Syllabus
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Course Code: B-MAT 507 Course Name: Practical -V |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | a) Problem Solving- Questions related to the following problems will be solved and record of those will be maintained in the Practical Notebook: Linear Algebra; 1. Practical problems to obtain basis by extending a given set of linearly independent set of vectors. 2. Practical problems to determine matrix representation of a linear transformation and to determine its rank and nullity. 3. Practical problems to determine Eigen Values & Eigen Vectors of a Linear Transformation. 4. Practical problems to find Dual of a Vector Space. 5. Practical problems to determine minimal polynomial of a linear transformation. 6. Practical problems to find orthogonal basis using Gram-Schmidt orthogonalisation process. 7. Practical problems to diagonalise symmetric matrices. 8. Practical problems to determine Jordan Canonical Form of a matrix. OR PDE and Integral Transforms; 1. Practical problems to reduce PDEs into canonical form and then solving those. 2. Practical problems of finding the characteristics of second order partial differential equations. 3. Practical problems to solve PDEs with Monge’s method. 4. Practical problems to solve wave equation (one and two dimensional). 5. Practical problems to solve Laplace equation. 6. Practical problems to solve heat equation. 7. Practical problems to solve differential equations by Laplace transform method. 8. Practical problems to solve differential equations by Fourier transform method. |
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| 2 | b) LATEX Practicals- Following practicals of typing documents using LATEX software
will be done and records of those will be maintained in the practical notebook and the
candidates will be asked by the examiner to type a document using more than one of
these listed commands at the time of Semester end practical examination: 1. Create a new file in the work directory with the name note1.tex and to write a simple document in latex using following commands: \documentclass [a4paper, 12pt]{article} \begin{document} A paragraph of text \end{document} 2. Create a document to write code for a title page using \title{...}, \author{...}, \date{...}, \today{...}, \maketitle {...} commands and \emph{...}, \texbf{...}, \texit{...} etc. commands. 3. Create a document to write a code to using \section{...}, \subsection{...}, \subsubsection{...}, \paragraph{...}, \subparagraph{…} commands and using environments to left justify, right justify, center and justify text. 4. Create a document to illustrate Latex commands for paper size, font size, font types and styles. 5. Create a document involving the mathematical equations. Use of $...$ and $$...$$ symbols and use of Power and Indices( ^, _ ), Fractions(\frac{numerator}{denominator}), Roots( \sqrt{...}, \sqrt[…]{...}), Sums (\sum_{…}^{…}{…}), Product (\prod_{…}^{…}{…}), Integral (\int_a^b f(x) dx) within $...$ or $$...$$ symbols. 5. Use of commands for Greek letters and the commands \Re, \Im, \partial, \infty, \forall, \exists, \prime, \emptyset, \nabla, \surd,\parallel, \angle, \triangle, \backslash, \div, \vee, \wedge, \cap, \cup, \propto, \perp, \cong for Mathematical symbols and operations. 6. Use of \pm, \mp, \setminus, \cdot, \times,\ast, \hat, \bar,\dot, \ddot, \vec, \leq, \geq, \subset, \supset, \subseteq, \supseteq, \in, \neq,\equiv, \sim, \simeq, \approx commands for mathematical symbols and operators. 7. Create a document to produce equations using \begin{equation} … \end{equation} command and involving mathematical symbols, Greek letters and fractions. 8. Create a Latex document to illustrate the effect of enumerate listing and itemize listing. |
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