Course title: Calculus for Engineers
Lecture hours: 3
Typical Slot: A
Description:
The goal of this course is to equip engineers with the mathematical tools that they would primarily require for data science and AI. The course will emphasize on understanding and applications of the concepts. On successful completion of the course, participants should be able to:
- Understand limits, convergence, gradients, and continuity.
- Solve differential and integral equations.
- Apply these concepts to analyze iterative algorithms, geometric problems, and optimization.
- Create models of systems and data using calculus, and analyze their properties.
Course content:
- Sequences, limits, convergence theorems and tests.
- Series, power series, Taylor series and Fourier series.
- Continuity, smoothness, Lipschitz, universal approximation theorems, JL lemma.
- Derivatives, sub-differentials, gradients, Jacobian, Hessian.
- Root-finding algorithms, Newton’s method, gradient descent and acceleration techniques.
- Evaluating gradients and integrals.
Prerequisite: None
Books:
- Advanced Engineering Mathematics, 10th Ed., E. Kreyszig, John Willey & Sons, 2010.
- Basic Multivariable Calculus, J.E. Marsden, A.J. Tromba, A. Weinstein, Springer Verlag, 1993.
- Differential and Integral Calculus, Vol. I and II, N. Piskunov, Mir Publishers, 1974.
- Calculus, G. Strang, Wellesley-Cambridge Press, 2010.
- Thomas Calculus, G.B. Thomas, Jr, M.D. Weir, J.R. Hass, Pearson, 2009.
Previous Instance of the course:
- 2025 (July-Nov; Dr. Ganapathy Krishnamurthi)
- 2024 (July-Nov; Dr. Sivaram Ambikasaran)