in Cartesian and Polar Coordinates:

  • Evaluating double integrals in different coordinate systems.

  • Applications to finding areas.

Change of Order of Integration:

  • Techniques to simplify integration by changing the order of integration.

Triple Integral to Find Volume:

  • Evaluating triple integrals in Cartesian coordinates.

  • Applications to finding volumes of simple shapes

List Of Important Books For BCA Mathematics Syllabus

Check out the list of important books for the BCA mathematics syllabus:

Author Book Name
R.K. Jain & S.R.K. Iyengar Advanced Engineering Mathematics
BCA Mathematics -III Krishna Publications
Seymour Lipschutz Schaum’s Outline of Linear Algebra
Howard Anton & Chris Rorres Elementary Linear Algebra
George B. Thomas & Maurice D. Weir Thomas’ Calculus
Ron Larson & Bruce H. Edwards Calculus
S.C. Malik & Savita Arora Mathematical Analysis
James Stewart Calculus: Early Transcendentals
K.B. Datta Matrix and Linear Algebra
B.S. Grewal Higher Engineering Mathematics
Michael Greenberg Advanced Engineering Mathematics
John Bird Engineering Mathematics
M.D. Raisinghania Linear Algebra
Shanti Narayan & P.K. Mittal A Textbook of Matrices

Conclusion

You will learn various mathematical topics and methods in the BCA Mathematics course, which is essential for your professional and academic advancement in computer applications. By exploring subjects like determinants, matrices, limits, continuity, differentiation, integration, vector algebra, and additional topics, you will have a strong basis to improve your ability to analyse and solve problems.

This syllabus will give you practical skills that you may use in real-world situations in addition to theoretical knowledge. Understanding these subjects will empower you to take on challenging issues, make wise choices, and participate in various scientific and technological domains.

FAQs

Q 1 Is BCA maths very tough?

BCA maths is not tough, but it is challenging. You need practice to score good marks in maths.

Q 2 Can I take BCA if I am weak in maths?

Yes, you can take BCA even if your maths is weak. Maths is required only in the first year of BCA. After that, you have to study subjects related to your specialisations.

Q 3 What is the syllabus for the BCA in the first year?

BCA first year includes subjects such as C Programming, Financial Accounting & Management, Digital Electronics & Computer Organisation, Organisation Behaviour, Mathematics- I & II, Principle of Management, Computer Laboratory and Practical Work of Office Automation.

Q 4 What type of maths is BCA?

Students are required to take math for a maximum of two semesters. BCA covers many subjects, including complex numbers, algebra, limits and continuity, probability, and differentiation.


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