# Mathematical Concepts I

Paper Code:
CHY 114
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Objective:

Course Objectives:

This course will enable the students to –

1. enable the students to learn about mathematical concepts which will be helpful in chemical derivations.

Course Outcomes (COs):

 Course Learning outcomes (at course level) Learning and teaching strategies Assessment Strategies Paper Code Paper Title CHY-114 Mathemat ical concepts I The students will be able to –   CO18: find maxima and minima, critical point and inflection points of functions. CO19: produce and interpret graphs of basic function like linear and sparabola. CO20: explain and apply basic concepts of probability. CO21: solve applied problem of chemistry using differentiation and integration. CO22: find roots of equations using numerical method like Newton -Raphson method, binary bisection method. CO23: apply numerical method of integration like Trapezoidal and Simpsons rule for integration. Interactive Lectures   Discussions   Tutorials   Problem solving The oral and written examinations (Scheduled and surprise tests)   Problem solving exercises   Assignments Quiz   Semester End Examination

9.00
Unit I:
Recapitulation

Fundamentals: Mathematical functions, odd and even functions, Trigonometric functions, polynomial expressions, logarithmic functions, exponential functions, constants and variables, standard forms of straight lines and parabolic equations with graphs.

9.00
Unit II:
Differential Calculus

Differentiation of simple functions like xn, ex, log x, higher order derivatives, partial differentiation of first and second order, total differentiation. Maxima and minima of one variable function.

10.00
Unit III:
Integral Calculus

Indefinite integrals, integration of standard function, methods of integration: integration by substitution, integration by parts, integration by means of a partial fraction, definite integrals and their properties.

10.00
Unit IV:
Numerical Calculus

Roots of quadratic equations analytically and iteratively (e.g. pH of a weak acid). Numerical methods of finding roots (Newton-Raphson, binary –bisection, e.g. pH of a weak acid not ignoring the ionization of water, volume of a van der Waals gas, equilibrium constant expressions), numerical integration (Trapezoidal and Simpson’s rule, e.g. entropy/enthalpy change from heat capacity data).

7.00
Unit V:
Mathematical Series and Statistics

Power series, Maclaurin, Taylor series, basic concepts of probability distributions (gas kinetic theory) and mean values; Binomial (gas kinetic theory).

Note: Calculations involving use of calculator is to be avoided.