paper
Structure of Mathematics Courses for the UG Program
Sem
Name of the courses to be offered by the Department of mathematics
1
Analysis and Linear
Algebra
2
Analysis and Linear
Algebra
3
Probability and
Statistics
4
Multivariable Calculus and Complex Variable
Elementary Algebra and
Number Theory
Elective
Elective
5
Algebra I
Linear Algebra
Analysis I
Topology I
6
Analysis II
Complex Analysis
ODE
Elective
7
Algebraic Topology I
Functional Analysis
PDE
8
Elective
Elective
Project
Electives include:
Algebra II, Galois Theory, Probability, Harmonic Analysis, Lie Groups, Commutative Algebra,
Numerical Analysis, Number Theory.
Detailed Syllabus:
Analysis and Linear Algebra I:
One-variable calculus: Real and Complex numbers; Convergence of sequences and series; Continuity, intermediate value theorem, existence of maxima and minima; Differentiation, mean value theorem,
Taylor series; Integration, fundamental theorem of Calculus, improper integrals.
Linear Algebra: Vector spaces (over real and complex numbers), basis and dimension; Linear
Transformations and matrices; Determinants.
References:
Apostol, Calculus, Volume I, 2nd. Edition, Wiley, India, 2007.
G. Strang, Linear Algebra And Its Applications, 4th Edition, Brooks/Cole,
2006
Analysis and Linear Algebra:
Linear Algebra continued: Inner products and Orthogonality; Eigenvalues and Eigenvectors;
Diagonalisation of Symmetric matrices.
Multivariable calculus: Functions on $\R^n$; Partial and Total derivatives; Chain rule; Maxima, minima and saddles; Lagrange multipliers; Integration in $\R^n$, change of variables, Fubini 's theorem; Gradient, Divergence and Curl; Line and Surface integrals in $\R^2$ and $\R^3$; Stokes,
Green 's and Divergence theorems.
Introduction to Ordinary Differential Equations; Linear ODEs and Canonical forms for linear transformations. References:
T. M. Apostol, Calculus,
Sem
Name of the courses to be offered by the Department of mathematics
1
Analysis and Linear
Algebra
2
Analysis and Linear
Algebra
3
Probability and
Statistics
4
Multivariable Calculus and Complex Variable
Elementary Algebra and
Number Theory
Elective
Elective
5
Algebra I
Linear Algebra
Analysis I
Topology I
6
Analysis II
Complex Analysis
ODE
Elective
7
Algebraic Topology I
Functional Analysis
PDE
8
Elective
Elective
Project
Electives include:
Algebra II, Galois Theory, Probability, Harmonic Analysis, Lie Groups, Commutative Algebra,
Numerical Analysis, Number Theory.
Detailed Syllabus:
Analysis and Linear Algebra I:
One-variable calculus: Real and Complex numbers; Convergence of sequences and series; Continuity, intermediate value theorem, existence of maxima and minima; Differentiation, mean value theorem,
Taylor series; Integration, fundamental theorem of Calculus, improper integrals.
Linear Algebra: Vector spaces (over real and complex numbers), basis and dimension; Linear
Transformations and matrices; Determinants.
References:
Apostol, Calculus, Volume I, 2nd. Edition, Wiley, India, 2007.
G. Strang, Linear Algebra And Its Applications, 4th Edition, Brooks/Cole,
2006
Analysis and Linear Algebra:
Linear Algebra continued: Inner products and Orthogonality; Eigenvalues and Eigenvectors;
Diagonalisation of Symmetric matrices.
Multivariable calculus: Functions on $\R^n$; Partial and Total derivatives; Chain rule; Maxima, minima and saddles; Lagrange multipliers; Integration in $\R^n$, change of variables, Fubini 's theorem; Gradient, Divergence and Curl; Line and Surface integrals in $\R^2$ and $\R^3$; Stokes,
Green 's and Divergence theorems.
Introduction to Ordinary Differential Equations; Linear ODEs and Canonical forms for linear transformations. References:
T. M. Apostol, Calculus,
References: Garabedian, P. R., Partial Differential Equations, John Wiley and Sons, 1964. Prasad. P. and Ravindran, R., Partial Differential Equations, Wiley Eastern, 1985. Renardy, M. and Rogers, R. C., An Introduction to Partial Differential Equations, SpringerVerlag, 1992. Fritz John, Partial differential Equations, Springer (International Students Edition), 1971.