I. K. Gujral Punjab Technical University, Punjab, Computer Engineering Semester 1, Maths-I Syllabus

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Unit - 1 Calculus

UNIT–1

Calculus

1.1 Rolle’s theorem

1.2. Mean value theorems

1.3. Taylor’s and Maclaurin’s theorem with remainders

1.4. Indeterminate forms L’Hospital rule

1.5. Maxima and minima

1.6. Evaluation of definite and improper integrals

1.7. Application of definite integrals to evaluate surface areas and volumes of revolutions

Unit - 2 Multivariable Calculus

UNIT–2

Multivariable Calculus

2.1. Limit continuity and partial derivatives

2.2. Total derivative

2.3. Tangent plane and normal line

2.4. Maxima minima and saddle point

2.5. Method of Lagrange’s multiplier

2.6. Multiple integration Double and triple integrals Cartesian and polar

2.7. Change of order of integration in double integrals

2.8. Change of variable Cartesian and polar

2.9. Applications Area and volume by double integration

2.10. Centre of mass and gravity

Unit - 3 Sequence and series

UNIT–3

Sequence and series

3.1. Convergence of sequence and series

3.2. Test for convergence of positive term series Root test

3.3. Ratio test

3.4. ptest

3.5. Comparison test

3.6. Alternate series and Leibnitz’s test

3.7. Power series

3.8. Taylor’s series

3.9. Series for exponentials

3.10. Trigonometric and logarithmic functions

Unit - 4 Matrices

UNIT–4

Matrices

4.1. Algebra of matrices

4.2. Inverse and rank of a matrix

4.3. Introduction of null space and kernel

4.4. Statement of ranknullity theorem

4.5. System of linear equations

4.6. Symmetric skewsymmetric and orthogonal matrices

4.7. Determinants

4.8. Eigen values and Eigen vectors

4.9 Similar matrices Diagonalization of matrices

4.10. CayleyHamilton theorem

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Other Subjects of Semester-1
English
Chemistry-i
Mechanics of solids
Basic electrical engineering
Engineering graphics & design
Programming for problem solving
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