Allied Mathematics for B.Sc. Computer Science
Mathematical foundations for B.Sc. Computer Science covering matrices, calculus, discrete structures and numerical methods.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Determine the rank of a matrix and solve linear systems relevant to graphics and data processing [Apply]
- Apply differential and integral calculus to analyse algorithms involving rates of change and accumulated cost [Apply]
- Apply propositional logic, set theory and Boolean algebra to formalise computational reasoning [Apply]
- Solve recurrence relations arising in algorithm analysis using iteration and characteristic equations [Apply]
- Analyze elementary graph-theoretic structures such as trees, paths and connectivity for use in data structures [Analyze]
- Apply numerical methods for root finding, interpolation and integration in computational settings [Apply]
📚 Chapters
- Unit I — Matrices, rank and solution of linear systems
- Unit II — Differential and integral calculus with applications
- Unit III — Mathematical logic, set theory and Boolean algebra
- Unit IV — Combinatorics, recurrence relations and graph theory basics
- Unit V — Numerical methods for equations, interpolation and integration
TutorDA LMS
Allied Mathematics for B.Sc. Chemistry
Mathematical methods for B.Sc. Chemistry including algebra, calculus, differential equations and elementary statistics.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Solve polynomial equations and evaluate determinants of matrices arising in stoichiometry and equilibrium problems [Apply]
- Apply partial differentiation to study rates of change in multivariable chemical relations such as state equations [Apply]
- Evaluate integrals using standard reduction formulae and apply them to area and volume calculations [Evaluate]
- Solve first and second order linear ODEs that arise in chemical kinetics and reaction modelling [Apply]
- Apply Laplace transforms to solve initial value problems describing time-dependent chemical processes [Apply]
- Compute measures of central tendency and dispersion to summarise experimental chemistry data [Apply]
📚 Chapters
- Unit I — Theory of equations, matrices and determinants
- Unit II — Differential calculus and partial differentiation
- Unit III — Integral calculus and reduction formulae
- Unit IV — Ordinary differential equations and Laplace transforms
- Unit V — Probability, measures of central tendency and dispersion
TutorDA LMS
Allied Mathematics for B.Sc. Physics
Mathematical methods supporting B.Sc. Physics including matrices, calculus, ODEs and vector calculus.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Compute eigenvalues and eigenvectors and verify the Cayley-Hamilton theorem with applications to physics problems [Apply]
- Apply differential calculus to determine maxima, minima and curvature of curves arising in mechanics and optics [Apply]
- Evaluate definite integrals using beta and gamma functions and reduction formulae [Evaluate]
- Solve first and second order ODEs that model oscillatory and decay phenomena in physics [Apply]
- Apply vector differential operators (gradient, divergence, curl) to scalar and vector fields [Apply]
- Apply Green's, Stokes' and Gauss's theorems to convert between line, surface and volume integrals [Apply]
📚 Chapters
- Unit I — Matrices, eigenvalues and Cayley-Hamilton theorem
- Unit II — Differential calculus and applications to maxima and curvature
- Unit III — Integral calculus, beta and gamma functions
- Unit IV — Ordinary differential equations of first and second order
- Unit V — Vector differentiation, integration and theorems of Green, Stokes and Gauss
TutorDA LMS