# Anna University MA3151 Matrices and Calculus: Syllabus and Practice

> Study guide for MA3151 Matrices and Calculus (Anna University, Regulations 2021): all five units, from eigenvalues to multiple integrals, with free practice.

Source: https://practicecalculus.com/courses/anna-university-ma3151
Updated: 2026-11-08

## At a glance

- **Course code:** MA3151 Matrices and Calculus
- **Regulation:** Regulations 2021, non-autonomous affiliated colleges (choice based credit system)
- **Credits:** 4 credits (L-T-P 3-1-0, 60 periods)
- **Semester:** Semester I (Basic Science course)
- **Prerequisites:** Not stated in the curriculum
- **Covers:** Matrices, differential calculus, functions of several variables, integral calculus and multiple integrals
- **Next course:** MA3251 Statistics and Numerical Methods in Semester II (Mechanical Engineering curriculum)
- **Practice here:** [Calculus 1](/learn/calculus-1), [integration techniques](/learn/calculus-2/integration-techniques/u-substitution-refresher) and [multiple integrals](/learn/calculus-3/multiple-integrals/iterated-integrals)

## Key takeaways

- MA3151 Matrices and Calculus is the Semester I mathematics course in Anna University Regulations 2021 for affiliated engineering colleges.
- It carries 4 credits (3-1-0) and has five units of 9 + 3 periods each.
- Units II to V are calculus: one variable differentiation, several variables, techniques of integration and multiple integrals.
- Unit I is linear algebra: eigenvalues, the Cayley-Hamilton theorem, diagonalisation and quadratic forms.
- Students admitted under Regulations 2025 take MA25C01 Applied Calculus instead.

**MA3151 Matrices and Calculus** is the first semester mathematics course for B.E. and B.Tech. students in **Anna University Regulations 2021**, the curriculum for non-autonomous affiliated colleges in Tamil Nadu. It is a 4 credit Basic Science course with 3 lecture periods and 1 tutorial period a week, 60 periods in total. Four of its five units are calculus. This guide follows the official Regulations 2021 curriculum for B.E. Mechanical Engineering and maps each calculus topic to free practice.

Students admitted under Regulations 2025 take [MA25C01 Applied Calculus](/courses/anna-university-ma25c01) instead.

## What MA3151 covers

The syllabus has five units of 9 lecture and 3 tutorial periods each.

- **Unit I, Matrices:** eigenvalues and eigenvectors of a real matrix, the characteristic equation, the Cayley-Hamilton theorem, diagonalisation by orthogonal transformation, reduction of a quadratic form to canonical form, and the nature of quadratic forms.
- **Unit II, Differential calculus:** representation of functions, limits, continuity, derivatives, the sum, product, quotient and chain rules, implicit and logarithmic differentiation, and maxima and minima of functions of one variable.
- **Unit III, Functions of several variables:** partial differentiation, homogeneous functions and Euler's theorem, total derivative, change of variables, Jacobians, Taylor's series in two variables, maxima and minima of two variables, and Lagrange's method of undetermined multipliers.
- **Unit IV, Integral calculus:** definite and indefinite integrals, the substitution rule, integration by parts, trigonometric integrals, trigonometric substitutions, partial fractions, irrational functions, improper integrals, and applications to hydrostatic force, moments and centres of mass.
- **Unit V, Multiple integrals:** double integrals, change of order of integration, polar coordinates, area enclosed by plane curves, triple integrals, volume of solids, change of variables, and moments, centres of mass and moment of inertia.

## MA3151 topic map

PracticeCalculus does not teach matrices, so Unit I is not in the table.

| MA3151 topic | Practice | Read |
| --- | --- | --- |
| Limits and continuity (Unit II) | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [Continuity](/blog/continuity) |
| Differentiation rules (Unit II) | [Product rule](/learn/calculus-1/derivative-rules/product-rule) | [Product and quotient rules](/blog/product-and-quotient-rules), [chain rule](/rules/chain-rule) |
| Implicit differentiation (Unit II) | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/rules/implicit-differentiation) |
| Logarithmic differentiation (Unit II) | [Exponential and log derivatives](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Logarithmic differentiation](/rules/logarithmic-differentiation) |
| Maxima and minima of one variable (Unit II) | [Critical points](/learn/calculus-1/applications-of-derivatives/critical-points) | [Optimization problems](/blog/optimization-problems) |
| Partial and total derivatives (Unit III) | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |
| Change of variables and chain rule (Unit III) | [Multivariable chain rule](/learn/calculus-3/partial-derivatives/multivariable-chain-rule) | [Clairaut's theorem](/theorems/clairauts-theorem) |
| Maxima, minima and Lagrange (Unit III) | [Lagrange multipliers](/learn/calculus-3/partial-derivatives/lagrange-multipliers) | [Lagrange multipliers](/blog/lagrange-multipliers) |
| Substitution rule (Unit IV) | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution rule](/rules/u-substitution-rule) |
| Integration by parts (Unit IV) | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) |
| Trigonometric integrals and substitutions (Unit IV) | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions (Unit IV) | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Improper integrals (Unit IV) | [Infinite discontinuities](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals](/blog/improper-integrals) |
| Moments and centres of mass (Units IV and V) | [Center of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) | [Double integral applications](/learn/calculus-3/multiple-integrals/double-integral-applications) |
| Double integrals and change of order (Unit V) | [Switching the order](/learn/calculus-3/multiple-integrals/switching-the-order) | [Double integrals](/blog/double-integrals) |
| Polar coordinates and change of variables (Unit V) | [Polar double integrals](/learn/calculus-3/multiple-integrals/polar-double-integrals) | [Change of variables](/learn/calculus-3/multiple-integrals/change-of-variables) |
| Triple integrals and volume (Unit V) | [Triple integrals](/learn/calculus-3/multiple-integrals/triple-integrals) | [Double integrals practice](/practice-problems/double-integrals) |

## Example problems at the MA3151 level

These are original practice problems, not past questions.

**1. Logarithmic differentiation (Unit II).** For $y = x^x$, take logs: $\ln y = x \ln x$. Differentiating, $\frac{y'}{y} = \ln x + 1$, so $y' = x^x(\ln x + 1)$.

**2. Euler's theorem (Unit III).** $u = x^3 + x^2 y$ is homogeneous of degree 3, so $x u_x + y u_y = 3u$. Check: $x(3x^2 + 2xy) + y(x^2) = 3x^3 + 3x^2 y$.

**3. Partial fractions (Unit IV).**

$$\int \frac{dx}{x^2 - 1} = \frac{1}{2}\int\left(\frac{1}{x - 1} - \frac{1}{x + 1}\right)dx = \frac{1}{2}\ln\left|\frac{x - 1}{x + 1}\right| + C$$

**4. Area in polar coordinates (Unit V).** The area inside $r = 2\cos\theta$ is $\int_{-\pi/2}^{\pi/2}\int_0^{2\cos\theta} r\,dr\,d\theta = \pi$.

## How to do well in MA3151

- **Treat the tutorial hour as practice time.** The 3-1-0 pattern gives one tutorial a week per unit, and the end semester paper rewards fast, accurate working.
- **Learn the integration toolkit in order:** substitution, parts, trig integrals, trig substitution, then partial fractions. The [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) lesson helps you decide which to try first.
- **Sketch the region before every double integral.** Most errors in change of order questions come from wrong limits, not wrong integration.
- **Revise with short sessions** on [practice](/practice) and keep the [formula sheet](/formulas) beside you. Our list of [common calculus mistakes](/blog/common-calculus-mistakes) covers the slips that cost the most marks.

## Frequently asked questions

### What is MA3151 at Anna University?

MA3151 Matrices and Calculus is the first semester mathematics course under Anna University Regulations 2021. It is a 4 credit Basic Science course with 3 lecture and 1 tutorial period a week, 60 periods in total, covering matrices, differential calculus, functions of several variables, integral calculus and multiple integrals.

### Which textbooks are prescribed for MA3151?

The curriculum lists Kreyszig, Advanced Engineering Mathematics (10th edition), B. S. Grewal, Higher Engineering Mathematics (44th edition), and James Stewart, Calculus: Early Transcendentals (8th edition) for Units II and IV. References include Anton, Thomas' Calculus, Bali, Jain and Iyengar, Narayanan and Manicavachagom Pillai, Ramana, and Pal and Bhunia.

### Is MA3151 still taught?

It is the course for students admitted under Regulations 2021, so it remains relevant for those batches and for arrear examinations. Anna University has since published Regulations 2025 curricula, where the first semester calculus course is MA25C01 Applied Calculus.

### Which MA3151 unit is the hardest?

Many students find Unit III (functions of several variables) and Unit V (multiple integrals) the hardest, because Jacobians, Lagrange multipliers and change of order of integration are new ideas. Short daily practice on these units helps most.