**I. Numerical Analysis **

Approximations and round off errors, Truncation errors and Taylor Series, Determination of roots of polynomials and transcendental equations by Newton-Raphson, Secant and Bairstow's method.

Solutions of linear simultaneous linear algebraic equations by Gauss Elimination and Gauss- Siedel iteration methods.

Curve fitting- linear and nonlinear regression analysis.

Backward, Forward and Central difference relations and their uses in Numerical differentiation and integration, Application t of difference relations in the solution of partial differential equations.

Numerical solution of ordinary differential equations by Euler, Modified Euler, Runge-Kutta and Predictor-Corrector method.

**II. Computer Programming**

Introduction to computer programming in C and C++ languages. Arithmetic expressions, Simple programs. The emphasis should be more on programming techniques rather than the language itself. The C programming language is being chosen mainly because of the availability of the compilers, books and other reference materials.

Example of some simple C program. Dissection of the program line by line.

Concepts of variables, program statements and function calls from the library (printf for example)

C data types, int, char, float etc.

C expressions, arithmetic operations, relational and logic operations.

C assignment statements, extension of assignment to the operations. C primitive input output using getchar and putchar, exposure to the scant and printf functions.

C statements, conditional execution using if, else. Optionally switch and break statements may be mentioned.

Concepts of loops, example of loops in C using for, while and do-while.

Optionally continue may be mentioned.

One dimensional arrays and example of iterative programs using arrays, 2-d arrays. Use in matrix computations.

Concept of Sub-programming, functions. Example of functions. Argument passing mainly for the simple variables.

Pointers, relationship between arrays and pointers. Argument passing using pointers.

Array of pointers, Passing arrays as arguments.

Strings and C string library.

Structure and unions. Defining C structures, passing structures as arguments.

Program examples.

File I/O. Use of fopen, fscanf and fprintf routines.

**Lab**

Development of computer program for

• Numerical integration by Trapezoidal and Simpson's rule.

• Gauss-Siedel iteration method

• Various matrix operation-and their use as sub-routines

*Suggested Text Books & References.*

*• Shastry, S.S., "Numerical Methods", Prentice Hall Inc., India, 1998.*

• Noble Ben, "Numerical Methods", New York International Publications, New York, 1964.

• Stanton Ralph G., "Numerical Methods for Engineering", Englewood cliffs, N.J., Prentice Hall Inc., 1961.

• Buckingham R.A., "Numerical Methods", Sir Isaac Pitman Sons. Ltd., London, 1957.

• Bakhvalov, N .S., "Numerical Methods", Mir. Pub., Moscow, 1977.

• Grewal, B.S., "Numerical Methods", Khanna Pub., New Delhi, 1998.

• Sudhit Kaicker, "The Complete ANSI C", BPB Publications, New Delhi, 1996.

• Kernighan, B. W. and D .M. Ritchie, "The C Programming Language", Prentice Hall of India, 1998.

• Byron, S. Gottfreid, "Programming with C", Tata McGraw Hill, 2nd edition 1998.