 # JNTUK R20 B.Tech M1 Mathematics 1 Syllabus 2021

JNTUK R20 M1 B.tech Syllabus along with Course Objectives and Course outcome and list of textbook and reference books is mentioned in this blog. The subject of Mathematics 1 has 5 units in total. Topic and sub-topics of Mathematics 1 are mentioned below in detail. If you have any problem in understanding Mathematics 1 or any other Engineering Subject in any semester or in any year then you can view the video lectures on the official CynoHub app.

#### JNTUK R20 M1 B.tech Syllabus Unit - 1:

##### Sequences, Series and Mean value theorems

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

Mean Value Theo rems (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.

#### JNTUK R20 M1 B.tech Syllabus Unit - 2:

##### 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 –

#### JNTUK R20 M1 B.tech Syllabus Unit - 3:

##### 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  e ax ,  sin  ax,  cos  ax,  polynomials  in  x n ,  e ax V(x)  and  x n V(x)     –    Method of Variation of parameters, Cauchy and Legendre’s linear equations.

Applications: LCR circuit, Simple Harmonic motion.

#### JNTUK R20 M1 B.tech Syllabus Unit - 4:

##### 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.

#### JNTUK R20 M1 B.tech Syllabus Unit - 5:

##### 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.

#### JNTUK R20 M1 B.tech Syllabus 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.

#### JNTUK R20 M1 B.tech Syllabus 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 )
##### JNTUK R20 M1 B.tech Syllabus Referance Books:
• B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers.
• B. V. Ramana, Higher Engineering Mathematics, 2007 Edition, Tata Mc. Graw Hill Education.
• Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India.
• Joel Hass, Christopher Heil and Maurice D. Weir, Thomas calculus, 14thEdition, Pearson.
• Lawrence Turyn, Advanced Engineering Mathematics, CRC Press, 2013.
• Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press
##### Scoring marks in JNTUK R20 M1 B.tech Syllabus

Scoring good grades in Mathematics 1 is a difficult task. CynoHub is here to help. We have made a video which will help Engineering Students get rank 1 in their B.tech exams this video will help students to score good grades in Mathematics 1. There are many reasons that scoring in Mathematics 1 exams is difficult so this video will help you to rectify the mistakes students make in exam.

JNTUK R20 M1 B.tech Syllabus was made clear in this article. To know about the syllabus of other Engineering Subjects of JNTUK check out the official CynoHub application.