Acharya Nagarjuna University, Andhra Pradesh, Computer Engineering Semester 1, MATHEMATICS I Syllabus

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Unit - 1 Matrix Operations and Solving Systems of Linear Equations
Unit 1
Matrix operations and solving systems of linear equations
1.1 Rank of a matrix by echelon form
1.2 Solving system of homogeneous and non – homogenous equations Linear equations
1.3 Eigen values and eigen vectors and their properties
1.4 Cayley – Hamilton theorem without proof
1.5 Finding inverse and power of a matrix by Cayley – Hamilton theorem
1.6 Diagonalisation of a matrix
1.7 Quadratic forms and nature of the quadratic forms
1.8 Reduction of quadratic form to canonical forms by orthogonal transformation
Unit - 2 Mean Value Theorems
Unit 2
Mean value theorems
2.1 Rolle’s theorem
2.2 Lagrange’s mean value theorem
2.3 Cauchy’s mean value theorem
2.4 Taylor’s and Maclaurin theorems with remainders without proof
Unit 2
Mean value theorems
2.1 Rolle’s theorem
2.2 Lagrange’s mean value theorem
2.3 Cauchy’s mean value theorem
2.4 Taylor’s and Maclaurin theorems with remainders without proof
Unit - 3 Multivariable calculus
Unit 3
Multivariable calculus
3.1 Partial derivatives
3.2 Total derivatives
3.3 Chain rule
3.4 Change of variables
3.5 Jacobians
3.6 Maxima and minima of function of two variables
3.7 Method of Lagrange multipliers
Unit - 4 Double Integrals
Unit 4
Double Integral
4.1 Double integrals
4.2 Change of order integration
4.3 Double integration in polar coordinates
4.4 Areas enclosed by plane curves
Unit - 5 Multiple Integrals and Special Functions
Unit 5
Multiple Integral and special function
5.1 Evaluation of triple integrals
5.2 Change of variables between Cartesian to polar
5.3 Cylinder and spherical polar coordinates
5.4 Beta and Gamma functions and their properties
5.5 Relation between beta and gamma functions
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Other Subjects of Semester-1
Engineering chemistry
Communicative english i
Programming for problem solving
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