DEPARTMENT OFMATHEMATICS
COURSE OUTCOME
SEMESTER TITLE OF THE COURSE

LEARNING OUTCOME

At the end of the course the students will be able to:

 

 

I SEMESTER

 

MAT1.1

Matrices, Differential calculus, Integral calculus, Theory of equations

 

 

·        Relate an augmented matrix to a system of linear equations.

·        Apply the Cayley-Hamilton Theorem to compute powers of a given square matrix.

  • Compute limits, derivatives, and definite & indefinite integrals of algebraic, logarithmic and exponential functions.
  • Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution.
  • Applied to solve higher degree polynomials.

 

 

 

 

II SEMESTER

 

 

 

MAT 2.1

Groups, Differential Calculus, Integral Calculus, Differential equations-I

 

·        Construct and describe groups. They will learn basic properties of groups and get familiar with important classes of groups. They will understand the crucial concept of simple groups.

  • Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.

·        Develop the ability to apply differential equations to significant applied and/or theoretical problems

 

 

III SEMESTER

MAT3.1

Groups, Sequences and Series of Real Numbers, Differential Calculus

·        Understand the proof, statement and simple uses of Lagrange’s Theorem.

·        Recognize the embedded infinite geometric series in geometric applications.

·        Understand the consequences of the intermediate value theorem for continuous functions.

 

 

 

 

IV SEMESTER

 

 

MAT4.1

Groups, Fourier series, Mathematical Methods-I, Differential Equations-II

·        Demonstrate familiarity with permutation groups and be able to decompose permutations into 2-cycles. Familiar with Fourier series and their applications and be notionally aware of their convergence.

·        Laplace transforms is used to simplify calculations in system modeling.

·        Demonstrate an understanding of solution techniques for second and higher order differential equations; be familiar with qualitative tools for linear equations applications.

 

 

 

 

 

 

V SEMESTER

 

 

 

 

MAT5.1

Rings, Integral domains, Fields, Vector Differentialcalculus,

Numerical methods-I

 

·        Demonstrate familiarity with some of the applications of algebra to other fields, e.g. cryptography.

  • Apply derivative concepts to find tangent lines to level curves and to solve optimization problems.
  • Analyze the error incumbent in any such numerical approximation.

MAT5.2

Calculus of variation, Line and multiple integral, Integral theorems

·        Compute the curl and the divergence of vector field.

·        Apply triple integrals to find volumes and center of mass.

·        Compute the area of parametric surfaces in 3-dimensional space.

 

 

 

 

VI SEMESTER

 

 

MAT6.1

Linear algebra, PDE

 

·        Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization.

·        Be familiar with the modeling assumptions and derivations that lead to PDEs.

 

 

MAT6.2

Complex analysis, Numerical methods-II

 

·        Applications in many scientific areas, including signal processing, control theory, electro magnetism etc.

·        Implement a variety of numerical algorithms using appropriate technology.