Maharaja Ranjit Singh Punjab Technical University, Punjab, Civil Engineering Semester 1, Mathematics-I (Calculus, Multivariable Calculus & Linear Algebra) Syllabus

Mathematics-I (Calculus, Multivariable Calculus & Linear Algebra) Lecture notes | Videos | Free pdf Download | Previous years solved question papers | MCQs | Question Banks| Syllabus
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Unit - 1 Calculus

1.1 Rolle’s theorem Mean value theorems

1.2 Taylor’s and Maclaurin theorems with remainders

1.3Indeterminate forms and LHospitals rule

1.4 Maxima and minima

1.5 Evaluation of definite and improper integrals

1.6 Beta and Gamma functions and their properties

1.7 Applications of definite integrals to evaluate surface areas and volumes of revolutions

1.8 Convergence of sequence and series

1.9 Tests for convergence power series Taylors series

1.10 Series for exponential trigonometric and logarithmic functions

Unit - 2 Multivariable calculus

2.1 Limit continuity and partial derivatives

2.2 Tangent plane and normal line

2.3 Maxima minima and saddle points

2.4 Method of Lagrange multipliers

2.5 Gradient curl and divergence Geometrical interpretation and basic properties

2.6 Directional derivative

Unit - 3 Multiple Integration

3.1 Double and triple integrals Cartesian and polar

3.2 Change of order of integration in double integrals

3.3 Change of variables Cartesian to polar

3.4 Applications areas and volumes by double integration Center of mass and Gravity constant and variable densities

3.5 Theorems of Green Gauss and Stokes Statement only

3.6 Simple applications involving cubes sphere and rectangular parallelepipeds

Unit - 4 Linear algebra

4.1 Inverse and rank of a matrix

4.2 Ranknullity theorem

4.3 System of linear equations

4.4 Symmetric skewsymmetric and orthogonal matrices

4.5 Determinants

4.6 Eigenvalues and eigenvectors

4.7 Diagonalization of matrices

4.8 CayleyHamilton Theorem and Orthogonal transformation

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Other Subjects of Semester-1
Basic electrical engineering
Engineering graphics & design
Physics (mechanics and mechanics of solids)
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