Mathematics

Mathematics


Course Outcomes

 


 

COURSE 1: ESSENTIALS AND APPLICATIONS OF MATHEMATICAL, PHYSICAL ANDCHEMICAL SCIENCES

 

  • Apply critical thinking skills to solve complex problems involving complex numbers, trigonometric ratios, vectors, and statistical measures.

  • To Explain the basic principles and concepts underlying a broad range of fundamental areas of physics and to Connect their knowledge of physics to everyday situations

  • To Explain the basic principles and concepts underlying a broad range of fundamental areas of chemistry and to Connect their knowledge of chemistry to daily life.

  • Understand the interplay and connections between mathematics, physics, and chemistry in various applications. Recognize how mathematical models and physical and chemical principles can be used to explain and predict phenomena in different contexts.

  • To explore the history and evolution of the Internet and to gain an understanding of network security concepts, including threats, vulnerabilities, and countermeasures.


 


 


 

COURSE 2: ADVANCES IN MATHEMATICAL, PHYSICALAND CHEMICAL SCIENCES

 

  • Explore the applications of mathematics in various fields of physics and chemistry, to understand how mathematical concepts are used to model and solve real-world problems.

  • To Explain the basic principles and concepts underlying a broad range of fundamental areas of physics and to Connect their knowledge of physics to everyday situations.

  • Understand the different sources of renewable energy and their generation processes and advances in nanomaterials and their properties, with a focus on quantum dots. To study the emerging field of quantum communication and its potential applications. To gain an understanding of the principles of biophysics in studying biological systems. Explore the properties and applications of shape memory materials.

  • Understand the principles and techniques used in computer-aided drug design and drug delivery systems, to understand the fabrication techniques and working principles of nanosensors. Explore the effects of chemical pollutants on ecosystems and human health.

  • Understand the interplay and connections between mathematics, physics, and chemistry in various advanced applications. Recognize how mathematical models and physical and chemical principles can be used to explain and predict phenomena in different contexts.

  • Understand and convert between different number systems, such as binary, octal, decimal, and hexadecimal. Differentiate between analog and digital signals and understand their characteristics.Gain knowledge of different types of transmission media, such as wired (e.g., copper cables, fiber optics) and wireless (e.g., radio waves, microwave, satellite).


 

COURSE 3: DIFFERENTIAL EQUATIONS

 

  • solve first order first degree linear differential equations.

  • convert a non-exact homogeneous equation to exact differential equation by using an integrating factor.

  • know the methods of finding solution of a differential equation of first order but not of first degree.

  • solve higher-order linear differential equations for both homogeneous and non-homogeneous, with constant coefficients.

  • understand and apply the appropriate methods for solving higher order differential equations.


 

COURSE 4: ANALYTICAL SOLID GEOMETRY

 

  • understand planes and system of planes

  • know the detailed idea of lines

  • understand spheres and their properties

  • know system of spheres and coaxial system of spheres

  • understand various types of cones

 

 

COURSE 5: GROUP THEORY

 

  • acquire the basic knowledge and structure of groups

  • get the significance of the notation of a subgroup and cosets.

  • understand the concept of normal subgroups and properties of normal subgroup

  • study the homomorphisms and isomorphisms with applications.

  • understand the properties of permutation and cyclic groups

 

 

COURSE 6: NUMERICAL METHODS

 

  • solve Algebraic and Transcendental equations

  • Understand various finite difference concepts and interpolation methods

  •  understand the subject of various numerical methods that are used to obtain approximate solutions

  • understand the concept of Curve fitting

 

COURSE 7: LAPLACE TRANSFORMS

 

  • understand the definition and properties of Laplace transformations

  • get an idea about first and second shifting theorems and change of scale property

  • understand Laplace transforms of standard functions like Bessel, Error function etc

  • know the reverse transformation of Laplace and properties

  • 5. get the knowledge of application of convolution theorem

 

 

 

 

COURSE 8: SPECIAL FUNCTIONS

 

 

  • Understand the Beta and Gamma functions, their properties and relation between these two functions, understand the orthogonal properties of Chebyshev polynomials and recurrence relations.

  • Find power series solutions of ordinary differential equations.

  • Solve Hermite equation and write the Hermite Polynomial of order (degree) n, also Find the generating function for Hermite Polynomials, study the orthogonal properties of Hermite Polynomials and recurrence relations.

  • Solve Legendre equation and write the Legendre equation of first kind, also find the generating function for Legendre Polynomials, understand the orthogonal properties of Legendre Polynomials.

  • Solve Bessel equation and write the Bessel equation of first kind of order n, also find the generating function for Bessel function understand the orthogonal properties of Bessel unction.

 

 


COURSE 9: RING THEORY

 

 

  • acquire the basic knowledge of rings, fields and integral domains

  • get the knowledge of subrings and ideals

  • construct composition tables for finite quotient rings

  • study the homomorphisms and isomorphisms with applications.

  • get the idea of division algorithm of polynomials over a field.

 

COURSE 10: INTRODUCTION TO REAL ANALYSIS

 

  • get clear idea about the real numbers and real valued functions.

  • Know the geometrical interpretation of meanvalue theorems.

  • know about the fundamental theorem of integral calculus

 


COURSE 11: INTEGRAL TRANSFORMS WITH APPLICATIONS

 

  • understand the application of Laplace transforms to solve ODEs
  • understand the application of Laplace transforms to solve Simultaneous DEs

  • understand the application of Laplace transforms to Integral equations

  • basic knowledge of Fourier-Transformations

 

 

 

COURSE 12: LINEAR ALGEBRA

 

  • understand the concepts of vector spaces, subspaces
  • understand the concepts of basis, dimension and their properties

  • understand the concept of linear transformation and its properties

  • apply Cayley- Hamilton theorem to problems for finding the inverse of a matrix and higher powers of matrices without using routine methods

  • learn the properties of inner product spaces and determine orthogonality in inner product spaces.

     

 

COURSE 13: VECTOR CALCULUS

  • Learnapplicationsintermsoffindingsurfaceareabydoubleintegralandvolumebytripleintegral
  • Determine the gradient, divergence and curl of a vector and vector identities.
  • Evaluateline, surface and volume integrals.
  • understand relation between surface and volume integrals (Gauss divergence theorem),relation between lineintegral and volumeintegral (Green’stheorem),relation between line and surface integral (Stokestheorem)