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S.No.
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SEMESTER
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COURSE
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CREDITS
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COURSE OUTCOMES
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1
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I
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Differential and Integral Calculus
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5
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- Understanding the derivative as a tool for analyzing the behavior of a function and its slopes.
- Applying differentiation techniques to a variety of functions, including polynomials, exponential, logarithmic, and trigonometric functions.
- Understanding the concept of integrals and how they can be used to find the area under a curve.
- Applying integration techniques to evaluate definite and indefinite integrals, including using substitution, integration by parts, and partial fraction decomposition.
- Understanding the connection between differentiation and integration, and how the two concepts can be used together to solve problems in physics, engineering, and other fields.
- Developing the ability to model real-world situations using mathematical concepts and techniques, and to interpret and communicate the results of mathematical models.
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2
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II
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Differential Equations
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5
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- Understanding of fundamental concepts and principles of differential equations: Students will gain a comprehensive understanding of the basic concepts, principles, and theories that form the foundation of differential equations.
- Ability to solve ordinary and partial differential equations: Students will develop the skills and techniques to solve various types of differential equations, including ordinary and partial differential equations.
- Knowledge of analytical methods for differential equations: Students will become familiar with analytical methods, such as separation of variables, Laplace transforms, and Fourier series, to solve differential equations.
- Familiarity with applications of differential equations: Students will learn how to apply differential equations to real-world problems, such as modeling physical and biological systems, solving engineering problems, and predicting financial markets.
- Understanding of the behavior of differential equations: Students will become familiar with the qualitative behavior of differential equations, such as stability, asymptotic behavior, and bifurcation.
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3
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III
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Real Analysis
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5
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- Understanding the basic concepts of real numbers and their properties
- Knowledge of different types of convergence, such as pointwise, uniform, and absolute convergence
- Ability to prove theorems and propositions using mathematical logic and techniques from Real Analysis
- Familiarity with various types of functions, such as continuous, differentiable, and integrable functions
- Understanding of the fundamental theorem of calculus
- Ability to analyze real-valued functions and their properties, including differentiability and integrability.
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4
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IV
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Algebra
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5
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- Understanding of Group theory: students will have a clear understanding of the theory of groups, including group operations, subgroups, cosets, normal subgroups, factor groups, homomorphisms, and isomorphisms.
- Knowledge of Ring theory: students will learn about rings, ideals, factor rings, ring homomorphisms, and ring isomorphisms.
- Familiarity with Field theory: students will learn about fields, extensions of fields, polynomial rings, and finite fields.
- Familiarity with Algebraic structures: students will learn about algebraic structures such as semi-groups, monoids, and lattices.
- Problem-solving skills: students will develop critical thinking and problem-solving skills by applying the concepts learned in the course to solve mathematical problems.
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5
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V
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Linear Algebra
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5
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- Understanding of linear systems of equations: Students will be able to solve and analyze systems of linear equations, including eigenvalue and eigenvector computations.
- Matrix algebra: Students will be able to perform matrix operations, including multiplication, inversion, and diagonalization.
- Vector spaces: Students will be able to understand the concept of vector spaces and perform operations within them, including linear combinations and subspaces.
- Orthogonality and Gram-Schmidt process: Students will understand the concepts of orthogonal and orthonormal sets and be able to perform the Gram-Schmidt process.
- Linear transformations: Students will understand linear transformations and be able to perform computations, including computing matrices, eigenvectors, and eigenvalues.
- Inner products and norms: Students will be able to understand and use inner products and norms, and understand the properties of norms and the Cauchy-Schwarz inequality.
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6
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VI
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Solid Geometry
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5
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- Understanding of the basic principles and concepts of analytical solid geometry.
- Ability to apply mathematical concepts to solve geometric problems.
- Ability to visualize and manipulate 3-dimensional objects and their projections.
- Knowledge of the properties of lines, planes, and intersections of geometric objects.
- Ability to use the Cartesian coordinate system to describe the positions of objects in space.
- Understanding of the applications of solid geometry in engineering, physics, and other scientific fields.
- Improved problem-solving skills and critical thinking abilities.
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