Anna University MA25C01 Applied Calculus: Syllabus and Practice

MA25C01 Applied Calculus is the first mathematics course for B.E. and B.Tech. students in Anna University's Regulations 2025 curriculum for non-autonomous affiliated colleges. It is taught in Semester I as a 4 credit Basic Science course, with 3 lecture periods and 1 tutorial period every week. This guide uses the official Regulations 2025 curriculum for B.E. Mechanical Engineering, published on the Anna University Centre for Academic Courses site, and maps every topic to free practice.

If you joined under Regulations 2021, your course is MA3151 Matrices and Calculus instead.

What MA25C01 covers

The curriculum lists four blocks of content. Each block also has activities such as plotting functions with open source software and solving competitive examination questions like GATE.

• Differential calculus: functions and their graphs, new functions from old functions, limit of a function, continuity, limits at infinity, the derivative as a function, maxima and minima of functions of one variable, the mean value theorem, and the effect of derivatives on the shape of a graph.
• Functions of several variables: partial derivatives, the chain rule, the total derivative, maxima and minima of functions of two variables, Lagrange's method of multipliers, and engineering applications.
• Integral calculus: the Fundamental Theorem of Calculus, indefinite integrals and the net change theorem, improper integrals, arc length, area of a region and the area of a surface of revolution.
• Multiple integrals: iterated integrals and Fubini's theorem, double integrals, change of order of integration, change of variables between Cartesian and polar coordinates, and triple integrals with cylindrical and spherical coordinates.

That is roughly a full Calculus 1 course plus the multivariable half of Calculus 3, compressed into one semester.

MA25C01 topic map

MA25C01 vs MA3151

Example problems at the MA25C01 level

These are original practice problems, not past papers.

1. Lagrange multipliers. Maximise f(x, y) = xy subject to x + y = 10. Setting \nabla f = \lambda \nabla g gives y = \lambda and x = \lambda, so x = y = 5 and the maximum is f = 25.

2. Change of order. Evaluate \int_0^1 \int_x^1 e^{y^2}\,dy\,dx. Reversing the order, 0 \le x \le y and 0 \le y \le 1, so

3. An improper integral. \int_0^{\infty} e^{-2x}\,dx = \lim_{t \to \infty}\left[-\tfrac{1}{2}e^{-2x}\right]_0^t = \tfrac{1}{2}.

How to do well in MA25C01

• Use the tutorial period well. One tutorial a week is built into the 3-1-0 pattern. Arrive having tried the problems, so you can ask about the ones that went wrong.
• Practise in short daily sessions on practice. Partial derivatives and Lagrange multipliers reward repetition more than rereading notes.
• Take the software and GATE components seriously. Together with assignments they make up most of the continuous assessment, which is 40% of the final mark.
• Keep the formula sheet close and read how to prepare for a calculus exam before the end semester examination.

Note: this guide is based on the Regulations 2025 curriculum for B.E. Mechanical Engineering. Check your own branch curriculum on the Anna University site for the semester in which MA25C01 is scheduled.