Mathematical Concepts -II

Paper Code: 
CHY-214(A)
Credits: 
3
Contact Hours: 
45.00
Objective: 

Course Objectives:

This course will enable the students to -

  1. be aware about the concept of matrix, determinant, vectors, differential equation, complex numbers, differential and integral calculus and their use in some important applications of chemistry

 

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

 

 

CHY-214 (a)

 

 

 

 

 

 

 

Mathematical Concepts - II

 

 

 

 

 

The students will be able to –

 

CO47: apply basic operations of matrices to solve simultaneous equations.

CO48: use basic operations of vectors, vector derivatives and coordinate systems.

CO49: apply the basic differential and integral calculus to determine extreme and stationary points of a function.

CO50: solve first order and first degree linear differential equation.

 CO51: apply the concept of complex numbers in solving the related problems.

Approach in teaching:

▪ Interactive Lectures,

▪ Explicit Teaching

▪ Discussion

▪ Didactic questions, Tutorials

▪ Multimedia Presentations

▪ Demonstration

Learning activities for the students:

▪ Self learning Assignments, Peer Assessment, Concept mapping,

▪ Think/Pair/Share, Problem Solving, Power Point Presentation, Handouts

 

  • The oral and written examinations (Scheduled and surprise tests)
  • Closed book and open book tests
  • Quiz
  • Problem solving exercises
  • Assignments
  • Presentation
  • Semester End Examinations

 

 

9.00
Unit I: 
Matrices and Determinants

Matrix algebra, Determinants, matrix inversion, Solving Simultaneous equations using inverse of a matrix, consistency and independence. Simultaneous equations with three unknowns (e.g. spectrophotometry) using Cramer’s rule. Homogeneous linear equations.

9.00
Unit II: 
Vectors

Vectors and coordinate systems: Unit vectors (application in solid state), Component of vectors, addition and subtraction of vectors, multiplication of vectors. Vector calculus: differentiation of vectors, Vector derivative operators(Basic concepts of gradient, divergence and curl).Coordinate systems in three dimensions (Cartesian, polar, spherical and their interconversion).

9.00
Unit III: 
Application of differential and integral calculus

Maximum and minimum values of functions of two variables. Extreme points and stationary points of a function, Euler’s theorem on homogenous function of two variable. Multiple integrals (Basic concepts of double and triple integral).Changeof order of double integration.

9.00
Unit IV: 
Differential Equations

Differential equations: Order and degree of differential equations, solution of first order and first degreedifferential equations with separable variables, homogeneous and linear differential equations, partial differential equation of first order PDE, types of integrals of a PDE, the integral of the Lagranje’s linear equation, solution of first order PDE using Charpit’s method.

9.00
Unit V: 
Complex Numbers

Complex numbers, complex plane, Argand diagram,complex conjugates, modulus of a complex number, square root of a complex number, Euler’s formula and polar form of complex numbers.

References: 
  • Mathematics for Physical Chemistry; Second Edition; McQuarrie, D. A.; University Science Books, 2008.
  • Mathematics for Physical Chemistry; Mortimer, R.. Fourth Edition. Elsevier, USA 2013.
  • The Chemical Maths Book; Second Edition Steiner, E. Oxford University Press, New York, 2011.
  • Chemical Calculations; Mathematics for Chemistry; Second Edition. Yates, P. CRC Press 2007.

 

Academic Year: 
2021-2022
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