Engineering Mathematics-II
Course: Linear Algebra and Differential Equations (LADE)
Institute: IIIT Pune — F.Y. B.Tech Semester II (AY 2025-2026)
Credits: 4 (3L + 1T)
Text Books: Serge Lang — Introduction to Linear Algebra; Erwin Kreyszig — Advanced Engineering Mathematics
This page organizes Unit-wise comprehensive notes covering the full EM-II syllabus. Each unit has detailed explanations, worked examples, and extensive practice questions.
Reference Pages
Geometry Reference for Linear Algebra
Vectors as arrows, lines, planes, dot product, cross product, projections, and the geometric meaning of span — all the geometry you need for this course.
Unit-wise Notes
Unit I — Linear Algebra: Vector Spaces, Rank & Gram-Schmidt (08 Hrs)
Systems of linear equations & Gauss elimination; Vector space, subspace, spanning sets; Linear independence & dependence; Basis & dimension; Rank of matrix; Inner product; Gram-Schmidt process.
Unit II — Eigenvalues & Matrix Decomposition (08 Hrs)
Eigenvalues and eigenvectors; Diagonalization; Cayley-Hamilton theorem; Quadratic forms; Singular Value Decomposition (SVD); Applications.
Unit III — First-Order ODEs (08 Hrs)
First-order ODEs: exact, linear, Bernoulli equations; Applications to engineering problems; Existence & uniqueness theorem.
Notes coming soon.
Unit IV — Higher-Order ODEs & Transforms (08 Hrs)
Second- and higher-order linear ODEs; Variation of parameters; Laplace transforms; System of ODEs; Applications.
Notes coming soon.