Applied Mathematics Syllabus: Semester Subjects and Course Topics
With median course fees standing at ₹55,400 in government institutions and ₹1.17 lakh in private colleges, choosing the right academic path requires clear visibility into subject modules. Below is a detailed guide covering semester-wise paper structures, elective choices, computational practical requirements, recommended textbooks, fee breakdowns, and admission procedures.
| Parameter | Details |
|---|---|
| Undergraduate Core Subjects | Calculus, Algebra, Real Analysis, Differential Equations, Mechanics, Numerical Methods & Programming |
| M.Sc Semester 1 Subjects (Osmania University) | Abstract Algebra, Mathematical Analysis, Ordinary Differential Equations, Linear Algebra |
| M.Sc Semester 2 Subjects (Osmania University) | Galois Theory, Lebesgue Measure and Integration, Complex Analysis, Topology |
| M.Sc Marking Scheme Per Paper | 100 Total Marks (30 Internal Assessment + 70 End-Semester Examination) |
| End-Semester Exam Duration | 3 Hours |
| Practical Computational Software | Maple and MATLAB for Differential Equations & Numerical Methods |
Applied Mathematics Subjects Year-wise
| Subject Title | Topics Covered | Subject Description |
|---|---|---|
| Calculus | Hyperbolic functions, Leibniz rule, reduction formulae, conics sketching, rotation of axes | Covers basic concepts of calculus and analytic geometry through theory and practicals. |
| Algebra | Polar complex numbers, De Moivre’s theorem, equivalence relations, linear transformations, matrices | Focuses on algebra, complex numbers, graph theory, and practical applications of linear algebra. |
| Real Analysis | Algebraic properties of R, countable/uncountable sets, sequences, infinite series, Cauchy Criterion | Deals with fundamental real analysis concepts, sequences, and series convergence. |
| Differential Equations | Compartmental, exponential decay, lake pollution & predator-prey models, phase plane analysis | Focuses on mathematical modeling and computing using Maple and MATLAB. |
| Theory of Real Functions | Caratheodory’s theorem, Cauchy mean value theorem, Riemann integration, uniform convergence | Provides elementary understanding and rigorous analysis of real-valued functions. |
| Group Theory | Permutation & quaternion groups, cyclic group subgroups, group homomorphisms, Cayley’s theorem | Deals with abstract algebra, group theory structure, and homomorphisms. |
| PDE and Systems of ODE | Derivation of Heat, Wave, and Laplace equations, linear systems, differential operators | Focuses on linear partial differential equations and systems of ordinary differential equations. |
| Multivariate Calculus | Double/triple integrals, Green’s theorem, directional derivatives, line and surface integrals | Covers multivariable calculus, vector calculus, and analytical space geometry. |
| Complex Analysis | Analytic functions, Cauchy integral formula, Liouville’s theorem, Laurent series, power series | Deals with complex variables, analytic functions, and complex integration theory. |
| Rings and Linear Algebra | Rings, integral domains, fields, vector spaces, dual spaces, linear transformations, annihilators | Integrates abstract algebra, vector spaces, and geometric linear transformations. |
| Mechanics | Coulomb friction, couple moment, conservative force fields, work-energy equation, centroid | Covers engineering mechanics, statics, and dynamics applications. |
| Numerical Methods & Programming | Bisection, Newton’s method, LU decomposition, Gauss-Seidel, Simpson’s rule, Euler’s method | Focuses on numerical analysis and computational algorithms for engineering computation. |
| Integral Equations & Calculus of Variation | Fredholm & Volterra integral equations, Hilbert transform, Euler’s equation, brachistochrone problem | Teaches integral equations and variational calculus for physics and engineering. |
| Laplace Transform | Standard & Finite Laplace transform, Z-transform, Hankel Transform, Fourier series & transforms | Covers advanced operational mathematics and transform techniques. |
The B.Sc Applied Mathematics curriculum spans foundational subjects including calculus, algebra, differential equations, and numerical methods across academic years. Postgraduate programs like M.Sc at Osmania University follow a Choice Based Credit System (CBCS) structured into semester schemes.
Books for Applied Mathematics
| Subject / Paper Title | Textbook Name & Edition | Author(s) & Publisher |
|---|---|---|
| Abstract Algebra & Galois Theory | Basic Abstract Algebra (Second Edition) | P.B. Bhattacharya, S.K. Jain, S.R. Nagpaul |
| Mathematical Analysis | Principles of Mathematical Analysis (3rd Edition) | Walter Rudin (McGraw-Hill) |
| Ordinary Differential Equations | Ordinary Differential Equations (Third Edition) | S.G. Deo, V. Raghavendra, Rasmita Kar, V. Lakshmikantham (McGraw-Hill) |
| Linear Algebra | Linear Algebra (2nd Edition) | Kenneth Hoffman and Ray Kunze (PHI) |
| Lebesgue Measure & Integration | Real Analysis (3rd Edition) | H. L. Royden (Prentice-Hall India) |
| Applied Mathematics (Diploma Level) | Applied Mathematics 2 (First Edition) | Sameer Shah (TechKnowledge Publications) |
These standard reference books cover foundational and advanced topics across degree and diploma courses. For MSBTE diploma engineering, Applied Mathematics 2 by Sameer Shah covers 400 pages of course material.
Colleges and Fee Structure for Applied Mathematics
| College | City | Ownership | Total course fee | NIRF rank |
|---|---|---|---|---|
| Manipal University Manipal | Manipal | — | ₹1.78 lakh | 3 (Overall, 2025) |
| Jamia Millia Islamia University | Delhi | Government | ₹43,100 | 4 (Overall, 2025) |
| Indian Institute of Technology Roorkee | Roorkee | — | ₹90,300 | 6 (Overall, 2025) |
| Aligarh Muslim University | Aligarh | — | ₹59,700 | 10 (Overall, 2025) |
| Siksha ‘O’ Anusandhan University | Bhubaneswar | — | ₹1.65 lakh | 15 (Overall, 2025) |
| Kalinga Institute of Industrial Technology | Bhubaneswar | — | ₹3.62 lakh | 17 (Overall, 2025) |
| Anna University | Chennai | Government | ₹1.16 lakh | 20 (Overall, 2025) |
| Amity University Noida | Noida | — | ₹2.14 lakh | 22 (Overall, 2025) |
| Andhra University | Visakhapatnam | — | ₹45,000 | 23 (Overall, 2025) |
| College | City | Ownership | Total course fee |
|---|---|---|---|
| University of Calcutta | Kolkata | Government | ₹8,300 |
| Garhbeta College | Medinipur | Government | ₹26,000 |
| JNTUA College of Engineering Kadapa | Kadapa | Government | ₹30,000 |
| Panskura Banamali College | Midnapore | Government | ₹34,800 |
| Osmania University | Hyderabad | Government | ₹42,580 |
| Jamia Millia Islamia University | Delhi | Government | ₹43,100 |
| CSJM Kanpur University | Kanpur | Government | ₹48,000 |
| Indira Gandhi Institute of Technology | Dhenkanal | Government | ₹62,800 |
| JNTUH College of Engineering | Hyderabad | Government | ₹63,000 |
| Delhi Technological University | Delhi | Government | ₹65,100 |
At least 131 colleges offer Applied Mathematics across India, including 18 government and 22 private institutions. Among colleges with fee data, 14 government colleges have a median fee of ₹55,400, while 18 private colleges have a median fee of ₹1.17 lakh.
How to Apply for Applied Mathematics Admission in 2026: Step by Step
- Check Eligibility: Verify completion of higher secondary (10+2) with Mathematics for undergraduate programs, or a relevant B.Sc degree in Mathematics/Applied Mathematics for postgraduate programs.
- Register for Entrance Exams: Apply for university-specific or state entrance exams such as LPUNEST (registration open from 01 Oct 2026 till 15 Jan 2027).
- Submit Application Form: Fill out online admission applications on official university or institute portals before specified deadlines.
- Attend Merit Counselling: Participate in merit allotment or entrance-based counselling rounds conducted by the respective college or university.
- Verify Documents and Pay Tuition Fees: Submit required academic transcripts, certificates, and clear admission fee payments to confirm enrollment.
| What to do | Where | Link |
|---|---|---|
| Compare colleges, fees and cutoffs | Applied Mathematics colleges in India | findmycollege.com |
FAQs
What core subjects are taught in the B.Sc Applied Mathematics syllabus?
B.Sc Applied Mathematics covers Calculus, Algebra, Real Analysis, Differential Equations, Mechanics, Numerical Methods & Programming, PDE, Multivariate Calculus, Complex Analysis, and Integral Equations.
What are the M.Sc Applied Mathematics First Semester subjects at Osmania University?
The first semester includes four core papers: Abstract Algebra (M 101), Mathematical Analysis (M 102), Ordinary Differential Equations (M 103), and Linear Algebra (M 104).
How is the examination assessment structured for M.Sc Applied Mathematics?
Each core paper carries 5 credits and is evaluated through Internal Assessment comprising 20 marks from internal tests and 10 marks from assignment submissions, combined with an end-semester examination.
Which software tools are used in Applied Mathematics practical sessions?
Practicals in differential equations and numerical modeling utilize mathematical computational software like Maple and MATLAB.
What standard reference book is recommended for Mathematical Analysis?
Principles of Mathematical Analysis (3rd Edition) by Walter Rudin (McGraw-Hill) is the standard text recommended for analysis units.
