## Details of MA1101 (Autumn 2016)

 Level: 1 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA1101 Mathematics I Narayan Banerjee

Syllabus
Part I: Calculus I

1. Curves & Surfaces: Curve tracing, tangent & normal to a curve. Surfaces, parametric representations, normal.

2. Functions of Several Variables: Partial derivatives, commutativity of mixed partial derivatives, total differential, applications to approximating functions. Exact and closed differential, gradient, curl and divergence.

3. Multiple Integrals: Double and triple integrals, iterated integrals. Change of variable formula, curvilinear co-ordinate systems; polar, spherical, cylindrical coordinates.

4. Vector Analysis: Line integral and surface integral. Greens Theorem, Stokes Theorem and Divergence theorem.

Part II: Matrix Theory

1. Linear System: System of linear equations and its solvability, Gauss elimination and Gauss-Jordan elimination methods.

2. Matrices & Determinants: Rank, inverse and transpose of a matrix. Some important classes of matrices: Symmetric, anti-symmetric, orthogonal, Hermitian and unitary matrices. Determinant of a matrix. Similarity transformation.

3. Eigenvalues: Eigenvalues and eigenvectors. Calculation of eigenvalues, Cayley-Hamilton theorem. Diagonalizability of matrices.

Part III: Calculus II

1. Sequence & Series: Notion of convergence, geometric and zeta series, tests of convergence.

2. Taylors Series: Taylors expansion of a function, calculation of power series.

References
Suggested Texts / Reference Books:

1. Apostol, T. M., Calculus I (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2011.

2. Apostol, T. M., Calculus II (2nd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2007.

3. Arfken, G. B., Weber, H. & Harris, F., Essential Mathematical Methods for Physicists and Engineers, Academic Press, 2003.

4. Boas, M. L., Mathematical Methods In The Physical Sciences (3rd Edition), Wiley India Pvt Ltd, Springer-Verlag, 2006.

5. Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd, 2010.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 1 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed