Comprehend trigonometric, exponential, inverse, logarithmic, and hyperbolic functions.
Apply exponential growth and decay models in finance and radioactivity.
Understand the notion of limit and limit laws.
Understand continuity of a function.
Comprehend the derivative of a function and differentiation rules.
Comprehend indefinite and definite integrals.
Apply definite integrals to find area between curves and arc length.
KU1DSCMAT111 : Basic Mathematics I
Comprehend trigonometric, exponential, inverse, logarithmic, and hyperbolic functions.
Understand limits, limit laws, and continuity of functions.
Apply differentiation, integration, and matrix operations.
Comprehend derivatives, differentiation rules, and partial derivatives.
Comprehend indefinite and definite integrals.
Evaluate rank of matrices and find solutions using Gauss–Jordan method.
Semester II - Mathematics Course Outcomes
KU2DSCMAT101 : Calculus II
Comprehend successive differentiation.
Employ derivatives to determine extreme values.
Understand mean value theorems.
Find expansions using Maclaurin’s and Taylor’s series.
Apply L’Hôpital’s rule to indeterminate forms.
Solve optimization problems in mathematics and economics.
Employ integration by successive reduction.
Comprehend functions of several variables.
Understand limits and continuity of two-variable functions.
Find partial derivatives and apply the chain rule.
KU2DSCMAT111 : Basic Mathematics II
Understand 3D coordinate systems, vectors, and planes.
Understand probability concepts and laws.
Use integration techniques for trigonometric functions.
Comprehend Fourier series.
Semester III - Mathematics Course Outcomes
KU3DSCMAT201 : Algebra
Comprehend the concept of relations and understand different types of relations.
Comprehend the concept of functions.
Understand the relation connecting the roots and coefficients of equations and the nature and position of roots, and solve equations.
Understand symmetric functions of roots of an equation and apply them to solve equations.
Comprehend logical concepts and understand quantified statements and truth sets.
KU3DSCMAT202 : Coordinate Systems and Multiple Integrals
Comprehend the concept of polar coordinates and the method of conversion between Cartesian and polar coordinate systems.
Understand the method of finding area and length of curves in polar coordinates.
Comprehend the concept of double integrals and evaluation of double integrals in Cartesian and polar coordinates.
Understand the method of finding area enclosed by curves using double integrals.
Comprehend the concept of three-dimensional coordinate systems and understand the method of evaluation of triple integrals in Cartesian coordinates.
Comprehend the concept of cylindrical and spherical coordinates and understand the evaluation of triple integrals in cylindrical and spherical coordinates.
Understand the method of parametrization of curves and comprehend concepts on cylinders and quadric surfaces.
KU3DSCMAT211 : Differential Equations, Laplace Transforms, Linear Programming and Numerical Methods
Understand methods of solving Differential Equations: Separable ODEs, Exact ODEs, Integrating Factors, and Linear ODEs.
Understand Laplace Transform, Linearity, First Shifting Theorem, Transforms of Derivatives, and Transform of Integrals.
Understand the definition of Linear Programming Problems (LPP), differentiate between canonical and standard forms, and apply graphical and simplex methods for solutions.
Apply numerical methods for solving algebraic and transcendental equations, including Bisection Method, False Position Method, Newton-Raphson Method, and numerical integration techniques such as the Trapezoidal Rule and Simpson’s 1/3 Rule.
KU3VACMAT202 : Mathematical Logic
Understand basic set operations and properties.
Analyze and construct logical arguments using propositional and predicate logic.
Translate between natural language and formal logic expressions.
Determine validity using truth tables, tautologies, and equivalences.
Semester IV - Mathematics Course Outcomes
KU4DSCMAT201 : Analytic Geometry
Understand alternative representations of plane curves.
Analyze and understand properties of conic sections.
Apply techniques to find tangents, normals, and curvature.
Understand lines and planes in space.
KU4DSCMAT202 : Number Theory and Complex Numbers
Understand division algorithm, GCD, and Diophantine equations.
Understand primes, Fundamental Theorem of Arithmetic, and Sieve of Eratosthenes.
Explain the concept of congruence.
Understand Fermat’s, Wilson’s, and Euler’s theorems.
Remember the concepts of complex numbers and their algebraic operations.
Understand roots of complex numbers.
Understand polar form, powers, and roots of complex numbers.
KU4DSCMAT203 : Ordinary Differential Equations and Laplace Transforms
Comprehend differential equations.
Classify differential equations by order and linearity.
Understand the meaning of solutions.
Understand particular solutions of Initial Value Problems (IVPs).
Comprehend the Existence-Uniqueness Theorem.
Apply appropriate solution methods.
Understand Laplace transforms.
Apply Laplace transforms to solve IVPs.
KU4VACMAT204 : Mathematics in Real Life through GeoGebra
Use GeoGebra tools to construct and analyze geometric figures.
Explore functions and graphs dynamically.
Apply calculus tools in GeoGebra to model and solve problems.
Visualize and build 3D mathematical models and real-life applications.
Semester V - Mathematics Course Outcomes
KU5DSCMAT301 : Real Analysis I
Understand finite and infinite sets, countable and uncountable sets, and Cantor’s theorem.
Understand algebraic properties, order properties and absolute values of ℝ. Understand the completeness property of ℝ and its applications to derive the Archimedean Property and Density Theorem.
Understand sequences and their limits and limit theorems.
Understand subsequences, the Bolzano-Weierstrass Theorem and the Cauchy Criterion.
Understand infinite series, absolute convergence and non-absolute convergence.
KU5DSCMAT302 : Basic Abstract Algebra
Comprehend binary operations and groups.
Classify abelian groups and non-abelian groups.
Understand permutation groups.
Determine subgroups of groups, cyclic subgroups and cyclic groups.
Comprehend generating sets, groups of permutations and cosets.
Understand factor groups, rings, fields and integral domains.
KU5DSCMAT303 : Matrices, Fourier Series and Partial Differential Equations
Comprehend basic matrix operations and rank of a matrix.
Apply Gauss-Jordan elimination, matrix inversion and the Cayley-Hamilton theorem to solve systems of linear equations efficiently.
Comprehend eigenvalues and eigenvectors of matrices.
Understand and construct Fourier series for periodic functions, including arbitrary periods and half-range expansions.
Understand and solve basic PDEs by separation of variables and Fourier series, including solutions of wave and heat equations.
KU5DSEMAT301 : Numerical Analysis
Understand solutions of transcendental equations.
Understand Bisection and Regula-Falsi methods.
Understand Lagrange interpolation, finite difference operators and finite differences, and Newton’s interpolation formulae.
Understand Trapezoidal Rule and Simpson’s Rule.
Understand Taylor Series Method, Euler Method and Runge-Kutta Methods (Second Order).
KU5DSEMAT303 : Programming in Python
Apply core Python syntax and semantics.
Use data types and variables effectively.
Use conditional statements to control the flow of programs.
Develop and use functions and modules.
KU5SECMAT301 : LaTeX
Understand the basics of LaTeX.
Learn document formatting in LaTeX through various examples.
Learn creating tables and figures in LaTeX through various examples.
Understand the use of Math Mode in LaTeX through various examples.
Learn the content through practical examples to create LaTeX documents.
Semester VI - Mathematics Course Outcomes
KU6DSCMAT301 : Vector Calculus
Understand curves in space, their tangents, normals and arc length in space.
Understand directional derivatives and gradient vectors, tangent planes and differentials.
Understand line integrals and solve for work, circulation and flux using line integrals.
Understand path independence, conservative fields and potential functions.
Understand Green’s Theorem and solve problems using Green’s Theorem.
Understand surface area and surface integrals.
Understand Stoke’s Theorem and Divergence Theorem and solve problems using them.
KU6DSCMAT302 : Real Analysis II
Understand the characterization of intervals.
Understand continuous functions, composition of continuous functions and continuous functions on intervals.
Understand uniform continuity, monotone functions and inverse functions.
Understand Riemann integrals and Riemann-integrable functions.
Understand the Fundamental Theorem of Calculus.
Understand improper integrals.
Understand Beta and Gamma functions and their properties.
KU6DSCMAT303 : Complex Analysis
Comprehend analytic functions, Cauchy-Riemann equations and Laplace’s equation.
Understand exponential, trigonometric, hyperbolic and logarithmic functions, and general powers of complex numbers.
Evaluate line integrals in the complex plane, Cauchy’s Integral Theorem, Cauchy’s Integral Formula and derivatives of analytic functions.
Understand convergence of sequences and series of complex functions.
Understand power series, functions given by power series, Taylor series, Maclaurin series and Laurent series.
Understand singularities and zeros of complex functions.
Understand the residue integration method and evaluate real integrals.
KU6DSEMAT301 : Graph Theory
Understand graphs, subgraphs, different types of graphs and their properties.
Understand and represent graphs as matrices.
Understand paths, cycles, trees, bridges and their properties.
Understand cut vertices and connectivity of graphs.
Understand Eulerian graphs, Hamiltonian graphs, the Chinese Postman Problem and the Travelling Salesman Problem.
Model real-world problems using the concept of graphs.
Solve real-world problems using graph-theoretic concepts.
KU6DSEMAT302 : Operations Research
Understand convex sets, convex functions and their properties.
Formulate and solve Linear Programming Problems (LPP) using graphical methods and the simplex algorithm.
Formulate transportation problems mathematically and obtain solutions.
Understand assignment problems and apply the Hungarian Assignment Method.
Apply sequencing techniques for processing n jobs through 2 machines, n jobs through k machines and 2 jobs through k machines.
KU6SECMAT301 : Scilab
Understand the SciLab interface, environment and basic syntax.
Apply SciLab commands for basic arithmetic and logical operations.
Plot 2D and 3D graphs and visualize mathematical functions using SciLab.
Solve algebraic and matrix problems using SciLab functions.
Practice mathematical modeling and simple simulations through SciLab scripting.
Semester VII - Mathematics Course Outcomes
KU7DSCMAT401 : Advanced Abstract Algebra
Use the concepts of finitely generated abelian groups, homomorphisms, normal subgroups and inner automorphisms to solve problems.
Comprehend the field of quotients of an integral domain.
Apply factor-group computations and simple groups to solve problems.
Understand group action on a set, isomorphism theorems, Sylow theorems, homomorphisms and factor rings.
Apply the concepts of prime and maximal ideals to solve problems.
KU7DSCMAT402 : Mathematical Analysis
Understand the basic facts and concepts of Real Analysis, including properties of the real number system, limits, continuity, differentiability and Riemann integration.
Construct correct mathematical proofs using the properties of the real number system and other analytical concepts.
Solve problems using the fundamental concepts of Real Analysis.
Explain how the rigorous mathematical structure of Real Analysis underlies Calculus.
KU7DSCMAT403 : Basic Topology
Demonstrate an understanding of metric spaces.
Understand the structure of topological spaces using continuous functions and homeomorphisms.
Understand different topologies such as product topology and metric topology.
Develop the concepts of topological properties.
Develop the concepts of metrizable spaces.
KU7DSCMAT404 : Linear Algebra
Understand the generalization of vectors from concrete geometric objects to abstract vector spaces.
Understand the notions of linear dependence and linear independence.
Understand the concept of basis in vector spaces.
Understand matrix representations of linear transformations and their applications.