# KTU Syllabus S1 S2 2019-20

This is the first year of your college life and out of the first 8 college semesters, these 2 semesters are the most important semesters of your college. You are not only going to make new friends but going to learn a lot more new things that would be necessary for your career.

Also, do read our article on Everything you need to know about KTU System.

## KTU Textbooks & Notes

The textbooks prescribed by KTU aren\’t always the best, hence we collect all textbooks on the internet based on our recent student\’s experience and update it on our website.

Notes are most helpful when it comes to understanding Calculus and Physics on the go. Do check out our materials before writing exams.

### KTU Semester S1 & S2 Notes

You can download the KTU first year S1 S2 syllabus by subjects using the table provided beside.

We also do have the syllabus for each subject in the written text below. Don\’t forge to bookmark the page for faster access.

## How hard is KTU Syllabus S1 S2?

This is the starting of the year for your college and KTU Syllabus S1 S2 is the simplest syllabus of all years, One of the best time to score a straight 10 CGPA.

### All About KTU Covid Cells

Are you aware of the great Initiative by KTU to deal with the worse situation going on...

### KTU 2020 Academic Calendar B.Tech (Revised & Updated)

The KTU 2020 Academic Calendar has been officially published on its site.Academic Calendar - January 2020- August...

### Examination POSTPONED! Nation wide strike & holidays coming immediately after the Christmas Vacation

KTU has postponed the examination for selected subjects due to the immediately proposed strikes in the nation.APJ...

### MODULE 2: Partial derivatives and its applications

Partial derivatives–Partial derivatives of functions of more than two variables – higher order partial derivatives – differentiability, differentials and local linearity –

The chain rule – Maxima and Minima of functions of two variables – extreme value theorem (without proof)-relative extrema.

### MODULE 3: Calculus of vector valued functions

Introduction to vector valued functions- parametric curves in 3-space

Limits and continuity – derivatives – tangent lines – derivative of dot and cross product- definite integrals of vector valued functions-

unit tangent-normal- velocity-acceleration and speed–Normal and tangential components of acceleration.

Directional derivatives and gradients-tangent planes and normal vectors

(For practice and submission as assignment only: Graphing parametric curves and surfaces using software packages )

### MODULE 4: Multiple integrals

Double integrals- Evaluation of double integrals – Double integrals in non-rectangular coordinates- reversing the order of integration-

Area calculated as a double integral-
Triple integrals(Cartesian coordinates only)- volume calculated as a triple integral- (applications of results only)

### MODULE 5: Topics in vector calculus

Vector and scalar fields- Gradient fields – conservative fields and potential functions – divergence and curl – the Δ operator – the

LaplacianΔ2, Line integrals – work as a line integral- independence of path-conservative vector field –

(For practice and submission as assignment only: graphical representation of vector fields using software packages)

### MODULE 6: Topics in vector calculus (continued)

Green’s Theorem (without proof- only for simply connected region in plane),surface integrals –Divergence Theorem (without proof for evaluating surface integrals), Stokes’ Theorem (without proof for evaluating line integrals)

(All the above theorems are to be taught in regions in the rectangular co ordinate system only)

### MODULE 1: Single Variable Calculus and Infinite series

Basic ideas of infinite series and convergence – .Geometric series- Harmonic series-Convergence tests-comparison, ratio, root tests (without proof). Alternating series- Leibnitz Test- Absolute convergence, Maclaurins series-Taylor series – radius of convergence.

(For practice and submission as assignment only:

Sketching, plotting and interpretation of hyperbolic functions using suitable software. Demonstration of convergence of series bysoftware packages)