MAT 102 Vector Calculus, Differential Equations and Transforms of KTU introduce the Maths concepts and applications of vector evaluation functions, equality equations, differential detection, and integration of Laplace and Fourier transformations. This course aims to introduce future engineers to some advanced mathematical concepts and techniques, including vector values, ordinary differential equations and fundamental variables such as Laplace and Fourier. An essential change to any engineer's math toolbox. The Vector Calculus covered in this course have applications in all engineering disciplines.
| Board | KTU |
| Scheme | 2019 New Scheme |
| Year | First Year |
| Semester | S2 |
| Subject | MAT 102 | Vector Calculus, Differential Equations and Transforms |
| Credit | 4 Credit |
| Category | KTU S1 & S2 |
KTU S2 Vector Calculus, Differential Equations and Transforms | MAT 102 | Notes (2019 Scheme)
Module 1
Module 1 - Syllabus
Calculus of vector functions
The vector-valued function of a single variable, a derivative of a vector function and geometrical interpretation, motion along a curve-velocity, speed and acceleration. Concept of scalar and vector fields, Gradient and its properties, directional derivative, divergence and curl, Line integral vector fields, work as the line integral, Conservative vector fields, independence of path and potential function(results without proof).
Module 1 - Notes
Module 1 Vector Calculus, Differential Equations and Transforms | MAT 102 PDF Notes
Module 2
Module 2 - Syllabus
Vector integral theorems
Green’s theorem (for simply connected domains, without proof) and applications to evaluating line integrals and finding areas. Surface integrals over surfaces of the form z = g(x, y), y = g(x, z) or x = g(y, z) , Flux integrals over surfaces of the form z = g(x, y), y = g(x, z) or x = g(y, z), theorem (without proof) and its applications to finding flux integrals, Stokes’ theorem (with out proof) and its applications to finding line integrals of vector fields and work done.
Module 2 - Notes
Module 2 Vector Calculus, Differential Equations and Transforms | MAT 102 PDF Notes
Module 3
Module 3 - Syllabus
Ordinary differential equations
Homogenous linear differential equation of second order, superposition principle, general solution, homogenous linear ODEs with a constant coefficients-general solution. Solution of Euler-Cauchy equations (second-order only).Existence and uniqueness (without proof).
Non-homogenous linear ODEs-general solution, solution by the method of undetermined coefficients (for the right-hand side of form x,e,sinax,cosax,e sinaxe cosaxand their linear combinations), methods of variation of parameters. Solution of higher-order equations-homogeneous and non-homogeneous with constant coefficient using the method of undetermined coefficient.
Module 3 - Notes
Module 3 Vector Calculus, Differential Equations and Transforms | MAT 102 PDF Notes
Module 4
Module 4 - Syllabus
Laplace transforms
Laplace Transform and its inverse, Existence theorem ( without proof), linearity, Laplace transform of basic functions, first shifting theorem, Laplace transform of derivatives and integrals, solution of differential equations using Laplace transform, Unit step function, Second shifting theorems.
Dirac delta function and its Laplace transform, Solution of an ordinary differential equation involving u step function and Dirac delta functions. Convolution theorem(without proof)and its application finding inverse Laplace transform of products of functions.
Module 4 - Notes
Module 3 Vector Calculus, Differential Equations and Transforms | MAT 102 PDF Notes
Module 5
Module 5 - Syllabus
Fourier Transforms
Fourier integral representation, Fourier sine and cosine integrals. Fourier sine and cosine transforms inverse sine and cosine transform. Fourier transform and inverse Fourier transform basic properties The Fourier transform of derivatives. Convolution theorem (without proof)
Module 5 - Notes
Module 5 Vector Calculus, Differential Equations and Transforms | MAT 102 PDF Notes
KTU S1 & S2 Related Links
| KTU S1 & S2 Study Materials | Click Here |
| KTU S1 & S2 Study Notes | Click Here |
| KTU S1 & S2 Syllabus | Click Here |
| KTU S1 & S2 Reference Textbook | Click Here |
| KTU S1 & S2 Previous Year Solved Question Papers | Click Here |
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