MAT201 / Mathematics

Syllabus

245KB

MAT201-Syllabus-BTECH-IT.pdf

pdf

References

https://www.slideshare.net/slideshow/higher-engineering-mathematics-by-bs-grewal/65781053

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Resources

M1: Ordinary differential equations

• Equations of First Order and First Degree

  • Exact equations

  • Linear equations

  • Bernoulli’s equations

• Equations of First Order and Higher Degree

  • Equations solvable for p

  • Equations solvable for y

  • Equations solvable for x

  • Clairaut’s type

• Higher Order Linear Differential Equations

  • Constant coefficients

  • Second-order linear differential equations with variable coefficients

  • Method of variation of parameters

  • Solution by series method

M2: Partial Differential Equations

• Formation of Partial Differential Equations

• First Order Partial Differential Equations [Video 1-5 in Playlist]

  • Solutions of first-order linear PDEs

• Second Order Partial Differential Equations [Video 6 onwards in Playlist]

  • Homogeneous and non-homogeneous linear PDEs

  • Complementary function and particular integral method (constant coefficients)

• Non-linear Partial Differential Equations of First Order

  • Charpit’s method

• Separation of Variable Method

  • Solution of wave and heat equations

M3: Laplace Transform and Fourier series

• Laplace Transform

  • Introduction and Laplace transform of elementary functions

  • Properties

    • Change of scale property

    • Second shifting property

  • Laplace transform of derivatives

  • Inverse Laplace transform and its properties

  • Convolution theorem

  • Applications of Laplace Transform to Solve ODEs

• Fourier Series

  • Introduction to Fourier series

  • Fourier series for discontinuous functions

  • Fourier series for even and odd functions

  • Half-range series

M4: Complex Variable– Differentiation

• Function of a Complex Variable

• Differentiation and Analytic Functions

  • Cauchy-Riemann equations

  • Harmonic functions and finding harmonic conjugates

• Elementary Analytic Functions

  • Exponential

  • Trigonometric

  • Logarithmic

• Conformal Mappings

  • Mobius transformations and their properties

M5: Complex Variable– Integration

• Contour Integrals

• Theorems (Without Proof)

  • Cauchy-Goursat theorem

  • Cauchy Integral formula

  • Liouville’s theorem

  • Maximum-Modulus theorem

• Series Representations

  • Taylor’s series

  • Laurent’s series

• Analysis of Analytic Functions

  • Zeros

  • Singularities

• Residues and Applications

  • Cauchy Residue theorem (without proof)

  • Evaluation of definite integrals involving sine and cosine

  • Evaluation of certain improper integrals

Notes

[⤓] MAT201-Midsem-Short-Notes

[⤓] MAT201-Endsem-All-Modules-KeyNotes

Questions Directory

Previous Year Questions

[⤓] [PDF] MidSem-PYQ-MAT201-Apr24-Btech

[⤓] [PDF] EndSem-PYQ-MAT201-Jun22-Btech

[⤓] [PDF] EndSem-PYQ-MAT201-Jun23-Btech

[⤓] [PDF] EndSem-PYQ-MAT201-Jun24-Btech

External Sources

Differential Equation of First Order

https://youtube.com/playlist?list=PLT3bOBUU3L9g0aergP43HK9ihc_UG7Kbx&si=JUeJN52eWyvvobee

Ref: IITK Notes on Mathematics includes topics:

• Linear Algebra

• Ordinary Differential Equation

• Laplace Transform

• Numerical Application

URL: https://home.iitk.ac.in/~peeyush/102A/Lecture-notes.pdf

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