##### 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.