Numerical Analysis (B.Sc. Mathematics)
Numerical methods for algebraic and transcendental equations, interpolation, integration and ODEs.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply bisection, Regula Falsi, Newton-Raphson and iteration methods to solve algebraic and transcendental equations [Apply]
- Solve simultaneous linear equations using Gauss elimination, Gauss-Jordan and Gauss-Seidel iterative schemes [Apply]
- Construct interpolating polynomials using Newton's forward, backward and divided difference formulae [Create]
- Estimate definite integrals using the trapezoidal rule, Simpson's 1/3 and 3/8 rules and analyse their errors [Evaluate]
- Apply Euler, modified Euler and Runge-Kutta methods to solve initial value problems for ODEs [Apply]
- Compare the accuracy and efficiency of competing numerical methods on representative problems [Evaluate]
📚 Chapters
- Unit I — Solution of algebraic and transcendental equations
- Unit II — Solution of simultaneous linear equations and matrix inversion
- Unit III — Finite differences and interpolation formulae
- Unit IV — Numerical differentiation and integration
- Unit V — Numerical solution of ordinary differential equations
TutorDA LMS
Discrete Mathematics (B.Sc. Mathematics)
Logic, set theory, combinatorics, recurrence relations, lattices and Boolean algebra.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply rules of propositional and predicate logic to construct formal proofs and check validity of arguments [Apply]
- Analyze relations on a set for properties such as reflexivity, symmetry, transitivity and equivalence [Analyze]
- Solve counting problems using permutations, combinations and the pigeonhole principle [Apply]
- Solve linear recurrence relations using characteristic roots and generating functions [Apply]
- Analyze partially ordered sets and lattices, and identify distributive and complemented lattices [Analyze]
- Simplify Boolean expressions using Karnaugh maps and apply them to logic circuit design [Apply]
📚 Chapters
- Unit I — Mathematical logic, propositions and predicate calculus
- Unit II — Set theory, relations and functions
- Unit III — Combinatorics, permutations, combinations and pigeonhole principle
- Unit IV — Recurrence relations and generating functions
- Unit V — Lattices and Boolean algebra
TutorDA LMS
Operations Research (B.Sc. Mathematics)
Linear programming, transportation, assignment, network analysis and game theory.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Formulate real-world decision problems as linear programming models with appropriate variables and constraints [Apply]
- Solve linear programming problems using the graphical method, simplex method, Big-M and two-phase methods [Apply]
- Analyze duality relationships and interpret shadow prices for managerial decision-making [Analyze]
- Solve transportation and assignment problems using the MODI method and the Hungarian algorithm [Apply]
- Construct project networks and compute critical paths and floats using CPM and PERT [Create]
- Evaluate two-person zero-sum games using saddle points, dominance and the graphical method [Evaluate]
📚 Chapters
- Unit I — Linear programming formulation and graphical method
- Unit II — Simplex method, Big-M and two-phase methods
- Unit III — Duality, transportation and assignment problems
- Unit IV — Network analysis, CPM and PERT
- Unit V — Game theory and sequencing problems
TutorDA LMS
Graph Theory (B.Sc. Mathematics)
Graphs, trees, connectivity, Eulerian and Hamiltonian graphs, planarity and graph colouring.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Define basic graph-theoretic concepts including subgraphs, degree sequences and graph isomorphism [Remember]
- Apply Kruskal's and Prim's algorithms to construct minimum spanning trees of weighted graphs [Apply]
- Analyze connectivity properties such as cut vertices, bridges and blocks of a graph [Analyze]
- Determine whether a given graph is Eulerian or Hamiltonian using standard characterisations [Evaluate]
- Apply Euler's formula and Kuratowski's theorem to test planarity of graphs [Apply]
- Compute chromatic numbers and chromatic polynomials for small graphs and apply them to colouring problems [Apply]
📚 Chapters
- Unit I — Graphs, subgraphs, degree sequences and isomorphism
- Unit II — Trees, spanning trees and minimum spanning tree algorithms
- Unit III — Connectivity, cut vertices, bridges and blocks
- Unit IV — Eulerian and Hamiltonian graphs
- Unit V — Planar graphs, graph colouring and chromatic polynomials
TutorDA LMS
Mechanics (B.Sc. Mathematics)
Statics and dynamics covering forces, equilibrium, projectiles, central forces and rigid body motion.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Analyze the equilibrium of coplanar forces acting at a point using Lami's theorem and the polygon law [Analyze]
- Apply the laws of friction and the principle of virtual work to determine equilibrium configurations [Apply]
- Compute trajectories of projectiles and motion under variable acceleration in resisting media [Apply]
- Evaluate problems on impact and collision of elastic bodies using the coefficient of restitution [Evaluate]
- Derive equations of motion for central orbits and apply Kepler's laws to planetary motion [Create]
- Examine the motion of a rigid body about a fixed axis using moments of inertia and angular momentum [Analyze]
📚 Chapters
- Unit I — Forces acting at a point and equilibrium of coplanar forces
- Unit II — Friction, centre of gravity and virtual work
- Unit III — Projectiles and motion under variable acceleration
- Unit IV — Impact, collision of elastic bodies and simple harmonic motion
- Unit V — Central orbits and motion of a rigid body
TutorDA LMS
Differential Equations (B.Sc. Mathematics)
Ordinary and partial differential equations with applications, including Laplace transform techniques.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Solve first-order ODEs including separable, homogeneous, linear and exact equations using integrating factors [Apply]
- Determine general and particular solutions of higher-order linear ODEs with constant and variable coefficients [Apply]
- Analyze simultaneous linear differential equations and total differential equations of three variables [Analyze]
- Formulate and solve partial differential equations of first and second order using Lagrange and Charpit methods [Apply]
- Apply Laplace transforms and inverse transforms to solve initial value problems for linear ODEs [Apply]
- Model simple physical phenomena such as growth, decay and oscillations as differential equations [Create]
📚 Chapters
- Unit I — First order ODEs and exact equations
- Unit II — Higher order linear ODEs with constant and variable coefficients
- Unit III — Simultaneous linear equations and total differential equations
- Unit IV — Partial differential equations of first and second order
- Unit V — Laplace transforms and applications to ODEs
TutorDA LMS
Linear Algebra (B.Sc. Mathematics)
Vector spaces, linear transformations, inner product spaces, eigenvalues and canonical forms.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Identify vector spaces and subspaces and determine basis and dimension over a given field [Understand]
- Represent linear transformations by matrices with respect to chosen bases and compute change-of-basis matrices [Apply]
- Apply the Gram-Schmidt orthogonalisation process to construct orthonormal bases in inner product spaces [Apply]
- Diagonalise matrices when possible and analyse obstructions to diagonalisation through minimal polynomials [Analyze]
- Reduce quadratic forms to canonical form and classify them by signature using Sylvester's law [Evaluate]
- Construct examples and counterexamples illustrating linear independence, rank and nullity relationships [Create]
📚 Chapters
- Unit I — Vector spaces, subspaces, basis and dimension
- Unit II — Linear transformations and their matrix representations
- Unit III — Inner product spaces and Gram-Schmidt orthogonalisation
- Unit IV — Eigenvalues, eigenvectors and diagonalisation
- Unit V — Quadratic forms and canonical forms
TutorDA LMS
Complex Analysis (B.Sc. Mathematics)
Analytic functions, complex integration, power series, residues and conformal mappings.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Verify analyticity of complex functions using the Cauchy-Riemann equations in Cartesian and polar form [Apply]
- Analyze elementary functions and bilinear transformations as conformal mappings of the complex plane [Analyze]
- Apply Cauchy's integral theorem and integral formula to evaluate contour integrals [Apply]
- Expand analytic functions into Taylor and Laurent series and classify isolated singularities [Analyze]
- Evaluate definite real integrals using the residue theorem and contour integration techniques [Evaluate]
- Distinguish between removable singularities, poles and essential singularities through worked examples [Understand]
📚 Chapters
- Unit I — Analytic functions and Cauchy-Riemann equations
- Unit II — Elementary functions and bilinear transformations
- Unit III — Complex integration and Cauchy's integral theorem
- Unit IV — Taylor and Laurent series expansions
- Unit V — Residues, contour integration and evaluation of real integrals
TutorDA LMS
Real Analysis (B.Sc. Mathematics)
Rigorous treatment of the real number system, sequences, series, continuity, differentiation and Riemann integration.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Analyze the convergence and divergence of sequences and series of real numbers using standard tests [Analyze]
- Apply the completeness property of R to prove fundamental results such as Bolzano-Weierstrass and the monotone convergence theorem [Apply]
- Determine the Riemann integrability of bounded functions on closed intervals using upper and lower sums [Evaluate]
- Prove standard theorems on continuity, uniform continuity and differentiability of real-valued functions [Create]
- Construct counterexamples that distinguish pointwise from uniform behaviour of functions [Create]
- Apply mean value theorems and Taylor's theorem to solve problems in single-variable calculus [Apply]
📚 Chapters
- Unit I — Real number system, supremum, infimum and completeness
- Unit II — Sequences of real numbers and their convergence
- Unit III — Infinite series and tests of convergence
- Unit IV — Limits, continuity and uniform continuity
- Unit V — Differentiation and Riemann integration
TutorDA LMS
Algebra (B.Sc. Mathematics)
Classical algebra covering theory of equations, matrices, groups, rings and fields for B.Sc. Mathematics students.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Recall the standard relations between roots and coefficients of polynomial equations and the structure of reciprocal equations [Remember]
- Apply elementary row operations to determine the rank of a matrix and solve systems of linear equations [Apply]
- Compute eigenvalues and eigenvectors and verify the Cayley-Hamilton theorem for square matrices [Apply]
- Analyze groups, subgroups and cyclic groups using Lagrange's theorem and coset decomposition [Analyze]
- Distinguish between rings, integral domains and fields through illustrative examples and counterexamples [Analyze]
- Construct proofs of basic structural results in group and ring theory at the undergraduate level [Create]
📚 Chapters
- Unit I — Theory of equations and reciprocal equations
- Unit II — Matrices, rank and system of linear equations
- Unit III — Eigenvalues, eigenvectors and Cayley-Hamilton theorem
- Unit IV — Groups, subgroups, cyclic groups and Lagrange's theorem
- Unit V — Rings, integral domains and fields
TutorDA LMS