MT-232 Advanced Calculus & Transformations

MT-232 ADVANCED CALCULUS & TRANSFORMATIONS

CREDIT HOURS

Theory = 2
Practical = 0

COURSE LEARNING OUTCOMES (CLOs)

COURSE CONTENT

Advanced calculus: Stationary point of a function of several variables, extreme value, and point of inflexion, partial derivatives of simple functions of two or more variables, double and triple integrations with applications (area, centroid, moment of inertia, surface area, and volume, use multiple integrals in solutions of engineering problems.
Vector Calculus: Vector differential operator, directional derivative, gradient, divergence, curl of a vector Field, and-Laplacian operators with applications, (Solenoid, conservative, etc).Vector Integrations; line integrals, apply line integrals to calculate work done, Green'stheorem in the plane, surface integrals, Jacobian transformation, Gauss divergence theorem and Stokes' theorem with applications in relevant engineering discipline.
Transformations: Laplace transforms and inverse transforms, shifting theorems, Laplace transform of the nth order derivative, Laplace transform of integrals, convolution theorem, Solutions of ordinary differential using Laplace transform. Fourier series and Fourier transformations, Fourier sine and cosine transformation, Properties of Fourier transformation, Discrete Fourier transformation (DFT), Fast Fourier transformation (FFT) and Fourier Spectrum.

RECOMMENDED BOOKS

Text Book(s)

Erwin Kreyszig, ‘Advanced Engineering Mathematics’, 10th ed., Wiley, 2020.
John Hubbard, Barbara Burke Hubbard, ‘Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach’, 5th ed., Matrix, 2015.

Reference Book(s)

Steven Krantz, Harold Parks, ‘Vector Calculus’, Chapman and Hall/CRC, 2024.
K.A. Stroud, Dexter Booth, ‘Advanced Engineering Mathematics’, 6th ed., Bloomsbury Academic, 2020.
Stanley J. Miklavcic, ‘An Illustrative Guide to Multivariable and Vector Calculus’, 1st ed., Springer, 2020.

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