Anna University MA3151 Matrices and Calculus: Syllabus and Practice

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 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.

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).

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 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 and keep the formula sheet beside you. Our list of common calculus mistakes covers the slips that cost the most marks.