B.Sc Mathematics 1st Semester Syllabus: University-wise Subjects and Topics

The B.Sc Mathematics 1st Semester Syllabus is the foundation for higher mathematics studied during graduation. Although the syllabus differs from one university to another, many core topics remain common. These include Differential Calculus, Integral Calculus, Differential Equations, Matrices, Complex Numbers, and applications of derivatives.

Here is a university-wise overview of the first-semester syllabus followed by several Indian universities, including the University of Delhi, Rajasthan, Kurukshetra, Lucknow, Patna, Mumbai, SPPU, Hyderabad, Kolkata, Punjab, CCSU Meerut, Allahabad, Kumaun, and HNB Garhwal University.

Common Topics in B.Sc Mathematics 1st Semester Syllabus

While every university follows its own curriculum, several subjects are covered in almost every B.Sc Mathematics 1st Semester Syllabus.

University-wise B.Sc Mathematics 1st Semester Syllabus

The B.Sc Mathematics 1st semester syllabus differs across universities based on their curriculum structure and academic requirements. However, most universities cover fundamental concepts of calculus, algebra, and differential equations to build a strong foundation in mathematics.

University of Delhi B.Sc Mathematics 1st Semester Syllabus

The University of Delhi covers Differential Calculus, Integral Calculus, and Differential Equations during the first semester.

Unit 1: Limits, Continuity and Differentiability

Topics include:

• Limit of a Function

• Epsilon-Delta Definition of Limits

• Continuity of a Function

• Types of Discontinuity

• Differentiability of Functions

• Successive Differentiation

• Leibniz Theorem

Unit 2: Applications of Derivatives

Students study:

• Increasing and Decreasing Functions

• Relative and Absolute Maxima and Minima

• Concavity

• Points of Inflection

• Asymptotes

• Curve Tracing

Unit 3: Integral Calculus

This unit includes:

• Introduction to Integral Calculus

• Applications of Integrals

• Area, Volume and Surface Area

• Reduction Formulae for Trigonometric Functions

• Applications of Reduction Formulae in Area Calculation

Differential Equations

Students also learn introductory concepts of Differential Equations, including:

• Variable Separable Equations

• Homogeneous Equations

• Exact Differential Equations

• Linear Differential Equations

• Bernoulli's Differential Equation

• Basic applications of Differential Equations

University of Rajasthan B.Sc Mathematics 1st Semester Syllabus

The University of Rajasthan divides the first-semester syllabus into different papers for the B.Sc Programme and B.Sc Physical Science students. The curriculum covers Differential Calculus with Algebra topics.

University of Rajasthan Paper I: Calculus - I

The University of Rajasthan offers Paper I: Calculus - I for B.Sc. Physical Science (Mathematics Group) Semester I students. The syllabus covers the following units and topics. 

Unit I: Real Numbers and Functions

• Real number system 

• Intervals and neighbourhoods 

• Functions and composite/inverse types 

Unit II: Limits and Continuity

• Standard limits and limit evaluation 

• Properties of continuous functions 

Unit III: Differentiation

• Derivative rules and methods

• Successive differentiation and Leibniz theorem 

Unit IV: Applications of Derivatives

• Increasing/decreasing and Maxima/minima 

• Tangents and normals 

• Curve tracing 

University of Rajasthan Paper II: Algebra - I

The University of Rajasthan Paper II: Algebra - I syllabus introduces fundamental algebraic concepts, including the theory of equations, complex numbers, matrices, and determinants. The unit-wise topics are given below.

Unit I: Theory of Equations

• Relation between roots and coefficients, transformation of equations. 

Unit II: Complex Numbers

• Algebra of complex numbers, De Moivre's theorem and polar systems.

Unit III: Matrices

Types, operations, matrix rank and inverse calculation.

Unit IV: Determinants

Determinant expansion, Cramer's Rule, linear system solutions

Kurukshetra University B.Sc Mathematics 1st Semester Syllabus

The first-semester syllabus at Kurukshetra University mainly focuses on Calculus and Differential Equations. It covers fundamental concepts of limits, derivatives, integration, special functions, and first-order differential equations.

Limits and Continuity

• ε-δ limits, continuity of real-valued functions

• L'Hospital's Rule and indeterminate forms

• Taylor's theorem with remainder, Maclaurin's series

Derivative Applications

• Increasing/decreasing, Maxima and minima

• Concavity, points of inflexion and asymptotes

• Curve tracing methods

Integrals and Equations

• Reduction formulae and definite integrals

• Beta and Gamma functions and their relations

• Variable separable, Exact, Linear and Bernoulli's DEs

University of Lucknow B.Sc Mathematics 1st Semester Syllabus

The University of Lucknow syllabus is divided into Differential Calculus and Integral Calculus. It introduces students to functions, differentiation techniques, series expansions, integration methods, and special functions.

Units 1 & 2: Limits and Differentiation

Topics covered include:

• Real-Valued Functions

• Domain and Range

• Composite and Inverse Functions

• Standard Limits

• Differentiability

• Higher Order Derivatives

• Leibniz Theorem

• Partial Differentiation

• Euler's Homogeneous Theorem

Units 3 & 4: Applications and Series Expansions

Students learn:

• Increasing and Decreasing Functions

• Maxima and Minima

• Tangents and Normals

• Curve Tracing

• Taylor's Theorem

• Maclaurin's Theorem

• Series Expansion of:

• Trigonometric Functions

• Exponential Functions

• Logarithmic Functions

• Hyperbolic Functions

Unit 5: Indefinite Integration

Topics include:

• Substitution Method

• Integration by Parts

• Partial Fractions

Definite Integrals

Students study:

• Evaluation of Definite Integrals

• Properties of Definite Integrals

Additional Topics

The syllabus also covers:

• Reduction Formulae

• Trigonometric Reduction Formulae

• Geometrical Area Applications

• Beta Functions

• Gamma Functions

• Fundamental Relations of Beta and Gamma Functions

• Simple Mathematical Applications of Beta and Gamma Functions

Patna University B.Sc Mathematics 1st Semester Syllabus

Patna University gives significant importance to Calculus in the first semester. The syllabus covers functions, differentiation, applications of derivatives, and integral calculus.

Unit 1: Functions, Limits and Continuity

Students study:

• Functions

• Domain, Co-domain and Range

• One-One and Onto Functions

• Types of Functions

• Standard Limits

• Properties of Continuity

Unit 2: Differential Calculus

Topics include:

• Successive Differentiation

• Leibniz Theorem

• Partial Differentiation

• Taylor's Series

• Maclaurin's Series

Unit 3: Applications of Derivatives

This unit covers:

• Increasing and Decreasing Functions

• Maxima and Minima

• Tangents and Normals

• Asymptotes

• Curve Tracing

Integral Calculus

The Integral Calculus section includes:

• Indefinite Integration

• Definite Integration

• Reduction Formulae

• Beta and Gamma Functions

• Relations of Beta and Gamma Functions

University of Mumbai B.Sc Mathematics 1st Semester Syllabus

The University of Mumbai places a strong emphasis on Calculus during the first semester. The syllabus covers differential calculus, integration techniques, and applications of integral calculus.

Units 1 & 2: Differential Calculus

The topics included are:

• Real-Valued Functions

• Domain and Range

• Standard Limits

• Continuity and Differentiability

• Successive Differentiation

• Leibniz Theorem

• Partial Differentiation

• Euler's Homogeneous Theorem

• Maxima and Minima

Units 3 & 4: Integral Calculus

Students study:

• Indefinite Integration

• Substitution Method

• Integration by Parts

• Partial Fractions

• Definite Integrals

• Geometrical Area Calculation

• Trigonometric Reduction Formulae

• Beta Functions

• Gamma Functions

Savitribai Phule Pune University (SPPU) B.Sc Mathematics 1st Semester Syllabus

The SPPU syllabus combines Algebra and Calculus to build a foundation in mathematical concepts.

Unit 1: Integers

Topics covered include:

• Well-Ordering Principle

• Mathematical Induction

• Divisibility in Z

• Division Algorithm

• Greatest Common Divisor (GCD)

• Least Common Multiple (LCM)

• Euclidean Algorithm

• Relatively Prime Integers

Unit 2: Polynomials

Students learn:

• Polynomials over Real Numbers

• Division Algorithm

• Roots and Relation with Coefficients

• Fundamental Theorem of Algebra (Basic Concepts)

Unit 3: Real Numbers and Functions

Topics include:

• Properties of Real Numbers

• Intervals and Neighbourhoods

• Real-Valued Functions

• Graphs of Algebraic Functions

• Graphs of Transcendental Functions

Unit 4: Limits and Continuity

Students study:

• Limit Evaluation

• Left-Hand and Right-Hand Limits

• Standard Limits

• Continuity and its Properties

University of Hyderabad B.Sc Mathematics 1st Semester Syllabus

The University of Hyderabad covers Differential Calculus, Integral Calculus, and Differential Equations in the first semester.

Units 1 & 2: Differential Calculus

Topics include:

• Real Numbers

• Intervals

• Domain and Range of Functions

• Limits

• Continuity

• Differentiability

• Successive Differentiation

• Leibniz Theorem

• Taylor's Theorem

• Maclaurin's Theorem

• Increasing and Decreasing Functions

• Maxima and Minima

Units 3 & 4: Integral Calculus and Differential Equations

Students study:

• Indefinite Integration

• Definite Integrals

• Properties of Definite Integrals

• Variable Separable Differential Equations

• Homogeneous Differential Equations

• Exact Differential Equations

• Linear Differential Equations

• Bernoulli's Differential Equations

University of Kolkata B.Sc Mathematics 1st Semester Syllabus

The first-semester syllabus at the University of Kolkata includes Calculus and Analytical Geometry.

Units 1, 2 & 3: Calculus

Topics covered are:

• Real Numbers

• Domain and Range

• Limits

• Continuity

• Differentiability

• Higher Order Derivatives

• Leibniz Theorem

• Rolle's Theorem

• Lagrange's Mean Value Theorem

• Taylor's Theorem

• Maclaurin's Theorem

• Maxima and Minima

• Indefinite Integration

• Definite Integration

Unit 4: Analytical Geometry

Students study:

• Plane Coordinates

• Straight Lines

• Different Forms of Line Equations

• Pair of Straight Lines

• Equation of Circle

• Basic Properties of Conic Sections

Punjab University B.Sc Mathematics 1st Semester Syllabus

Punjab University includes both Algebra and Calculus in its first-semester curriculum.

Unit 1: Algebra

Topics include:

• Divisibility

• Division Algorithm

• Greatest Common Divisor (GCD)

• Euclidean Algorithm

• Relatively Prime Integers

• Polynomial Equations

• Relation Between Roots and Coefficients

Unit 2: Matrices and Linear Algebra

Students study:

• Types of Matrices

• Matrix Operations

• Determinants

• Matrix Rank

• Linear Systems

• Eigenvalues

• Eigenvectors

• Algebraic Multiplicity

• Geometric Multiplicity

Unit 3: Differential Calculus

Topics covered are:

• Real Functions

• Limits

• Continuity

• Differentiability

• Leibniz Theorem

• Mean Value Theorem

Unit 4: Applications of Derivatives

Students learn:

• Maxima and Minima

• Taylor's Series

• Maclaurin's Series

• Tangents and Normals

• Curve Tracing

Unit 5: Integral Calculus

Topics include:

• Indefinite Integration

• Definite Integration

• Reduction Formulae

• Beta Functions

• Gamma Functions

CCSU Meerut y B.Sc Mathematics 1st Semester Syllabus

The syllabus followed by CCSU Meerut includes Differential and Integral Calculus.

Part A: Differential Calculus

Students study:

• Epsilon-Delta Limits

• Continuity

• Differentiation

• Successive Differentiation

• Leibniz Rule

• Concavity

• Points of Inflexion

• Asymptotes

• Curve Tracing

• Rolle's Theorem

• Lagrange's Mean Value Theorem

• Taylor's Theorem

• Maclaurin's Series

Part B: Integral Calculus

Topics include:

• Indefinite Integrals

• Definite Integrals

• Trigonometric Reduction Formulae

• Beta Functions

• Gamma Functions

University of Allahabad B.Sc Mathematics 1st Semester Syllabus

The University of Allahabad syllabus focuses on sequences, differential calculus, and integral calculus.

Part A: Sequences, Limits and Derivatives

Topics covered include:

• Monotonic Sequences

• Cauchy Sequences

• Convergence of Sequences

• Differentiability of Functions

• Leibniz Theorem

• Mean Value Theorems

• Taylor's Series

• Maclaurin's Series

• Maclaurin's Expansion

Part B: Integrals

Students study:

• Standard Integration Formulae

• Definite Integrals

• Properties of Definite Integrals

• Beta and Gamma Relations

• Beta Functions

• Gamma Functions

Kumaun University B.Sc Mathematics 1st Semester Syllabus

Kumaun University introduces students to Real Analysis, Algebra, Calculus, and Differential Equations during the first semester.

Unit 1: Elementary Real Analysis

Topics include:

• Set Theory

• Logic

• Venn Diagrams

• Relations

• Injective Functions

• Surjective Functions

• Bijective Functions

Unit 2: Complex Numbers

Students study:

• Modulus and Argument

• Polar Form

• De Moivre's Theorem

• Complex Roots

Unit 3: Matrices and Determinants

Topics covered are:

• Matrix Operations

• Matrix Rank

• Matrix Properties

• Matrix Inverse

• System of Linear Equations

Unit 4: Differential Calculus

Students learn:

• Limits

• Continuity

• Differentiability

• Successive Differentiation

• Maxima and Minima

Unit 5: Integral Calculus

Topics include:

• Indefinite Integration

• Definite Integration

• Properties of Definite Integrals

Unit 6: Differential Equations

Students study:

• Order and Degree

• Variable Separable Equations

• Homogeneous Equations

• Linear Differential Equations

HNB Garhwal University B.Sc Mathematics 1st Semester Syllabus

The HNB Garhwal University syllabus covers Differential Calculus, Mean Value Theorems, Series Expansions, and applications of derivatives.

Unit 1: Functions and Limits

Topics include:

• Sets

• Intervals

• Neighbourhoods

• Limit of a Function

• Continuity of a Function

Unit 2: Differentiation

Students study:

• Derivative of a Function

• Differentiability

• Successive Differentiation

• Leibniz Theorem

• Basic Partial Differentiation

Unit 3: Mean Value Theorems

Topics covered are:

• Lagrange's Mean Value Theorem

• Rolle's Theorem

• Applications of Mean Value Theorems

Unit 4: Maxima and Minima

Students learn:

• Increasing and Decreasing Functions

• Maxima and Minima of Single Variable Functions

• Second Derivative Test

Unit 5: Taylor's and Maclaurin's Series

Topics include:

• Taylor's Theorem

• Maclaurin's Theorem

• Maclaurin's Expansion

• Series Expansions of Trigonometric, Hyperbolic, Logarithmic, Exponential, and Combined Functions