TTWRDC (G), JANAGAON

COURSE OUTCOMES

(2024-2025)

Semester I

Differential and Integral Calculus

• The main Objective of Differential and Integral Calculus is to focus on rate of change concepts such as derivatives, limits, functions with single variable and two variable differentiations and also understand integrals, finding area using surfaces and volume integration.
•  It is also provides a Mathematical foundation and modeled to solve the problem in Various fields

 

Semester II

Differential Equations

• The main Objective of Differential Equations course is to equip students with a strong foundation in the theory and applications of Differential Equations
• To Grasp fundamental concepts like order, degree and different types of differential equations
• Learn various methods for solving ordinary differential equation and partial differential equations
• To develop analytical skills to analyze type of different equations like exact, homogeneous, non homogeneous etc.
• Work with systems of differential equations of higher order and solve to acquire solutions which can apply in various fields.
• Master various analytical techniques for solving differential equations such as variable separable methods.
• Enhance critical thinking skills by formulating and solving problems using differential equations

 

SEMESTER III

Real Analysis

• The course outcome related to rigorous study of Real number system including ordered and completeness axiom.
• Sequences and series –Analysing the convergence and divergence properties.
• By applying distinguished tests we can analyze the sequence and series nature.
• It also demonstrates the complete relation of sequence by using Bolzano Weistrass theorem.
• Understanding the concepts of Limits, Continuity and differentiability of real valued functions.
• Explore the concepts of Differentiation and integration including some basic theorems like fundamental theorem of Calculus.
• Study of Power series, its properties, representation in terms of Taylor’s series, Maclaurins series..
• Develop a deep understanding the properties of integrals under Riemann Sums by using Partition of intervals.
• Learn and apply integration techniques, applying Riemann integration to find area and volumes.
• Investigate the convergence and divergence of improper integral.
• It effectively communicate, recognize and articulate connection between Riemann integration and other concepts in science and engineering fields.

 

Semester IV

                                                              Algebra

In an Algebra Course

• Students are expected to achieve several learning outcomes related to fundamental concepts and applications of algebra.

• Proficiency in fundamental concepts including elementary properties and factoring the concepts internally
• Definitions of subgroups, ability to identify the construction of subgroups and analyze subgroup understand the importance in group theory.
• Understanding and establishing isomorphism, properties of Cayley’s theorem, familiarity with Lagrange’s theorem and its consequence. .
• Mastery of application of Cosets to Permutation group, including Rotation group, Normal subgroups and application of Factor groups.
• Understanding Group Homomorphism and with their specific properties.
• These outcomes collectively aim to provide deep understanding of all concepts related to a algebraic structure.

Semester V

Linear Algebra

• In a Linear Algebra course students are expected to achieve specific learning outcomes related to concepts and applications of Linear Algebra.
• It demonstrates a thorough understanding of vector space, Subspaces, Null Spaces, Column Spaces including properties like closure, commutative and scalar multiplication.
• Identify linearly independent and linearly dependent set of vectors and also understands the construction of bases.
• To analyze the concept of dimension of vector space, its rank and nullity.
• Understand and articulate the concepts of Eigen values and Eigen vectors. And also extended to their application in vector fields.
• Diagonalize the conditions of a Matrix under which diagonalization are possible to represent Linear Transformation.
• Hence this course is aimed to equip students with a solid foundation in Linear Algebra providing them with essential tools for further education in Mathematics.

Semester VI

Numerical Analysis

    Numerical Analysis Courses cover

• Various topics related to numerical methods and algorithms for solving mathematical problems. The Outcomes are
•      Students can gain a strong understanding of numerical techniques such as solving of equations in one variable using different methods.
•      Ability to apply numerical methods for proficiency in analyzing and finding roots , managing errors intent in numerical calculations under error analysis, including both rounding and termination errors.
•      Understanding of numerical techniques such as interpolation and Polynomial approximation.