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MATHEMATICS FOR COMPUTER ENGINEERING & INFORMATION TECHNOLOGY
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GANPAT UNIVERSITY |
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FACULTY OF ENGINEERING & TECHNOLOGY |
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Programme |
Bachelor of Technology |
Branch/Spec. |
Computer Engineering/Information Technology/ Computer Engineering (Artificial Intelligence) |
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Semester |
IV |
Version |
2.0.0.1 |
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Effective from Academic Year |
2023-24 |
Effective for the batch Admitted in |
July 2022 |
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Subject code |
2BS4101 |
Subject Name |
Mathematics for Computer Engineering & Information Technology |
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Teaching scheme |
Examination scheme (Marks) |
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(Per week) |
Lecture (DT) |
Practical (Lab.) |
Total |
CE |
SEE |
Total |
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L |
TU |
P |
TW |
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3 |
1 |
0 |
0 |
4 |
Theory |
40 |
60 |
100 |
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Hours |
3 |
1 |
0 |
0 |
4 |
Practical |
0 |
0 |
0 |
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Pre-requisites: |
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Basic knowledge of Differentiation, Integration and Differential Equations. |
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Course Outcome (COs): |
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CO |
Description |
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CO1 |
Express physical phenomenon in Fourier Series & Laplace Transforms. |
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CO2 |
Solve Complex integrations. |
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CO3 |
Use basic knowledge of Numerical techniques and their applications in CE & IT to cater various problems |
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Theory syllabus |
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Unit |
Content |
Hrs |
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1 |
Laplace Transforms Definition, Laplace transform of elementary functions, Formulas of Laplace transform, Inverse Laplace transforms, Properties: Laplace transform of derivatives, Laplace transform of integration. Multiplication by tn, Division by t, Convolution theorem, Unit step and Heaviside’s unit function, Dirac-delta function, Application of Periodic functions to solve ordinary linear differential equations. |
10 |
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2 |
Fourier Series Definition of periodic function, Euler’s formula, Functions having points of discontinuity, Change of intervals, Odd and even functions, Expansion of odd and even periodic functions, Half range sine and cosine series and their applications. |
08 |
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3 |
Fourier Transforms Definition, Fourier integral, Fourier sine and cosine integration, Complex form of Fourier integral, Fourier sine transform, Fourier cosine transform, Inverse Fourier transforms , Application of Fourier transform in computer engineering & Information technology . |
05 |
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4 |
Theory Of Complex Variables Analytic functions, Cauchy-Riemann Equations, Necessary and Sufficient condition for analyticity, Properties of Analytic Functions, Laplace Equation, Harmonic Functions, Finding Harmonic Conjugate functions Exponential, Trigonometric, Hyperbolic functions and its properties, Line integral, Cauchy’s theorem and Cauchy’s integral formula, Application of the solution of two-dimensional problems for Simple form of conformal transformation. |
10 |
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5 |
Numerical Methods Roots of algebraic equations, Solution of linear simultaneous equations, Numerical differentiation and Numerical integration, Numerical methods to solve first order & first degree ordinary differential equations. |
08 |
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6 |
Finite Differences And Difference Equations Finite differences interpolation, Newton’s and LaGrange’s formula, Difference equation with constants co-efficient, Solution of ordinary and partial differential equations with boundary conditions by finite difference method. |
04 |
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Practical content: |
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Assignments and tutorials are based on the above syllabus. |
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Text Books |
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1. |
Higher engineering mathematics. By B.S.Grewal. |
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2. |
Advanced engineering mathematics By Erwin Kreyzing |
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3. |
Computer Oriented Statistical and Numerical Methods By E.Balagurusamy,TMH |
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Reference Books |
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1. |
Dr. K. R. Kachot, “Higher Engineering Mathematics”, Vol.2, Mahajan Publication. |
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2. |
Engineering mathematics. By Srivastava. |
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3. |
Textbook of engineering mathematics By A.B.Mathur and V.P.Jaggi. |
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4. |
Introductory Methods in Numerical Analysis By S.S.Sastry |
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ICT/MOOCS |
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1. |
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2. |
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3. |
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4. |
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5. |
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6. |
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7. |
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8. |
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9. |
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10 |
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Mapping of CO-PO and CO-PSO: |
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PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
PSO1 |
PSO2 |
PSO3 |
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CO1 |
1 |
0 |
1 |
1 |
1 |
0 |
2 |
0 |
2 |
1 |
2 |
1 |
2 |
1 |
1 |
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CO2 |
2 |
1 |
0 |
1 |
2 |
3 |
2 |
2 |
1 |
1 |
1 |
2 |
2 |
1 |
1 |
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CO3 |
3 |
2 |
1 |
2 |
2 |
1 |
3 |
0 |
2 |
1 |
2 |
1 |
2 |
2 |
1 |
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