Six units covering matrices and linear systems, differential calculus, integral calculus, multivariable differentiation, multiple integrals and Fourier series — with theory, fully worked examples, comparison tables, exam tips, practice questions and solutions. Every unit is a self-contained HTML file you can open, print, or study offline.
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Matrices and their elementary operations, rank of a matrix, linear independence, consistency of linear systems, matrix inverse, eigenvalues and eigenvectors, diagonalisation, and the Cayley–Hamilton theorem with applications.
Limits and derivatives, parametric and implicit differentiation, logarithmic differentiation, successive derivatives, Rolle's theorem, Lagrange's Mean Value Theorem, Taylor and Maclaurin expansions, L'Hospital's rule, and optimisation.
Standard integrals, integration by substitution, integration by parts, partial fractions, and the powerful properties of definite integrals including the King property and even/odd function simplifications.
Limits and continuity in two dimensions, partial derivatives, total derivatives, the chain rule for several variables, Euler's theorem on homogeneous functions, maxima and minima of two variables, and the method of Lagrange multipliers.
Double and triple integrals, changing the order of integration, transformation to polar, cylindrical and spherical coordinates, and applications to area, volume, centre of mass and moments of inertia.
Periodic functions and Dirichlet's conditions, Fourier series expansions over standard and arbitrary intervals, even and odd symmetry simplifications, half-range sine and cosine series, and Parseval's identity with applications.
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The six COs as defined in the MTH165 syllabus — mapped across all units.
Apply matrix methods to solve systems of linear equations and compute eigenvalues and eigenvectors.
Unit IApply differential calculus techniques to analyze functions, limits, series expansions and optimisation problems.
Unit IIEvaluate integrals using standard techniques including substitution, integration by parts and partial fractions.
Unit IIIAnalyze functions of several variables using partial derivatives, Euler's theorem and Lagrange multipliers.
Unit IVEvaluate multiple integrals and apply them to area, volume, centre of mass and moments of inertia.
Unit VExpand periodic functions as Fourier series and apply symmetry and Parseval's identity.
Unit VIHow the course is evaluated across the semester.
| Component | Full Form | Marks | Units Covered |
|---|---|---|---|
| ATT | Attendance | 5 | All units |
| CA | Continuous Assessment | 25 | Units I – III |
| MTT | Mid-Term Test | 20 | Units I – III |
| ETT | End-Term Test | 50 | Units I – VI |
Focus on Units I – III for the MTT (20 marks) and cover all six units for the ETT (50 marks). The heaviest scoring areas in the ETT are usually Unit I (matrices), Unit II (differential calculus), and Unit VI (Fourier series) — make sure you can solve a full-length problem from each without hesitation.
A quick suggested workflow for studying the course efficiently.
Units I → VI build on each other. Matrix methods from Unit I are used throughout the later units.
Don't just read the solutions — redo them on paper. Mathematics is learned by doing, not by reading.
Before the exam, revise only the standard results, formula boxes and summary tables at the end of each unit.
Each unit ends with graded practice questions and full solutions. Attempt before reading the solutions.
Every unit has print rules built in — use Ctrl + P and choose "Save as PDF" for a clean A4 layout.
Click "Mark done" on each card as you finish a unit. Progress is saved in your browser's local storage.
Textbooks, references and online tools aligned with the MTH165 syllabus.
Advanced Engineering Mathematics
Erwin Kreyszig · Wiley · 10th Edition
Higher Engineering Mathematics
B. S. Grewal · Khanna Publishers · 44th Edition
Engineering Mathematics
B. V. Ramana · McGraw Hill Education
Web Resources
nptel.ac.in · khanacademy.org · wolframalpha.com · symbolab.com