BSc Maths 1st Year Syllabus, Subjects, Elective, Semester, Colleges

BSc 1st Year Maths Syllabus

The first year of B.Sc Mathematics is divided into two semesters - the first and second semesters. Each semester is four to six months. The syllabus of BSc 1st year Maths is listed below.

BSc 1st Year Maths Subjects

In BSc 1st Year Mathematics, there are six subjects. These subjects are Calculus, Geometry, Algebra I, Vector Analysis, Mechanics I, Differential Equations I, and Algebra II.

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BSc 1st Year Maths Subjects: Calculus 

• Differential and Integral Calculus: The topics covered in this chapter are real line and its geometrical representation, e-S treatment of limit and continuity, Properties of limit and classification of discontinuities, Properties of continuous functions, Successive differentiation and Leibnitz Theorem, Statement of Rolle's Theorem, Mean Value Theorem, Taylor and Maclaurin's Theorems, Definite integrals, and Statement of the Fundamental Theorem.
• Applications: The topic covered are Asymptotes, Concavity, convexity, Plane curves, tangent and normal in parametric form, and points of inflection.
• Quadrature: The topics covered are Rectifiability and length of a curve, Arc length as a parameter, Curvature, and Volumes and surface areas of solids of revolution.

BSc 1st Year Maths Subjects: Geometry

• Analytical geometry of two dimensions: The topics covered in this chapter are Transformation of rectangular axes, General equation of the second degree and its reduction to normal form, Systems of conics, and Polar equation of a conic. 
• Analytical geometry of three dimensions: The topics covered in this chapter are Direction cosines, Straight lines, Plane, Sphere, Cone, Cylinder, Central conicoids, paraboloids, plane sections of conicoids, Generating lines, Reduction of second-degree equations to normal form, and classification of quadrics.

See Also:

BSc 1st Year Maths Subjects: Algebra I

• Matrix Theory and Linear Algebra in R": The topics covered in this chapter are Systems of linear equations, Gauss elimination, and consistency, Subspaces of R", linear dependence, and dimension, Matrices, elementary row operations, row-equivalence, and row space, Row-reduced matrices, row-reduced echelon matrices, row-rank, and using these as tests for linear dependence, etc.
• Theory of Equations: The topics covered in this chapter are Polynomials in one variable and the division algorithm, Relation s between the roots and the coefficients, Transformation of equations, Descartes's rule of signs, and Solution of cubic and biquadratic (quartic) equations.

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BSc 1st Year Maths Subjects: Vector Analysis

• Vector Algebra: This chapter covers Operations with vectors, Scalar and vector product of three vectors, Reciprocal vectors, and Product of four vectors.
• Vector Calculus: This chapter covers Scalar-valued functions over the plane and the space, Vector differentiation, Directional derivatives, Vector integration, etc.

See Also:

BSc 1st Year Maths Subjects: Mechanics I

• Statics: The topics covered are Forces, Couples, Co-planar forces, Astatic equilibrium, Friction, Equilibrium of a particle on a rough curve, Virtual work, Catenary, Forces in three dimensions, Reduction of a system of forces in space, Invariance of the system, General conditions of equilibrium, Stable and unstable equilibrium, and Centre of gravity for different bodies. 

BSc 1st Year Maths Subjects: Differential Equations I 

• Elementary Methods in Ordinary Differential Equations: The topics covered are the First order exact equations and integrating factors, Degree, and order of a differential equation, Equations of the first order and first degree, Homogeneous equations, Linear equations, and equations reducible to linear form, Linear differential equations of second order, Method of variation of parameters, etc.

BSc 1st Year Maths Subjects: Algebra II

• Modern Algebra: The topics covered in this chapter are Commutative rings, integral domains, and their elementary properties, Ordered integral domain, Finite induction, Divisibility, the division algorithm, primes, GCDs, and the Euclidean algorithm, Sets, relations, and mappings, Bijective, injective, and surjective maps, Direct and inverse images and their properties, etc.
• Trigonometry: The topics covered in this chapter are De-Moivre's theorem and applications, Direct and inverse, circular and hyperbolic functions, Logarithm of a complex quantity, and Expansion of trigonometric functions.

Elective Courses in BSc 1st Year Maths Syllabus

The list of electives in BSc 1st year Maths are listed below.

• Analytical Geometry
• Vector Calculus
• Theory of Equations

Books in BSc 1st Year Maths Syllabus