Students will be able to

1. Find maxima and minima of function of two variables.
2. Expand trigonometric terms.

Students will be able to

1. Describe the relation between roots and coefficients.
2. Transform the equation through roots multiplied by a given number.
3. Solve the reciprocal equations.

1. Describe the various forms of equation of a Plane, Straight line, Sphere, Cone  and Cylinder.
2. Find the angle between planes, Bisector planes, Perpendicular distance from a point to a plane, Image of a line on a plane and Intersection of two lines
3. Compute the angle between a line and a plane and length of perpendicular from a point to a line.

1. Explain properties of Beta functions.
2. Solve Basic Integral Calculus problems.
3. Explain properties of definite integrals.
4. Prove reduction formulae and solve some problems by using this formula.
5. Evaluate double and triple integrals

1. Extract the solution of differential equations of the first order and of the first degree by variables separable, Homogeneous and Nonhomogeneous methods.
2. Find a solution of differential equations of the first order and of a degree higher than the first by using methods of solvable for p, x and y.
3. Compute all the solutions of second and higher order linear differential equations with constant coefficients, linear equations with variable coefficients.
4. Solve simultaneous linear equations with constant coefficients and total differential equations.

1. Define subgroup, Center, Normalizer of a subgroup.
2. Find cycles and transpositions of a given permutations.
3. Prove Lagrange’s theorem, Euler’s theorem and Fermat’s theorem.
4. Define normal subgroups, quotient groups and index of a subgroup.
5. Understanding the concept of the rings and integral domain.

1. Understand different types of sequence.
2. Discuss the behavior of the geometric sequence.
3. Prove properties of convergent and divergent sequence.
4. Verify the given series is convergent or divergent by using different tests.

1. Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra
2. Use computational techniques and algebraic skills essential for the study of systems of linear equations matrix algebras, vector spaces, Eigen values, Eigen vectors, orthogonality and diagonalization.

1. Ability to compute the Fourier series of the function with one variable.
2. Understand the nature of the Fourier series that represent even and odd functions.
3. Understand the concepts of Fourier transforms to the real world problems of circuit analysis and control system design.
4. Apply z-transforms to solve the difference equation.

1. Learn the concepts for understanding and analyzing abstract mathematics on the metric space.
2. Acquire the knowledge of real functions, limit of functions and their properties.

1. Understand fundamental definitions of graph theory.
2. Learn a clear perspective of solving real life problems using graph theory.
3. Use a combination of theoretical knowledge and independent mathematical thinking for creative research in graph theory.

1. Develop a general understanding of the operation research methodology to decision making.
2. Identify best techniques to solve a specific problem in linear model of operation research.

1. Learn a sufficient exposure in constructing difference tables and to use newton’s forward and backward formula for interpolation in equal intervals.
2. Understand the numerical integration by using trapezoidal and Simpson’s rule.

1. Understand the importance of analytic function.
2. Demonstrate and understand the concepts in complex integration.

1. Understand the mathematical techniques to model and analyze decision problems with effective application to real life in optimization of objectives.
2. Formulate simple reasoning and learning optimization problems.
3. Analyze a problem and select a suitable strategy.
4. Apply an approximate method to obtain a solution for a problem.

1. Understand the concepts of statics and dynamics applicable in real life.
2. Acquire wide knowledge of handling problems related to mechanics.
3. Acquire sufficient knowledge for further studies in mechanics at a higher level.

1. Recall the basic concepts of divisibility.
2. Demonstrate renowned theorems in solving congruence.
3. Discuss on quadratic congruence equations.
4. Analyze various arithmetical functions.
5. Identify the numbers of special form and apply divisibility rules in solving Diophantine equations.

• Explain the fundamental concepts of algebraic structures.
• Demonstrate accurate and efficient use of ring theory.

• Acquire knowledge on the concepts of compact and connectedness
• Understand the base of Limit function and monotonic functions.

• Understand the advanced concepts in differential geometry of space curves.
• Acquire the knowledge for the study of surfaces leading to advanced courses in geometry

• Acquire the knowledge of mathematical techniques for solving higher order ODE.
• Understand the conditions for the existence and uniqueness of solution for initial and boundary value problems.

• Understand the concepts of Lioville’s function, bell series and Dirichlet multiplication.
• Acquire the skills to solve simultaneous congruence problems.

• Perform Algebraic operations on polynomial expressions.
• Identify the degree leading coefficient and leading term of a polynomial expression.

• Acquire the knowledge on the concept of some special functions.
• Realize that this course had laid the foundation for the variety of courses

• Understand the various concepts based on partial differential equations.
• Develop clear thinking and analyzing for solving problems in partial  differential equations.

• Acquire the knowledge of different distributions like beta, t and F.
• Understand standard concepts and methods of distributions.

• Gain an in-depth knowledge in the concept of fuzzy set theory.
• Acquire knowledge in solving fuzzy mathematical problems.

• Understand the various intrinsic concepts and the theory of complex analysis.
• Acquire the knowledge of analyticity and complex integration.

• Demonstrate an understanding of the concepts of metric spaces and topological spaces and their role in mathematics.
• Demonstrate familiarity with a range of examples of topological structures.

• Acquire fundamental knowledge of finding shortest paths.
• Develop the skills on five colour theorem and four colour conjecture.

• Work with the equations of motion using different principles.
• Understand the techniques involved in Hamilton’s principle.

• Understand basic theoretical and applied principles of statistics.
• Gain a thorough knowledge of applied statistics for problems solving.

• Understand the three structure theorems of functional analysis.
• Gain knowledge about Hilbert spaces.

• Prove basic results about completeness, compactness and connectedness within these structures.
• Understand the theory of complete metric spaces and function spaces.

• Develop few simple mathematical models and logical skill to problem solving.
• Acquire knowledge of queuing models.