 # JNTUK B.TECH R20 1-1 Syllabus For Mathematics – i PDF 2022

### Get Complete Lecture Notes for Mathematics – i on Cynohub APP  You will be able to find information about Mathematics – i along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Mathematics – i after reading this blog. Mathematics – i has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Mathematics – i can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

All of the Topic and subtopics related to Mathematics – i are mentioned below in detail. If you are having a hard time understanding Mathematics – i or any other Engineering Subject of any semester or year then please watch the video lectures on the official CynoHub app as it has detailed explanations of each and every topic making your engineering experience easy and fun.

### Mathematics – i Unit One

#### Sequences, Series and Mean value theorems

Sequences and Series: Convergences and divergence – Ratio test – Comparison tests – Integral test – Cauchy’s root test – Alternate series – Leibnitz’s rule.

Mean Value Theorems (without proofs): Rolle’s Theorem – Lagrange’s mean value theorem – Cauchy’s mean value theorem – Taylor’s and Maclaurin’s theorems with remainders, Problems and applications on the above theorem.

### Mathematics – i Unit Two

#### Differential equations of first order and first degree

Linear differential equations – Bernoulli’s equations – Exact equations and equations reducible to exact form.

Applications: Newton’s Law of cooling – Law of natural growth and decay – Orthogonal trajectories

Electrical circuits.

### Get Complete Lecture Notes for Mathematics – i on Cynohub APP  ### Mathematics – i Unit Three

#### Linear differential equations of higher order

Homogeneous and Non-homogeneous differential equations of higher order with constant coefficients – with non-homogeneous term of the type eax, sin ax, cos ax, polynomials in xn, eaxV(x) and xnV(x) – Method of Variation of parameters, Cauchy and Legendre’s linear equations.

Applications: LCR circuit, Simple Harmonic motion.

### Mathematics – i Unit Four

#### Partial differentiation:

Introduction – Homogeneous function – Euler’s theorem – Total derivative – Chain rule – Jacobian – Functional dependence – Taylor’s and MacLaurin’s series expansion of functions of two variables.

Applications: Maxima and Minima of functions of two variables without constraints and Lagrange’s method.

### Mathematics – i Unit Five

#### Multiple integrals:

Double and Triple integrals – Change of order of integration in double integrals – Change of variables to polar, cylindrical and spherical coordinates.

Applications: Finding Areas and Volumes.

### Mathematics – i Course Objectives

To familiarize a variety of well-known sequences and series, with a developing intuition about the behaviour of new ones.

To enlighten the learners in the concept of differential equations and multivariable calculus.

To equip the students with standard concepts and tools at an intermediate to advanced level mathematics to develop the confidence and ability among the students to handle various real world problems and their applications.

### Mathematics – i Course Outcomes

At the end of the course, the student will be able to

utilize mean value theorems to real life problems (L3)

solve the differential equations related to various engineering fields (L3)

familiarize with functions of several variables which is useful in optimization (L3)

apply double integration techniques in evaluating areas bounded by region (L3)

students will also learn important tools of calculus in higher dimensions. Students will become familiar with 2- dimensional and 3-dimensional coordinate systems (L5 )

### Mathematics – i Text Books

B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.

B. V. Ramana,Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.

### Mathematics – i Reference Books

Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India.

Joel Hass, Christopher Heil and Maurice D. Weir, Thomas calculus, 14th Edition, Pearson.

Lawrence Turyn, Advanced Engineering Mathematics, CRC Press, 2013.

Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press.

### Scoring Marks in Mathematics – i  