### DEPARTMENT OF MATHEMATICS

The Department of Mathematics was established in MVJCE in Bangalore in the year 1982 with the objective of imparting quality education in the field of Mathematics. Since Mathematics is the back bone of Science, Engineering and Technology. The department tries hard to develop the students in the fundamental concepts of mathematics to shine in their respective fields of engineering. The Department of Mathematics also has expertise in various fields of Applied Mathematics which has enabled them to teach several subjects pertaining to mathematics and its applications like Graph Theory, Discrete Mathematics for Under Graduate Courses and Numerical Methods, Advanced Mathematics, Optimization Techniques, Applied Mathematics and Probability and Random Process for Post Graduate Courses.

### VISION OF THE DEPARTMENT

Department of Mathematics strives to be recognized for academic excellence through the depth of its teaching and research. It will distinguish itself as a regional leader in higher education for teaching. The department strives to earn regional recognition for its expertise in the field of Mathematics and the teaching of Mathematics. We will be a source for the promotion of problem solving, analytical thinking and utilizing technology.

### MISSION OF THE DEPARTMENT

- Making engineers to develop Mathematical thinking where students can learn and become competent users of Mathematics and Mathematical application.
- To interweave real world experiences and practical life skills with the applications of Mathematics.
- We achieve this through an innovative curriculum.
- We, the faculty, collaborate with other researchers in solving engineering and scientific problems.

### COURSES TAUGHT

- Engineering Mathematics – I
- Engineering Mathematics – II
- Engineering Mathematics – III
- Engineering Mathematics – IV
- Discrete Mathematical Structures

### COURSE OUTCOMES:

**Engineering Mathematics – I**

On completion of this course, students are able to

C101.1 | Use nth derivative of product of two functions and to visualize and calculate the area between two polar curves. |

C101.2 |
Use partial derivatives to calculate rates of change of multivariate functions |

C101.3 |
Analyze position, velocity, and acceleration in two or three dimensions using the calculus of vector valued functions. |

C101.4 |
Recognize and solve first-order ordinary differential equations, Newton’s law of cooling |

C101.5 |
Use matrices techniques for solving systems of linear equations in the different areas of Linear Algebra. |

**Engineering Mathematics – II**

On completion of this course, students are able to,

C109.1 | solve differential equations of electrical circuits, forced oscillation of mass spring and elementary heat transfer. |

C109.2 | solve partial differential equations fluid mechanics, electromagnetic theory and heat transfer. |

C109.3 | Evaluate double and triple integrals to find area , volume, mass and moment of inertia of plane and solid region. |

C109.4 | Use curl and divergence of a vector valued functions in various applications of electricity, magnetism and fluid flows. |

C109.5 | Use Laplace transforms to determine general or complete solutions to linear ODE |

** **

**Engineering Mathematics – III**

**Course Outcomes: **On completion of this course, students are able to:

C201.1 | Know the use of periodic signals and Fourier series to analyze circuits and system communications. |

C201.1 |
Explain the general linear system theory for continuous-time signals and digital signal processing using the Fourier Transform and z-transform. |

C201.1 |
Employ appropriate numerical methods to solve algebraic and transcendental equations. |

C201.1 | Apply Green’s Theorem, Divergence Theorem and Stokes’ theorem in various applications in the field of electro-magnetic and gravitational fields and fluid flow Problems. |

C201.1 | Determine the extremals of functionals and solve the simple problems of the calculus of variations. |

**Engineering Mathematics – IV**

On completion of this course, students are able to:

C209.1 | Use appropriate single step and multi-step numerical methods to solve first and second order ordinary differential equations arising in flow data design problems. |

C209.2 | Explain the idea of analyticity, potential fields residues and poles of complex potentials in field theory and electromagnetic theory. |

C209.3 | Employ Bessel’s functions and Legendre’s polynomials for tackling problems arising in continuum mechanics, hydrodynamics and heat conduction. |

C209.4 | Describe random variables and probability distributions using rigorous statistical methods to analyze problems associated with optimization of digital circuits, information, coding theory and stability analysis of systems. |

C209.5 | Apply the knowledge of joint probability distributions and Markov chains in attempting engineering problems for feasible random events. |

**Discrete Mathematical Structures:**

After studying this course, students will be able to:

C204.1 | Verify the correctness of an argument using propositional and predicate logic and truth tables. |

C204 .2 | Demonstrate the ability to solve problems using counting techniques and combinatorics in the context of discrete probability. |

C204 .3 | Solve problems involving recurrence relations and generating functions. |

C204 .4 | Construct proofs using direct proof, proof by contraposition, proof by contradiction, proof by cases, and mathematical induction. |

C204 .5 | Explain and differentiate graphs and trees |

**Graduate Attributes (as per NBA)**

- Engineering Knowledge
- Problem Analysis
- Conduct Investigations of Complex Problems

### RESEARCH AND DEVELOPMENT

Department of Mathematics is actively involved in the research activities. The Department consists Four Part-time Ph.D candidates:

- Sampoorna. V : Area of research is Homotopy Analysis. She has cleared the Course work and currently doing the literature survey. Also she has published one research paper in Homotopy analysis.
- Naveen Bala. A : Area of research is Fluid Dynamics (Stretching the sheets and cylinders ). He has cleared the Course work and currently doing the literature survey.
- Raghu. N : Area of research is Fluid Dynamics (Conviction of Di-electric fluid ). He has cleared the Course work and currently doing the literature survey.
- S. Sowmya: Area of research is Graph theory