Page 8 - Microsoft Word - B.Tech. Course Structure (R20) WITH 163 CREDITS

JNTUA College of Engineering (Autonomous), Ananthapuramu
Department of Computer Science & Engineering
LINEAR ALGEBRA AND CALCULUS
Course Code: Semester I(R20) L T P C: 3 0 0 3
Course Objectives:
• This course will illuminate the students in the concepts of calculus and linear algebra.
• 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.

Course Outcomes:
CO1: develop the use of matrix algebra techniques that is needed by engineers for practical
applications
CO2: Utilize mean value theorems to real life problems.
CO3: familiarize with functions of several variables which is useful in optimization.
CO4: Students will also learn important tools of calculus in higher dimensions. Students will
become familiar with 2- dimensional coordinate systems
CO5: Students will become familiar with 3- dimensional coordinate systems and also learn the
Utilization of special functions.

UNIT- I: Matrices
Rank of a matrix by echelon form, normal form. Solving system of homogeneous and non-
homogeneous equations linear equations. Eigenvalues and Eigenvectors and their properties,
Properties of Eigen values and Eigen vectors on special matrices, Cayley-Hamilton theorem (without
proof), finding inverse and power of a matrix by Cayley-Hamilton theorem, diagonalization of a
matrix.

UNIT – II: Mean Value Theorems
Rolle’s Theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, Taylor’s and
Maclaurin theorems with remainders (without proof), related problems.

UNIT – III: Multivariable calculus
Partial derivatives, total derivatives, chain rule, change of variables, Jacobians, maxima and minima of
functions of two variables, method of Lagrange multipliers.

UNIT – IV: Multiple Integrals
Double integrals, change of order of integration, change of variables. Evaluation of triple integrals,
change of variables between Cartesian, cylindrical and spherical polar co-ordinates. Finding areas and
volumes using double and triple integrals.

UNIT – V: Beta and Gamma functions
Beta and Gamma functions and their properties, relation between beta and gamma functions,
evaluation of definite integrals using beta and gamma functions.

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