Department of Mathematics

Syllabus

Course Outcome

Theory

I Sem MAT.T1-1

CO1.1 Row reduced echelon form, normal form is introduced to help in solving the system of equations using matrix method supplemented with free mathematical software. The mathematical software helps the students in completing the projects/real world problem with ease.

CO1.2 The continuation of the chapter Differential calculus I from II PUC level, helps them to learn the differentiation at higher orders and the partial derivatives which help them to learn the basics concepts of higher mathematics.

CO1.3 The continuation of calculus to continuity, discontinuity, related topics through the mean value theorems their proofs, examples and verifying the same through the mathematical software like maxima and Scilab as a practical component. The introduction of Taylor’s series and Maclurin’s series completes the chapter.

C01.4 Introduction to Number theory gives us an experience of fun with numbers, their importance and rich heritage apart from a thorough understanding of the basic tools of pure mathematics that is groups introduced in the II Semester.

II Sem MAT.T2-2

CO2.1 Introduction to the polar co-ordinates, helping them to look at the polar tangents, related things, helpful in tracing the curves. Visualizing the curves, and exploring the nature area, volume. etc. through the mathematical software is a matter of hands-on session to the students creating a research culture, which is a necessary in today’s world.

CO2.2 The continuation of Integral calculus from II PUC level helps them to apply the awesome reduction formulae and enjoy the rate at which the example gets reduced so instantly. Visualizing the curves, and exploring the nature area, volume, etc. through the mathematical software is a matter of hands-on session to the students creating a research culture, which is a necessary in today’s world.

CO2.3 Sequence of real numbers is an important concept in pure mathematics wherein they come across various types of sequences, their nature in different contexts, various theorems to help in discussing their nature. Later, this helps the students in learning the chapter series, of equal importance in pure mathematics.

CO2.4 The continuation of Differential equations from II PUC, intentionally introduced to like, learn, enjoy solving the types of first order differential equations, understand them by plotting graphs in mathematical software, termed as FOSS tools. The above chapter helps them in projects in mathematical biology and interpreting the real-world problem in interdisciplinary areas

III Sem MAT.T3-3

CO3.1 Group theory involves basic concepts of abstract mathematics and related concepts, a must for students inclined towards pure mathematics.

CO3.2 After the ode of first order in the previous semester , the third semester syllabus has higher order differential equations specially of order 2 and 3 to find the solutions in various types and explore the vastness of differential equations. To conclude, the simultaneous differential equations and their solutions, followed by total and simultaneous differential equations and their solutions.

CO3.3 Series of real numbers involves finding of the nature of series by various methods through several theorems and most fascinating summation of different series.

CO3.4 Introduction to basics of statistics. The interpretation of statistical data is studied through the concepts of correlation and regression. The above is also available as a lab component under the FOSS tool R – programming.

IV Sem MAT.T4-4

CO4.1 Group theory incorporates, the further topics like order of an elements involved in understanding cyclic groups, theorems, variety of examples to understand the above said abstract concepts.

CO4.2 Analysing the curves, limits of integration through the sketches of the different curves to solve double and triple integration. They have their applications in finding the area, surface area and volume. The visualization of the above in mathematical software is commendable.

CO4.3 Integral theorems helps in connecting line integrals, surface integrals and volume integrals. Has wide applications in engineering mathematics.

CO4.4 Discrete and Continuation distributions are introduced to solve some simple problems. Students develop critical computing knowledge with statistics which helps them in taking up projects an internship in data analysis. The above is also available as a lab component under the FOSS tool R – programming.

V Sem MAT.T5-5

CO5.1 The definition of the algebraic structure ring, examples, theorems and concepts related to the same are studied. The above are vital concepts in abstract algebra have wide applications in various fields of science. The lab component in the above is an appreciable approach.

CO5.2 Introduction to different types of PDE, general form (Clairaut’s equation). Solutions of Heat and wave equation and verifying the same with soft wares is a part of the lab component.

CO5.3 Improper integral throws light on beta and gamma functions which are very special, simple, easy to learn and apply while integrating a certain set of integrals. These integrals are also involved in Laplace transforms, which is a part of their syllabus for next sem. Also helps students to score better amidst the topic in pure mathematics.

V Sem MAT.T6-5

CO6.1 Differential calculus for scalar and vector fields helps in understanding the mathematical physics and hence an interdisciplinary approach trend is set for the students.

CO6.2 Fourier series and transforms helps us in understanding that the given function can be expressed as a sum of sine and cosine functions or one of them in a given interval. The plotting of the same and visualizing the graph in different angles is a practical component. Its applications are left to the students for topics of project. The Fourier transform are also a part of the conclusion of the chapter.

CO6.3 Mathematical modelling is introduced to highlight interdisciplinary approach to solve real world problem and interpret the same using mathematical software and promote research culture in students.

VI Sem MAT.T7-6

CO7.1 The topic linear algebra has concepts of vector spaces, properties, examples, theorems, transformation, different types, examples, changing the transformation into matrices and vice versa. The same can be visualizes using the software maple (trial version). The above has applications in image processing.

CO7.2 Numerical methods involves forward differences, finite differences, interpolation, numerical differentiation, and integration. For certain examples where integration is not possible, numerical integrations are made use of in obtaining approximation solutions.

CO7.3 The numerical solutions of algebraic, transcendental and non - linear PDE by various methods and program for the same helps the students to do projects and motivates the young mind to the research culture and higher studies.

VI Sem MAT.T8-6

CO8.1 The harmonic function and the transformation, help in solving a lot of problems in engineering mathematics and projects. The above also form a part of the lab component.

CO8.2 Mathematical methods involves the definition, properties, problems, and related concepts. Its application in solving differential equations of first order and second order involving is a part of the lab component.

Practical

I Sem MAT.P1-1

• Introducing the free open source soft-wares namely SCILAB and MAXIMA.
• To execute program using scilab for verifying the solutions worked out manually for the  problems involving matrices under the chapter algebra.

          The above helps the students to use the software while solving real world problem.

• To execute program using maxima for verifying the solutions worked out manually for the  problems under the chapter differential calculus.

II Sem MAT.P2-2

• Executing program using scilab to visualize the various cartesian and polar curves and their properties.
• Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter sequences, differential calculus and differential equations.

III Sem MAT.P3-3

• Introducing the free open source software R and R studio.
• Executing program using scilab for verifying the solutions worked out manually for the problems under the chapter group theory.
• Executing program to verify the solutions worked out manually for the problems under the chapter series and differential calculus using maxima.
• Executing R programming for verifying the solutions worked out manually for the problems under Statistics.

IV Sem MAT.P4-4

• Executing program using scilab for problems under the chapter group theory.
• Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter multiple integrals and integral theorem.
• Executing R programming for verifying the solutions worked out manually for the problems under Statistics.

V Sem MAT.P5-5

• Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter rings & fields and partial differential equations.

V Sem MAT.P6-5

• Demonstration of differential calculus of scalar & vector fields and Fourier series and transformations using free software maxima.

VI Sem MAT.P7-6

• Solving algebraic and transcendental equations through the mathematical software scilab.
• Executing program using maxima for verifying the solutions worked out manually for the problems under the chapter linear algebra.

VI Sem MAT.P8-6

• Executing program using maxima for verifying the solutions worked out manually for the problems under complex analysis and mathematical modelling.

Reports

Groups