BSc Maths 2nd Year Syllabus, Subjects, Electives, Skill Enhancement, Colleges, Books

BSc 2nd Year Maths Syllabus

B.Sc 2nd Year Maths consists of two semesters, the third and fourth semesters. Each semester is four to six months. The syllabus for both semesters is listed below.

BSc 2nd Year Maths Subjects

Top BSc Maths subjects in 2nd year are explained below:

BSc 2nd Year Maths Subjects: Mechanics II

• Dynamics: The topics covered in this chapter are the Motion of a particle in two dimensions, Velocities and accelerations in Cartesian, polar, and intrinsic coordinates, the Motion of a particle in a plane under different laws of resistance, Central forces, Kepler's laws, Tangential and normal accelerations, etc.

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BSc 2nd Year Maths Subjects: Differential Equations II

• Ordinary Differential Equations: The topics covered in this chapter are Series solutions of differential equations, Bessel, Legendre, and Hypergeometric functions and their properties, Orthogonality of functions, Sturra-Liouville problem, Reality of eigenvalues, Orthogonality of Bessel functions and Legendre polynomials.
• Laplace transforms: The topics covered in this chapter are Introduction to infinite integrals, Linearity of Laplace transforms, Existence theorem for Laplace transforms, Laplace transforms of derivatives and integrals, Shifting theorems, Differentiation, and integration of transforms, Convolution theorem, etc.

BSc 2nd Year Maths Subjects: Analysis I 

• Countability of Z and Q: The topics covered are Order properties of Q and its order incompleteness, Construction of R from Q using Dedekind cuts, Order completeness of R, Uncountability of R Bounds, bounded sets, and Bolzano-Weierstrass theorem.
• Sequences: The topics covered are Bounded sequences, monotone sequences and their convergence, subsequences, and Cauchy sequences, and their convergence criterion.
• Limits and Continuity: The topics covered are Basic properties of continuous functions, Uniform continuity, Bounded functions, Continuous functions defined on a compact set, attainment of bounds, Intermediate Value Theorem, Discontinuities, Infinite series and their convergence, Geometric series, etc.

BSc 2nd Year Maths Subjects: Vector Analysis

• Vector Algebra: The topics covered in this chapter are Operations with vectors, Scalar, and vector products of three vectors, Product of four vectors, and Reciprocal vectors.
• Vector Calculus: The topics covered in this chapter are Scalar-valued functions over the plane and the space, Vector function of a scalar variable, Curves and Paths, Vector fields, Vector differentiation, Directional derivatives, the tangent plane, total differential, gradient, divergence, and curl, Vector integration, etc.

See Also:

BSc 2nd Year Maths Subjects: Differential Equations III

• Partial differential equations: The topics covered are the formation of partial differential equations, PDEs of the first order, Lagrange's solution, Charpit's and Jacobi's general method of solution, Partial differential equations of second and higher order, Homogeneous and non-homogeneous equations with constant coefficients, Partial differential equations reducible to equations with constant coefficients, and Monge's methods.
• Calculus of variations: The topics covered are Euler's equation for functionals containing first-order derivative and one independent variable, Extremals, Functionals dependent on higher order derivatives, Functionals dependent on more than one independent variable, Variational problems in parametric form, etc.

BSc 2nd Year Maths Subjects: Analysis II

• Differentiation: The topics covered in this chapter are Derivatives, Rolle's theorem, Darboux's theorem on the intermediate value property of derivatives, Mean Value Theorem, Taylor's theorem, and Indeterminate forms.
• Integration: The topics covered are Riemann Integral and its properties, the integrability of continuous and monotonic functions, Functions of bounded variation, their relation with monotonic functions, integrability, the fundamental theorem of calculus, etc.

See Also:

BSc 2nd Year Maths Subjects: Theory of Real Functions

Limit & Continuity of functions: The topics covered in this chapter are Limits of functions, the sequential criterion for limits, Algebra of limits for functions, the effect of limits on inequality involving functions, Infinite limits and limits at infinity, Continuity of a function on an interval and at an isolated point, Bounded functions, etc.

Differentiability of functions: The topics covered are differentiability of a function at a point and in an interval, the Darboux theorem, the Statement of L’ Hospital’s rule and its consequences, the application of Taylor’s theorem to inequalities, etc.

BSc 2nd Year Maths Subjects: Ring Theory

• Ring Theory: This chapter covers the following topics, definitions, and examples of rings, properties of rings, subrings, integral domains and fields, subfield, necessary and sufficient conditions for a nonempty subset of a ring to be a subring, First isomorphism theorem, second isomorphism theorem, third isomorphism theorem, etc.

See Also:

BSc 2nd Year Maths Subjects: Linear Algebra

• Vector Spaces: The topics covered are subspaces, algebra of subspaces, quotient spaces, the linear combination of vectors, linear span, linear independence, basis and dimension, and the dimension of subspaces. 
• Linear Transformations: The topics covered are null space, range, rank and nullity of a linear transformation, matrix representation of a linear transformation, algebra of linear transformations, etc.
• Isomorphisms: The topics covered are Isomorphism theorems, invertibility and isomorphisms, and change of coordinate matrix.

Elective Courses in BSc 2nd Year Maths Syllabus

The list of elective courses in BSc 2nd Year Maths is listed below.

• Logic and Sets
• Analytical Geometry
• Integral Calculus
• Vector Calculus
• Theory of Equations
• Number Theory

Books in BSc 2nd Year Maths Syllabus

Skill Enhancement Courses in 2nd Year

The list of Skill Enhancement courses in the 2nd year of B.Sc. Mathematics is listed below.

• C Programming Language
• Mathematical Logic
• Object Oriented Programming in C++
• Scientific computing with SageMath & R