**Instructing following courses in Spring 2019:**

1. PDEs (M.Sc.)

2. ODEs (M.Sc.)

§ For students:

Email id:

1. PDEs (M.Sc.)

2. ODEs (M.Sc.)

§ For students:

Email id:

*bmandal@iitbbs.ac.in*

**Office:**

*SBS, Room 333.*

**Office hours:**

*by appointment.*

**Course Description:**

1. Mathematics-I (B.Tech)

*Past Teaching:*1. Mathematics-I (B.Tech)

*Basic course in differential/integral calculus. Topics include: Rolle’s theorem, Lagranges theorem, Cauchy’s mean value theorem, Maxima-Minima of a function, Polar curve tracing, Calculus of several variables, Vector calculus, Lagrange’s method of multipliers, Double and triple integrals and Techniques of solving Ordinary Differential Equations.*

**2. Mathematics-II (B.Tech)**

Course Description:

*Limit, continuity, differentiability and analyticity of complex functions, Cauchy-Riemann equations, Harmonic functions, Elementary complex functions, Line integrals, Cauchy’s integral theorem, Cauchy’s integral formula, derivatives of analytic functions, Power series, Taylor’s series, Laurent’s series, Zeros and singularities, Residue theorem, evaluation of improper integrals by residue theorem.*

**3. PDEs (M.Sc.)**

Course Description:

*First order quasi-linear equations. Nonlinear equations. Cauchy-Kowalewski’s theorem (for first order). Classification of second order equations and method of characteristics. One dimensional wave equation and De’Alembert’s method. Duhamel’s principle. Solutions of equations in bounded domains and uniqueness of solutions. BVPs for Laplace’s and Poisson’s equations. Maximum principle and applications. Green’s functions and properties. Existence theorem by Perron’s method. Heat equation, Maximum principle. Uniqueness of solutions via energy method. Uniqueness of solutions of IVPs for heat conduction equation. Green’s function for heat equation.*

**4. Optimization Techniques LAB (M.Sc.)**

Course Description:

*Assignments based on materials covered in Optimization Techniques class in MATLAB. Topics include: Linear programming problems, simplex method, revised simplex method, duality, sensitivity analysis, transportation and assignment problems, Nonlinear optimization, method of Lagrange multipliers, Karush - Kuhn - Tucker theory, convex optimization, Line search methods, Gradient methods, Newton’s method, Conjugate direction methods, quasi - Newton methods, projected gradient methods, penalty methods.*

**5. Mathematical Methods (M.Tech. & Ph.D.)**

*Course Description:*

*Numerical methods of ODE and PDE: Runge-Kutta and finite difference methods for ODE, Finite difference methods for solving 2-D Laplace’s equation, Poisson’s equation, 1-D heat equation : Bender Schmidt, Crank Nicholson method and Du Fort Frankel methods, 1-D wave equation using Explicit method. Consistency and stability analysis.*

**Textbooks:**

*1. Mathematics - I & II:*

i)Kreyszig E.

i)

*Advanced Engineering Mathematics*, John Wiley & Sons.

*ii)*Jain R. K. and Iyengar S. R. K.

*Advanced Engineering Mathematics,*Narosa.

*iii)*Churchill and Brown,

*Complex Variables and Applications*

*2. Optimization Techniques LAB :*

*i)*Rao, S.S

*, Optimization, Theory and Applications.*

ii)Chong and Zak,

ii)

*An Introduction to Optimization.*

iii)Hunt, Lipsman and Rosenberg

iii)

*, A guide to MATLAB.*

3. PDEs :

3. PDEs :

*i)*Sneddon I. N.

*Elements of Partial Differential Equations*.

*ii)*John F.

*Partial Differential Equations*.

*iii)*Evans L.C.,

*Partial Differential Equations*.

*4. Mathematical Methods :*

*i)*Grewal, B.S.

*Numerical Methods.*

*ii)*Jain, Iyengar and Jain,

*Numerical Methods-problem and Solutions.*

*iii)*Hamming, R.W.,

*Numerical Methods for Scientist and Engineers.*

**Grading Policy:**

*Class Tests: 20%; Mid-Sem: 30% ; End-Sem: 50%. See also.*

**P.S.:**

*See Regulation Policies for more details on attendance, grading, institute guidelines etc.*- Instructor for Calculus-II (MTH 133) Michigan State University, USA in Fall 2016.

Course Description:*Advance course in integral calculus. Topics include: Review of calculus-I, inverse functions, indefinite and definite integrals, applications of integration, sequence, infinite series and parametric equations.*

**Hours:**

*Mon, Wed, Fri; 9.10 am - 10 am.*

**Recitation & Quiz:**

**:**

TA

TA

*Samuel Johannes Ryskamp*

**Class Information:**

**Textbook:**

*Calculus, Special version for MTH 133, James Stewart (7th Edition)*

**Grading Policy:**

*WeBWorK: 10%; Surveys: 2%; Quizzes: 18%; Midterms: 40% (20% each); Final: 30%. See also.*

- Teaching Assistant for Analyse Numérique, Université de Genève, 2010–11, 2011–12, 2012–13 and 2013-14.

Course Description:

*Introduction to Scientific Computing and Numerical Analysis. Topics include: numerical integration, interpolation and approximation, numerical solution of ODEs, numerical linear algebra and least squares, eigen-value problems, solution of nonlinear system of equations.*