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)

**Calculus**, Differential Equations and Transforms

**MAT 102**of first-year KTU is the maths subject that help's you to calculate derivatives and line coordinates of vector functions and surface and shape coordinates to find their applications and their correlations and applications. Solve equations of homogeneous and homogeneous linear equations with constant coefficients and calculate Laplace transform and use them to solve problems derived from engineering.

#### 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

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