MALLA REDDY COLLEGE OF
ENGINEERING & TECHNOLOGY
(An Autonomous Institution – UGC, Govt.of India)
Recognizes under 2(f) and 12(B) of UGC ACT 1956
(Affiliated to JNTUH, Hyderabad, Approved by AICTE –Accredited by NBA & NAAC-“A” Grade-ISO 9001:2015
Certified)
Mathematics-I
B.Tech – I Year – I Semester
DEPARTMENT OF HUMANITIES AND SCIENCES
, MATHEMATICS - I
(R18A0021) Mathematics -I
Course Objectives: To learn
1. The concept of rank of a matrix which is used to know the consistency of system of
linear equations and also to find the eigen vectors of a given matrix.
2. Finding maxima and minima of functions of several variables.
3. Applications of first order ordinary differential equations. ( Newton’s law of cooling,
Natural growth and decay)
4. How to solve first order linear, non linear partial differential equations and also
method of separation of variables technique to solve typical second order partial
differential equations.
5. Solving differential equations using Laplace Transforms.
UNIT I: Matrices
Introduction, types of matrices-symmetric, skew-symmetric, Hermitian, skew-Hermitian,
orthogonal, unitary matrices. Rank of a matrix - echelon form, normal form, consistency of
system of linear equations (Homogeneous and Non-Homogeneous). Eigen values and Eigen
vectors and their properties (without proof), Cayley-Hamilton theorem (without proof),
Diagonalisation.
UNIT II:Functions of Several Variables
Limit continuity, partial derivatives and total derivative. Jacobian-Functional dependence and
independence. Maxima and minima and saddle points, method of Lagrange multipliers,
Taylor’s theorem for two variables.
UNIT III: Ordinary Differential Equations
First order ordinary differential equations: Exact, equations reducible to exact form.
Applications of first order differential equations - Newton’s law of cooling, law of natural
growth and decay.
Linear differential equations of second and higher order with constant coefficients:
Non-homogeneous term of the type f(x) = eax, sinax, cosax, xn, eax V and xn V. Method of
variation of parameters.
UNIT IV: Partial Differential Equations
Introduction, formation of partial differential equation by elimination of arbitrary constants
and arbitrary functions, solutions of first order Lagrange’s linear equation and non-linear
equations, Charpit’s method, Method of separation of variables for second order equations
and applications of PDE to one dimensional (Heat equation).
UNIT V: Laplace Transforms
Definition of Laplace transform, domain of the function and Kernel for the Laplace
transforms, Existence of Laplace transform, Laplace transform of standard functions, first
shifting Theorem, Laplace transform of functions when they are multiplied or divided by “t”,
Laplace transforms of derivatives and integrals of functions, Unit step function, Periodic
function.
Inverse Laplace transform by Partial fractions, Inverse Laplace transforms of functions when
they are multiplied or divided by ”s”, Inverse Laplace Transforms of derivatives and integrals
of functions, Convolution theorem, Solving ordinary differential equations by Laplace
transforms.
DEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) 1
, MATHEMATICS - I
TEXT BOOKS:
i) Higher Engineering Mathematics by B V Ramana ., Tata McGraw Hill.
ii) Higher Engineering Mathematics by B.S. Grewal, Khanna Publishers.
iii) Advanced Engineering Mathematics by Kreyszig, John Wiley & Sons.
REFERENCE BOOKS:
i)Advanced Engineering Mathematics by R.K Jain & S R K Iyenger, Narosa Publishers.
ii)Advanced Engineering Mathematics by Michael Green Berg, Pearson Publishers .
iii)Engineering Mathematics by N.P Bali and Manish Goyal.
Course Outcomes: After learning the concepts of this paper the student will be able to
1.Analyze the solution of the system of linear equations and to find the Eigen values and
Eigen vectors of a matrix.
2.Find the extreme values of functions of two variables with / without constraints.
3.Solve first and higher order differential equations.
4.Solve first order linear and non-linear partial differential equations.
5.Solve differential equations with initial conditions using Laplac
DEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) 2
, MATHEMATICS - I
UNIT-I
DEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) 3
ENGINEERING & TECHNOLOGY
(An Autonomous Institution – UGC, Govt.of India)
Recognizes under 2(f) and 12(B) of UGC ACT 1956
(Affiliated to JNTUH, Hyderabad, Approved by AICTE –Accredited by NBA & NAAC-“A” Grade-ISO 9001:2015
Certified)
Mathematics-I
B.Tech – I Year – I Semester
DEPARTMENT OF HUMANITIES AND SCIENCES
, MATHEMATICS - I
(R18A0021) Mathematics -I
Course Objectives: To learn
1. The concept of rank of a matrix which is used to know the consistency of system of
linear equations and also to find the eigen vectors of a given matrix.
2. Finding maxima and minima of functions of several variables.
3. Applications of first order ordinary differential equations. ( Newton’s law of cooling,
Natural growth and decay)
4. How to solve first order linear, non linear partial differential equations and also
method of separation of variables technique to solve typical second order partial
differential equations.
5. Solving differential equations using Laplace Transforms.
UNIT I: Matrices
Introduction, types of matrices-symmetric, skew-symmetric, Hermitian, skew-Hermitian,
orthogonal, unitary matrices. Rank of a matrix - echelon form, normal form, consistency of
system of linear equations (Homogeneous and Non-Homogeneous). Eigen values and Eigen
vectors and their properties (without proof), Cayley-Hamilton theorem (without proof),
Diagonalisation.
UNIT II:Functions of Several Variables
Limit continuity, partial derivatives and total derivative. Jacobian-Functional dependence and
independence. Maxima and minima and saddle points, method of Lagrange multipliers,
Taylor’s theorem for two variables.
UNIT III: Ordinary Differential Equations
First order ordinary differential equations: Exact, equations reducible to exact form.
Applications of first order differential equations - Newton’s law of cooling, law of natural
growth and decay.
Linear differential equations of second and higher order with constant coefficients:
Non-homogeneous term of the type f(x) = eax, sinax, cosax, xn, eax V and xn V. Method of
variation of parameters.
UNIT IV: Partial Differential Equations
Introduction, formation of partial differential equation by elimination of arbitrary constants
and arbitrary functions, solutions of first order Lagrange’s linear equation and non-linear
equations, Charpit’s method, Method of separation of variables for second order equations
and applications of PDE to one dimensional (Heat equation).
UNIT V: Laplace Transforms
Definition of Laplace transform, domain of the function and Kernel for the Laplace
transforms, Existence of Laplace transform, Laplace transform of standard functions, first
shifting Theorem, Laplace transform of functions when they are multiplied or divided by “t”,
Laplace transforms of derivatives and integrals of functions, Unit step function, Periodic
function.
Inverse Laplace transform by Partial fractions, Inverse Laplace transforms of functions when
they are multiplied or divided by ”s”, Inverse Laplace Transforms of derivatives and integrals
of functions, Convolution theorem, Solving ordinary differential equations by Laplace
transforms.
DEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) 1
, MATHEMATICS - I
TEXT BOOKS:
i) Higher Engineering Mathematics by B V Ramana ., Tata McGraw Hill.
ii) Higher Engineering Mathematics by B.S. Grewal, Khanna Publishers.
iii) Advanced Engineering Mathematics by Kreyszig, John Wiley & Sons.
REFERENCE BOOKS:
i)Advanced Engineering Mathematics by R.K Jain & S R K Iyenger, Narosa Publishers.
ii)Advanced Engineering Mathematics by Michael Green Berg, Pearson Publishers .
iii)Engineering Mathematics by N.P Bali and Manish Goyal.
Course Outcomes: After learning the concepts of this paper the student will be able to
1.Analyze the solution of the system of linear equations and to find the Eigen values and
Eigen vectors of a matrix.
2.Find the extreme values of functions of two variables with / without constraints.
3.Solve first and higher order differential equations.
4.Solve first order linear and non-linear partial differential equations.
5.Solve differential equations with initial conditions using Laplac
DEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) 2
, MATHEMATICS - I
UNIT-I
DEPARTMENT OF HUMANITIES & SCIENCES ©MRCET (EAMCET CODE: MLRD) 3
