Course Syllabus
Engineering Mathematics-I
Course Code: MAL 151
(L-T-P: 3-0-2), 4 Credits
Type of Course: Programme Core
Brief Syllabus
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Unit: 1 Ordinary Differential Equations and Applications Hours: |
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Exact differential equations, Equations reducible to exact differential equations. Applications of differential equations of first order & first degree to simple electric circuits, Newton's law of cooling, heat flow, and orthogonal trajectories. Linear differential equations of second and higher-order. Complete solution, Complementary function, and particular integral. Method of variation of parameters to find particular integral, Cauchy's and Legendre's linear equations. Simultaneous linear equations with constant co-efficient, Applications of linear differential equations to a simple pendulum, oscillatory electric circuits. |
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Unit: 2 Laplace Transforms and its Applications Hours: |
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Laplace transforms of elementary functions, Properties of Laplace transforms, Existence conditions. Transforms of derivatives, Transforms of integrals, Multiplication by t, Division by t. Evaluation of integrals by Laplace transforms. Laplace transform of a unit step function, Unit impulse function and periodic function, Inverse transforms, Convolution theorem, Application to linear differential equations and simultaneous linear differential equations with constant coefficients and applications to integral equations. |
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Unit: 3 Fourier Series and Fourier Transforms Hours: |
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Euler’s formulae, Conditions for a Fourier expansion. Change of interval, Fourier expansion of odd and even functions, Fourier expansion of square wave, Rectangular wave, Saw-toothed wave, Half and Full rectified wave, Half range sine, and cosine series. Fourier integrals, Fourier transforms, Shifting theorem (both on time and frequency axes), Fourier transforms of derivatives, Fourier transforms of integrals. Convolution theorem, Fourier transform of Dirac-delta function. |
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Unit: 4 Partial Differential Equations and Its Applications Hours: |
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Formation of partial differential equations (PDE). Lagrange’s linear partial differential equation, First-order non-linear partial differential equation, Charpit’s method. Method of separation of variables. |
Course Outcomes
CO 1 |
Solve 1st order and higher-order linear differential equations and their applications to scientific and engineering problems, e.g., LCR circuits, Heat flow, Simple pendulum, etc. |
CO 2 |
Understand the concept of Laplace transform and apply the method of Laplace transform to solve differential equations (both initial value and boundary value problems). |
CO 3 |
Determine Fourier series expansions of periodic functions including various waveforms and apply Fourier analysis to diverse problems in Physics, Engineering, Financial Mathematics, and other mathematical contexts. |
CO 4 |
Demonstrate capacity to model physical phenomena using PDEs (in particular using the heat and wave equations) and apply various methods to solve them. |
Text/Reference Books:
1. E. Kreyszig, “Advanced Engineering Mathematics”, John Wiley & Sons, 10th edition, 2015.
2. B. S. Grewal, “Higher Engineering Mathematics”, Khanna Publications, 43rd edition, 2010.
3. G. B. Thomas, R. L. Finney, “Calculus and Analytic Geometry”, Pearson Education, Asia, 9th edition, 2002.
4. Shanti Narayan, “A Text Book of Matrices”, S. Chand Limited, 2010.
Evaluation scheme:
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TYPE OF COURSE |
PARTICULAR |
ALLOTTED RANGE OF MARKS |
PASS CRITERIA |
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Theory (L-T-P/L-0-P) |
Minor Test |
25% |
Must Secure 30% Marks Out of Combined Marks of Major Test Plus Minor Test with Overall 40% Marks in Total. |
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Major Test |
45% |
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Continuous Evaluation Through Class Tests/Lab/Practice/Assignments/Presentation/Quiz |
20% |
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Online Quiz |
10% |
Course Summary:
| Date | Details | Due |
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