Here you can download the free lecture Notes of Engineering Mathematics – I Notes pdf – EM I Notes Pdf materials with multiple file links to download. The Engineering Mathematics – I Notes pdf – EM I Notes Pdf book starts with the topics covering Basic definitions of Sequences and series, Cauchy’s mean value Theorem, Evolutes and Envelopes Curve tracing, Integral Representation for lengths, Overview of differential equations, Higher Order Linear differential equations and their applications, Gradient- Divergence, Etc.

**Engineering Mathematics – I Notes pdf – EM I notes pdf file**

Engineering Mathematics – I Notes pdf – EM I pdf notes – EM I notes pdf file to download are listed below please check it –

**Complete Notes**

**Link:Complete Notes**

**Note :-** These notes are according to the R09 Syllabus book of JNTU.In R13 and R15,8-units of R09 syllabus are combined into 5-units in R13 and R15 syllabus. If you have any doubts please refer to the JNTU Syllabus Book.

**UNIT – I**

Sequences – Series

Basic definitions of Sequences and series – Convergences and divergence – Ratio test – Comparison test – Integral test – Cauchy’s root test – Raabe’s test – Absolute and conditional convergence

**UNIT – II**

Functions of Single Variable

Rolle’s Theorem – Lagrange’s Mean Value Theorem – Cauchy’s mean value Theorem – Generalized Mean Value theorem (all theorems without proof) Functions of several variables – Functional dependence- Jacobian- Maxima and Minima of functions of two variables with constraints and without constraints

**UNIT – III**

Application of Single variables

Radius, Centre and Circle of Curvature – Evolutes and Envelopes Curve tracing – Cartesian , polar and Parametric curves.

**UNIT – IV**

Integration & its applications

Riemann Sums , Integral Representation for lengths, Areas, Volumes and Surface areas in Cartesian and polar coordinates multiple integrals – double and triple integrals – change of order of integration- change of variable

### Engineering Mathematics – I Notes pdf – EM I Notes Pdf

**UNIT – V**

Differential equations of first order and their applications

Overview of differential equations- exact, linear and Bernoulli. Applications to Newton’s Law of cooling, Law of natural growth and decay, orthogonal trajectories and geometrical applications.

**UNIT – VI**

Higher Order Linear differential equations and their applications

Linear differential equations of second and higher order with constant coefficients, RHS term of the type f(X)= e ax , Sin ax, Cos ax, and xn, e ax V(x), x n V(x), method of variation of parameters. Applications bending of beams, Electrical circuits, simple harmonic motion.

**UNIT – VII**

Laplace transform and its applications to Ordinary differential equations

Laplace transform of standard functions – Inverse transform – first shifting Theorem, Transforms of derivatives and integrals – Unit step function – second shifting theorem – Dirac’s delta function – Convolution theorem – Periodic function – Differentiation and integration of transforms-Application of Laplace transforms to ordinary differential equations.

**UNIT – VIII**

Vector Calculus

Vector Calculus: Gradient- Divergence- Curl and their related properties Potential function – Laplacian and second order operators. Line integral – work done ––- Surface integrals – Flux of a vector valued function. Vector integrals theorems: Green’s -Stoke’s and Gauss’s Divergence Theorems (Statement & their Verification).

**Reference –** Engineering Mathematics – I – EM I notes pdf – EM I pdf notes – EM I Pdf – EM I Notes

1. Engineering Mathematics – I by T.K. V. Iyengar, B. Krishna Gandhi & Others, S. Chand.

2. Engineering Mathematics – I by D. S. Chandrasekhar, Prison Books Pvt. Ltd.

3. Engineering Mathematics – I by G. Shanker Rao & Others I.K. International Publications.

4. Higher Engineering Mathematics – B.S. Grewal, Khanna Publications.

5. Advance Engineering Mathematics by Jain and S.R.K. Iyengar, Narosa Publications.

6. A text Book of KREYSZIG’S Engineering Mathematics, Vol-1 Dr .A. Ramakrishna Prasad. WILEY publications

**Text books –** Engineering Mathematics – I – EM I notes pdf – EM I pdf notes – EM I Pdf – EM I Notes

1. Engineering Mathematics – I by P.B. Bhaskara Rao, S.K.V.S. Rama Chary, M. Bhujanga Rao.

2. Engineering Mathematics – I by C. Shankaraiah, VGS Booklinks.