Basic Calculus 1 Course | Prof. Arindama Singh IIT Madras | Undergraduate Math
Course Details
| Exam Registration | 433 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics, Foundations of 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 | 17 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Master the Language of Change: An Introduction to Basic Calculus - 1
Welcome to a foundational journey into the world of rigorous calculus. This course, Basic Calculus - 1, is meticulously designed to bridge the gap between the intuitive calculus learned in school and the precise, logical framework required for advanced mathematics and its applications. Taught by Prof. Arindama Singh of IIT Madras, this 12-week program is your gateway to truly understanding the 'why' behind the powerful tools of calculus.
Your Guide: Prof. Arindama Singh
Learning from an expert shapes understanding. Your instructor for this course is Prof. Arindama Singh, a professor in the Department of Mathematics at the prestigious Indian Institute of Technology Madras. With a teaching portfolio spanning Logic, Theory of Computation, Linear Algebra, and Differential Equations, and research interests in Computational Mathematics, Prof. Singh brings a unique, depth-oriented perspective.
He believes in the maxim "Think in front of students," favoring interactive, Socratic-style teaching (inspired by Moore's method) over one-way lectures. This means you won't just memorize formulas; you'll be guided to discover the logical structure of calculus, developing problem-solving skills and mathematical maturity crucial for any STEM field.
Who Is This Course For?
This course is specifically intended for:
- Undergraduate Students, particularly those pursuing a B.Sc. in Mathematics, Physics, Engineering, or related sciences.
- Learners who have completed school-level calculus and seek a more rigorous and formal understanding.
- Anyone preparing for competitive exams or advanced studies that demand a solid grasp of foundational mathematical analysis.
Prerequisite: A firm grounding in School Mathematics is essential to build upon.
Course Overview & Learning Objectives
Moving beyond computational tricks, this course aims to treat the core concepts of calculus—continuity, differentiability, and integrability—with the rigor they deserve. You will learn to construct logical arguments, understand precise definitions (like the epsilon-delta definition of a limit), and apply theorems correctly. By the end of 12 weeks, you will have a robust framework for analyzing change, areas, volumes, and much more.
Detailed 12-Week Course Layout
| Week | Topics Covered |
|---|---|
| Week 1 | Real numbers, Functions and their graphs. |
| Week 2 | Limits of functions, Left and Right hand limits. |
| Week 3 | Continuity, Intermediate value property. |
| Week 4 | Differentiation, Chain rule, Implicit differentiation. |
| Week 5 | Extreme values, Rolle’s theorem, Mean value theorems. |
| Week 6 | Local extrema. |
| Week 7 | Limits at infinity, Infinite limits, Asymptotes, Differentials. |
| Week 8 | Definite integrals, Area, Mean value theorem for integrals. |
| Week 9 | The Fundamental Theorem of Calculus, Indefinite integral. |
| Week 10 | Integration by substitution, Area between curves. |
| Week 11 | Volume by slicing, Volume of revolution, Cylindrical shells. |
| Week 12 | Lengths of plane curves, Area of surface of revolution. |
Primary Reference Text
The course will closely follow key chapters from a classic and highly respected textbook:
- Calculus by Thomas & Finney, 9th Edition, Pearson, 2002. (Chapters 1 – 5).
This text provides excellent explanations, examples, and problems that align perfectly with the course's goal of building both conceptual understanding and practical skill.
Why Enroll in Basic Calculus - 1?
Calculus is more than a subject; it's the language of science, engineering, economics, and data analysis. A shaky foundation can hinder future learning. This course ensures you build that foundation on solid rock, not sand.
- Rigorous Understanding: Transition from "how to do it" to "why it works."
- Expert Instruction: Learn from an IIT Madras professor renowned for his interactive and thoughtful teaching methodology.
- Structured Progression: A logical 12-week journey from real numbers to applications of integration.
- Career & Academic Edge: A strong command of fundamental calculus is indispensable for success in higher education and technical careers.
Embark on this 12-week journey with Prof. Arindama Singh to unlock the true power and beauty of calculus. Move beyond computation and start thinking like a mathematician.
Enroll Now →