Basic info Academic Calendar Timetable
Midsem: Practice Exam General Info Actual Exam
Teaching Assistants:
Ayan Dey at ISI Delhi
Bidwan Chakraborty at ISI Kolkata
Sneha B at ISI Bangalore
Class Timings:
Lectures: Mondays and Wednesdays (10:40 AM - 12:00 PM on both days)
Tutorials: Tuesdays (4:00 PM - 4:50 PM) and Fridays (2:30 PM - 3:20 PM) - tentatively
Grading Policy:
Midsem Exam: 50% of the total credit.
Semestral Exam: 50% of the total credit.
Exercises:
Problem-solving exercises will be given in the class on a regular basis.
Each examination will have problems similar to the exercises given in the class.
Students do NOT need to submit the solutions to the exercises given in the class. However, it is strongly recommended to solve them all and write down the solutions for better performance in the exams.
Exams:
Each examination will be a closed-note examination.
As mentioned above, a portion of the exam questions will be similar to the exercises given in the class.
References:
Linear Algebra and its Applications by Gilbert Strang
Introduction to Linear Algebra by Gilbert Strang
Calculus: One-Variable Calculus with an Introduction to Linear Algebra, Vol 1 by Tom Apostol
Calculus and Analytical Geometry by George B. Thomas and Ross L. Finney
Advanced Engineering Mathematics (especially Chapters 7-8) by E. Kreyzig
Linear Algebra by A. Ramachandra Rao and P. Bhimasankaram
Course Outline:
Calculus (approximately, 16 lectures)
Sets: basic operations and examples. Properties of real numbers. Infimum and supremum.
Functions: injective and surjective functions. Composition of functions. Inverse of a bijective function. Countable and uncountable sets.
Catalogue of essential functions (Polynomial, Trigonometric, Exponential, Logarithmic).
Sequences and their limits. Convergent sequences. Cauchy sequences. Series, sum of a series.
Limit and continuity of a function. Computation of limits. Properties of continuous functions.
Derivative of a function. Derivatives of polynomial, exponential and trigonometric functions. Chain rule.
Properties of differentiable functions. Mean Value Theorem, Taylor’s theorem. Maxima/minima of a function, L'Hospital's rule.
Riemann integration. Some classes of integrable functions. Rules of Integration: Integration by parts, substitution rule. (Trigonometric integrals. Trigonometric substitution.) Fundamental Theorems of Calculus.
Improper Riemann integrals.
Sequence of functions: definition and examples.
Linear Algebra (approximately, 8 lectures)
Vector spaces, subspaces, linear independence. Basis. Dimension. Sum and intersection of subspaces.
Linear transformations, matrix of a linear transformation.
Column space and row space. Rank of a matrix.
Elementary row operations on matrices. Operations with partitioned matrices. Trace and determinant of a matrix.
Linear equations. Homogeneous and inhomogeneous system of equations. Consistency. Solution space.