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Shivaji University, Maharashtra
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Engineering MathematicsI
Shivaji University, Maharashtra, Computer Engineering Semester 1, Engineering MathematicsI Syllabus
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Unit  1 Matrices and Solution of Linear System Equations
Unit 1
Matrices and Solution of Linear System Equations
1.1 Rank of matrix definition normal form and echelon form
1.2 Consistency of linear system equations
1.3 System of linear homogeneous equations
1.4 System of linear Nonhomogeneous equations
Unit  2 Eigen Values and Eigen vectors
Unit 2
Eigen Values and Eigen vectors
2.1 Eigen Values
2.2 Properties of Eigen Values
2.3 Eigen vector Properties of Eigen vectors
2.4 CayleyHamiltons theorem Without proof
Unit  3 Complex Numbers
Unit 3
Complex Numbers
3.1 De Moivres Theorem Without proof
3.2 Roots of complex numbers by using De Moivres Theorem
3.3 Expansion of sinnθ and cosnθ in powers of sinθ and or cosθ
3.4 Circular functions of a complex variable – definitions
3.5 Hyperbolic and Inverse Hyperbolic Functions definitions
Unit  4 Numerical Solution of linear simultaneous equations
Unit 4
Numerical Solution of linear simultaneous equations
4.1 Gauss elimination method
4.2 Gauss Jordan method
4.3 Jacobi’s iteration method
4.4 GaussSeidel iteration method
Unit  5 Expansion of Functions and Indeterminate forms
Unit 5
Expansion of Functions and Indeterminate forms
5.1 Maclaurins theorem
5.2 Taylors theorem
5.3 Indeterminate forms and L Hospitals rule
Unit  6 Partial Differentiation
Unit 6
Partial Differentiation
6.1 Partial derivatives Introduction
6.2 Total derivatives
6.3 Differentiation of implicit function
6.4 Eulers theorem on homogeneous function of two variables
6.5 Jacobian and its Properties
6.6 Maxima and Minima of functions of two variables
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Other Subjects of Semester1
Applied mechanics
Engineering physics
Engineering graphics
Engineering chemistry
Basic civil engineering
Basic electrical engineering
Basic mechanical engineering
Professional communicationi
Fundamentals of electronics and computer
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