Mathematics Course Outcome

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 Differential calculus,
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.

VI SEMESTER

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.