Advanced Engineering Mathematics Online Course | IIT Kharagpur | NPTEL
Course Details
| Exam Registration | 1488 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Undergraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 25 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Master the Language of Engineering: A Comprehensive Guide to Advanced Engineering Mathematics
For every aspiring engineer, a strong foundation in mathematics is not just an academic requirement; it's the essential language for modeling, analyzing, and solving real-world problems. If you're a BTech or BSc first-year student looking to build an unshakeable command over core mathematical concepts, your search ends here. We are thrilled to introduce a meticulously designed 12-week online course on Advanced Engineering Mathematics, taught by one of India's premier educators from the Indian Institute of Technology Kharagpur.
Meet Your Instructor: Prof. Hari Shankar Mahato
Learning from an expert makes all the difference. This course is led by Prof. Hari Shankar Mahato, an Assistant Professor in the Department of Mathematics at IIT Kharagpur. Prof. Mahato brings a wealth of international academic and research experience to the virtual classroom. His academic journey includes a PhD from the University of Bremen, Germany, followed by postdoctoral research at prestigious institutions like the University of Georgia, USA, and the University of Erlangen-Nuremberg and TU Dortmund in Germany.
His research expertise in Partial Differential Equations, Applied Analysis, and Variational Methods ensures that the course content is both rigorous and relevant. With a proven ability to teach a wide spectrum of courses—from foundational calculus and differential equations to advanced graduate-level topics—Prof. Mahato is uniquely positioned to guide students from first principles to advanced applications with clarity and depth.
Course Overview: What You Will Learn
This 12-week course is structured to transform your understanding of engineering mathematics. It is specifically crafted to be self-explanatory, with ample examples and theoretical explanations. The curriculum progresses logically from foundational calculus to sophisticated analytical tools used in engineering.
Detailed 12-Week Course Layout
| Week | Core Topics Covered |
|---|---|
| Week 1-2: Advanced Calculus | Mean Value Theorems, Taylor's series, Multivariable calculus (limits, partial derivatives, Jacobian), Maxima/Minima, Lagrange multipliers, Improper integrals, Gamma/Beta functions, Multiple integrals & applications. |
| Week 3: Ordinary Differential Equations (ODEs) | First and second-order ODEs, Integrating factors, Exact equations, Methods for finding auxiliary solutions. |
| Week 4-5: Numerical Methods | Solving linear systems (Jacobi, Gauss-Seidel), Root-finding methods (Bisection, Newton-Raphson), Interpolation (Newton, Lagrange), Numerical integration (Trapezoidal, Simpson's rules). |
| Week 6-8: Linear Algebra | Vector spaces, basis, linear transformations, Gauss elimination, Rank of a matrix, Eigenvalues & eigenvectors, Diagonalization, Special matrices (Hermitian, Unitary). |
| Week 9-11: Vector Calculus | Vector fields, Gradient, Divergence, Curl, Directional derivatives, Line/Surface/Volume integrals, Fundamental theorems (Green's, Stokes', Gauss' Divergence). |
| Week 12: Complex Analysis | Analytic functions, Cauchy-Riemann equations, Complex integration, Cauchy's integral theorem & formula, Taylor & Laurent series, Residue theorem & applications. |
Who Should Enroll?
This course is perfectly tailored for:
- BTech 1st Year Students across all engineering branches.
- BSc 1st Year Students majoring in Mathematics or related fields.
- Any undergraduate student or professional seeking a strong, application-oriented refresher in core engineering mathematics.
Prerequisites: A basic understanding of differential and integral calculus of one variable is recommended to get the most out of this course.
Why Choose This Course?
- IIT Pedigree: Learn from an IIT Kharagpur professor, ensuring top-tier pedagogical quality.
- Structured Learning Path: A logical 12-week progression from fundamentals to advanced topics.
- Applied Focus: Concepts are explained with examples relevant to engineering mechanics and other applications.
- Comprehensive Coverage: From solving equations to modeling physical systems, this course covers the mathematical toolkit every engineer needs.
Recommended Textbooks
To supplement your learning, the following textbooks are highly recommended:
- Advanced Engineering Mathematics by E. Kreyszig (Wiley, 10th Ed.).
- Differential and Integral Calculus by N. Piskunov (Vol. I & II).
- Integral Calculus by S. Narayan & R. K. Mittal (S. Chand).
Embark on this 12-week journey to master the mathematical foundations of engineering. Enroll today and build the analytical prowess that will power your academic and professional success.
Enroll Now →