# Anna University MA25C01 Applied Calculus: Syllabus and Practice

> Study guide for MA25C01 Applied Calculus (Anna University, Regulations 2025): limits, derivatives, partial derivatives, integrals and multiple integrals.

Source: https://practicecalculus.com/courses/anna-university-ma25c01
Updated: 2026-11-08

## At a glance

- **Course code:** MA25C01 Applied Calculus
- **Regulation:** Regulations 2025, non-autonomous affiliated institutions
- **Credits:** 4 credits (L-T-P 3-1-0, 4 contact periods a week)
- **Semester:** Semester I (Basic Science course)
- **Prerequisites:** Not stated in the curriculum
- **Assessment:** Continuous assessment 40%, end semester examination 60%
- **Covers:** Differential calculus, functions of several variables, integral calculus and multiple integrals
- **Practice here:** [Calculus 1](/learn/calculus-1) plus [partial derivatives](/learn/calculus-3/partial-derivatives/functions-of-several-variables) and [multiple integrals](/learn/calculus-3/multiple-integrals/iterated-integrals) from Calculus 3

## Key takeaways

- MA25C01 Applied Calculus is the first semester mathematics course in the Anna University Regulations 2025 B.E. curriculum for affiliated colleges.
- It is a 4 credit course with 3 lecture and 1 tutorial period a week.
- The syllabus has four blocks: differential calculus, functions of several variables, integral calculus and multiple integrals.
- Assessment includes software work and GATE style questions, not only internal tests and the end semester exam.
- Students admitted under Regulations 2021 take MA3151 Matrices and Calculus instead.

**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](/courses/anna-university-ma3151) 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 topic | Practice | Read |
| --- | --- | --- |
| Functions and graphs | [Function notation](/learn/calculus-1/functions-warmup/function-notation) | [Polynomial functions](/functions/polynomial-functions) |
| Limits and continuity | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Limits at infinity | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Limits at infinity](/blog/limits-at-infinity) |
| The derivative as a function | [Derivative notation and meaning](/learn/calculus-1/the-derivative/derivative-notation-and-meaning) | [Power rule](/rules/power-rule), [chain rule](/rules/chain-rule) |
| Maxima and minima of one variable | [Absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Extreme value theorem](/theorems/extreme-value-theorem) |
| Mean value theorem | [Linear approximation and the MVT](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean value theorem](/theorems/mean-value-theorem) |
| Shape of a graph | [Second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Partial derivatives and chain rule | [Multivariable chain rule](/learn/calculus-3/partial-derivatives/multivariable-chain-rule) | [Partial derivatives](/blog/partial-derivatives) |
| Maxima and minima of two variables | [Second derivative test](/learn/calculus-3/partial-derivatives/critical-points-and-second-derivative-test) | [Partial derivatives practice](/practice-problems/partial-derivatives) |
| Lagrange multipliers | [Lagrange multipliers](/learn/calculus-3/partial-derivatives/lagrange-multipliers) | [Lagrange multipliers](/blog/lagrange-multipliers) |
| Fundamental Theorem and net change | [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/theorems/fundamental-theorem-of-calculus-part-2) |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Arc length and surface area | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Definite integrals practice](/practice-problems/definite-integrals) |
| Area of a region | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves) |
| Double integrals and order of integration | [Switching the order](/learn/calculus-3/multiple-integrals/switching-the-order) | [Double integrals](/blog/double-integrals) |
| Polar, cylindrical and spherical coordinates | [Cylindrical and spherical](/learn/calculus-3/multiple-integrals/cylindrical-spherical) | [Double integrals practice](/practice-problems/double-integrals) |

## MA25C01 vs MA3151

| | MA25C01 Applied Calculus | MA3151 Matrices and Calculus |
| --- | --- | --- |
| Regulation | 2025 | 2021 |
| Credits | 4 (3-1-0) | 4 (3-1-0) |
| Matrices unit | No | Yes, eigenvalues and quadratic forms |
| Techniques of integration | Not listed as a separate block | Parts, trig integrals, partial fractions |
| New topics | Limits at infinity, mean value theorem, arc length, surface area | Jacobians, Euler's theorem on homogeneous functions |

## 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

$$\int_0^1 \int_0^y e^{y^2}\,dx\,dy = \int_0^1 y e^{y^2}\,dy = \frac{e - 1}{2}$$

**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](/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](/formulas) close** and read [how to prepare for a calculus exam](/blog/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.

## Frequently asked questions

### What is MA25C01 at Anna University?

MA25C01 Applied Calculus is the Semester I mathematics course in the Anna University Regulations 2025 curriculum for non-autonomous affiliated colleges. It carries 4 credits (L-T-P 3-1-0) and covers single variable calculus, functions of several variables, integrals and multiple integrals.

### Is MA25C01 the same as MA3151?

No. MA3151 Matrices and Calculus belongs to Regulations 2021 and includes a unit on matrices. MA25C01 belongs to Regulations 2025, has no matrix unit, and adds topics such as limits at infinity, the mean value theorem, arc length and surface area. In the Mechanical Engineering curriculum, matrices move to MA25C02 Linear Algebra in Semester II.

### How is MA25C01 assessed?

The curriculum gives continuous assessment a 40% weight and the end semester examination 60%. Within continuous assessment it lists assignments (20%), solutions to application oriented problems using software (20%), solving GATE questions (20%) and internal examinations (40%).

### Which textbooks does MA25C01 use?

The references include Anton, Bivens and Davis, Calculus: Early Transcendentals; Larson and Falvo, Calculus: An Applied Approach; Stewart, Calculus: Early Transcendentals; Thomas' Calculus; K. Singh, Engineering Mathematics through Applications; and B. S. Grewal, Higher Engineering Mathematics.

### How should I prepare for MA25C01?

Revise Class 12 differentiation and integration first, then practise a few problems every day from each block. Partial derivatives and double integrals become much easier once single variable rules are automatic.