MA3271 — Numerical Methods
Anna University R-2021 elective / lateral-entry paper covering numerical solutions of algebraic, transcendental and differential equations and interpolation.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Solve algebraic and transcendental equations using bisection, fixed-point iteration, Newton-Raphson, and secant methods, and compute eigenvalues using the power method [Apply]
- Solve systems of linear equations using Gauss elimination, Gauss-Jordan, Gauss-Seidel, and matrix inversion methods [Apply]
- Construct interpolating polynomials using Newton's divided difference, Newton's forward/backward, Lagrange, and cubic spline methods [Apply]
- Evaluate numerical derivatives and definite integrals using trapezoidal rule, Simpson's 1/3 and 3/8 rules, Romberg integration, and Gaussian quadrature [Evaluate]
- Apply single-step (Taylor, Euler, modified Euler, Runge-Kutta) and multi-step (Adams-Bashforth, Milne) methods to solve initial-value problems for ODEs [Apply]
- Solve boundary-value problems and elliptic, parabolic, and hyperbolic partial differential equations using finite-difference methods [Apply]
📚 Chapters
- Unit I — Solution of Equations and Eigenvalue Problems
- Unit II — Interpolation and Approximation
- Unit III — Numerical Differentiation and Integration
- Unit IV — Initial Value Problems for Ordinary Differential Equations
- Unit V — Boundary Value Problems in Ordinary and Partial Differential Equations
TutorDA LMS
MA8402 — Probability and Queueing Theory
Anna University paper for CSE covering probability, random variables, random processes, queueing models and advanced queueing/non-Markovian queues.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply axioms of probability, Bayes' theorem, and properties of standard discrete and continuous distributions to solve probability problems [Apply]
- Analyze two-dimensional random variables using joint, marginal, and conditional distributions, covariance, correlation, and regression [Analyze]
- Classify random processes as stationary, ergodic, Markovian, or Poisson and compute autocorrelation and power spectral density functions [Analyze]
- Apply Markovian queueing models (M/M/1, M/M/c, finite-capacity, finite-source) to determine performance measures such as average queue length, waiting time, and utilization [Apply]
- Evaluate advanced queueing models including M/G/1 (Pollaczek-Khinchine formula), open and closed Jackson networks, and series queues for system-performance analysis [Evaluate]
- Formulate computer-system and network problems as appropriate queueing models and interpret the results for design decisions [Create]
📚 Chapters
- Unit I — Probability and Random Variables
- Unit II — Two-Dimensional Random Variables
- Unit III — Random Processes
- Unit IV — Queueing Models
- Unit V — Advanced Queueing Models
TutorDA LMS
MA3303 — Probability and Complex Functions
Anna University R-2021 third-semester paper for ECE covering probability, random variables, analytic and complex-variable functions, and complex integration.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply axioms of probability, Bayes' theorem, and properties of moment-generating functions to discrete and continuous random variables and standard distributions [Apply]
- Analyze joint distributions of two-dimensional random variables using marginal/conditional densities, correlation, regression, and the central limit theorem [Analyze]
- Verify analyticity of complex functions using Cauchy-Riemann equations and construct harmonic conjugates and conformal mappings (bilinear and elementary transformations) [Apply]
- Evaluate complex integrals using Cauchy's integral theorem and formula, and apply Taylor and Laurent series and residue theorem to evaluate real integrals [Evaluate]
- Compute Laplace transforms and inverse Laplace transforms using shifting theorems, convolution, and partial fractions [Apply]
- Solve linear ordinary differential equations and integral equations relevant to ECE systems using Laplace transform techniques [Apply]
📚 Chapters
- Unit I — Probability and Random Variables
- Unit II — Two-Dimensional Random Variables
- Unit III — Analytic Functions
- Unit IV — Complex Integration
- Unit V — Laplace Transforms
TutorDA LMS
MA3391 — Probability and Statistics
Anna University R-2021 third-semester paper for CSE/IT covering probability, random variables, two-dimensional distributions, testing of hypotheses and design of experiments.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply axioms of probability, conditional probability, and Bayes' theorem to solve problems involving discrete and continuous random variables [Apply]
- Compute moments, moment-generating functions, and parameters of standard distributions such as Binomial, Poisson, Geometric, Uniform, Exponential, Normal, and Gamma [Apply]
- Analyze joint, marginal, and conditional distributions of two-dimensional random variables and compute correlation, regression, and covariance [Analyze]
- Apply large-sample (z) and small-sample (t, F, chi-square) tests for testing means, variances, proportions, and goodness-of-fit [Apply]
- Analyze experimental data using completely randomized, randomized block, and Latin square designs through ANOVA techniques [Analyze]
- Construct and interpret control charts (X-bar, R, p, c) for variables and attributes in statistical quality control [Evaluate]
📚 Chapters
- Unit I — Probability and Random Variables
- Unit II — Two-Dimensional Random Variables
- Unit III — Testing of Hypothesis
- Unit IV — Design of Experiments
- Unit V — Statistical Quality Control
TutorDA LMS
MA3354 — Discrete Mathematics
Anna University R-2021 third-semester paper for CSE/IT covering logic, combinatorics, graph theory and algebraic structures.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Construct truth tables, evaluate propositional and predicate logic statements, and prove arguments using rules of inference and quantifier reasoning [Apply]
- Apply mathematical induction, the pigeonhole principle, recurrence relations, and generating functions to solve counting and combinatorial problems [Apply]
- Analyze graph properties such as connectivity, Eulerian and Hamiltonian paths, isomorphism, and matrix representations of graphs [Analyze]
- Examine algebraic structures including semigroups, monoids, groups, subgroups, homomorphisms, cosets, and Lagrange's theorem [Analyze]
- Derive properties of partially ordered sets, lattices, and Boolean algebras and apply Boolean simplification to logic-circuit problems [Evaluate]
- Formulate solutions to discrete computational problems using appropriate logic, combinatorial, or graph-theoretic models [Create]
📚 Chapters
- Unit I — Logic and Proofs
- Unit II — Combinatorics
- Unit III — Graphs
- Unit IV — Algebraic Structures
- Unit V — Lattices and Boolean Algebra
TutorDA LMS
MA3351 — Transforms and Partial Differential Equations
Anna University R-2021 third-semester common paper covering PDEs and integral transforms applied to engineering boundary-value problems.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Formulate first-order partial differential equations by elimination of arbitrary constants/functions and solve linear and non-linear PDEs using Lagrange's and Charpit's methods [Apply]
- Expand periodic functions as Fourier series including half-range sine and cosine series and apply Parseval's identity and harmonic analysis [Apply]
- Solve one-dimensional wave, heat, and two-dimensional steady-state heat equations using the method of separation of variables for engineering boundary-value problems [Apply]
- Compute Fourier transforms, Fourier sine/cosine transforms, and apply convolution and Parseval's theorem to evaluate integrals and solve transform-domain problems [Apply]
- Determine Z-transforms and inverse Z-transforms and use them to solve linear difference equations arising in discrete-time engineering systems [Apply]
- Analyze engineering boundary-value problems by selecting appropriate transform or PDE technique and interpreting the solution physically [Analyze]
📚 Chapters
- Unit I — Partial Differential Equations
- Unit II — Fourier Series
- Unit III — Applications of Partial Differential Equations
- Unit IV — Fourier Transforms
- Unit V — Z-Transforms and Difference Equations
TutorDA LMS
MA3251 — Statistics and Numerical Methods
Anna University R-2021 second-semester paper for Mechanical, Civil and EEE branches covering testing of hypotheses, design of experiments and numerical methods.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Apply large-sample and small-sample tests (z, t, F, chi-square) to test hypotheses about population means, variances, and proportions in engineering data [Apply]
- Analyze experimental data using completely randomized, randomized block, and Latin square designs through one-way and two-way ANOVA [Analyze]
- Solve algebraic and transcendental equations and systems of linear equations using Newton-Raphson, Gauss elimination, Gauss-Seidel, and power methods [Apply]
- Construct interpolating polynomials using Newton's forward/backward and Lagrange formulas, and evaluate numerical derivatives and integrals using trapezoidal and Simpson's rules [Apply]
- Solve initial-value problems for ordinary differential equations using Taylor, Euler, modified Euler, Runge-Kutta, and predictor-corrector methods [Apply]
- Evaluate the suitability and accuracy of numerical and statistical methods for solving real-world engineering problems [Evaluate]
📚 Chapters
- Unit I — Testing of Hypothesis
- Unit II — Design of Experiments
- Unit III — Solution of Equations and Eigenvalue Problems
- Unit IV — Interpolation, Numerical Differentiation and Numerical Integration
- Unit V — Numerical Solution of Ordinary Differential Equations
TutorDA LMS
MA3151 — Matrices and Calculus
Anna University R-2021 first-semester core mathematics paper covering matrices, differential and integral calculus for all B.E./B.Tech branches.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Compute eigenvalues and eigenvectors of real matrices and apply Cayley-Hamilton theorem to diagonalization and quadratic-form reduction [Apply]
- Analyze functions of one variable using limits, continuity, mean-value theorems, and Taylor/Maclaurin series expansions [Analyze]
- Solve problems involving partial derivatives, total differentials, Jacobians, Taylor's series for two variables, and constrained maxima/minima using Lagrange multipliers [Apply]
- Evaluate definite and improper integrals using reduction formulae, Beta and Gamma functions, and standard integration techniques [Evaluate]
- Compute double and triple integrals in Cartesian and polar coordinates and apply them to area, volume, and change-of-variable problems [Apply]
- Formulate and solve engineering problems by selecting appropriate calculus and matrix techniques [Create]
📚 Chapters
- Unit I — Matrices
- Unit II — Differential Calculus
- Unit III — Functions of Several Variables
- Unit IV — Integral Calculus
- Unit V — Multiple Integrals
TutorDA LMS