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Rajasthan Technical University, Rajasthan, Computer Engineering Semester 1, Engineering Mathematics-I Syllabus
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Unit - 1 Calculus
1.1 Improper integrals Beta and Gamma functions and their properties1.2 Applications of definite integrals to evaluate surface areas and volumes of revolutions
1.1 Improper integrals Beta and Gamma functions and their properties
1.2 Applications of definite integrals to evaluate surface areas and volumes of revolutions
Unit - 2 Sequence and series
2.1 Convergence of sequence and series2.2 Tests for convergence
2.3 Power series Taylors series
2.4 Series for exponential trigonometric and logarithm functions
2.1 Convergence of sequence and series
2.2 Tests for convergence
2.3 Power series Taylors series
2.4 Series for exponential trigonometric and logarithm functions
Unit - 3 Fourier series
3.1 Periodic functions Fourier series Euler’s formulae3.3 Half range expansions Half range sine and cosine series
3.4 Parseval’s theorem
3.1 Periodic functions Fourier series Euler’s formulae
3.3 Half range expansions Half range sine and cosine series
3.4 Parseval’s theorem
Unit - 4 Multivariable calculus (Differentiation)
4.1 LIMIT CONTINUITY AND PARTIAL DERIVATIVES4.2 DIRECTIONAL DERIVATIVES
4.3 TOTAL DERIVATIVE
4.4 TANGENT PLANE AND NORMAL LINE
4.5 MAXIMA MINIMA AND SADDLE POINTS
4.6 METHOD OF LAGRANGE MULTIPLIERS
4.7 GRADIENT CURL AND DIVERGENCE
4.1 LIMIT CONTINUITY AND PARTIAL DERIVATIVES
4.2 DIRECTIONAL DERIVATIVES
4.3 TOTAL DERIVATIVE
4.4 TANGENT PLANE AND NORMAL LINE
4.5 MAXIMA MINIMA AND SADDLE POINTS
4.6 METHOD OF LAGRANGE MULTIPLIERS
4.7 GRADIENT CURL AND DIVERGENCE
Unit - 5 Multivariable calculus (Integration)
5.1 Multiple integration Double Integrals Cartesian 5.2 Change of order of integration in double integrals
5.3 Change of variable Cartesian to polar
5.4 Applications Areas and volumes
5.5 Centre of mass and gravity constant and variable densities
5.6 Triple integrals
5.7 Simple applications involving cubes sphere and rectangular parallelepipeds
5.8 Scalar line integrals scalar surface integrals volume integrals vector surface integrals
5.9 Theorems of Green’s Stokes and Gauss
5.1 Multiple integration Double Integrals Cartesian
5.2 Change of order of integration in double integrals
5.3 Change of variable Cartesian to polar
5.4 Applications Areas and volumes
5.5 Centre of mass and gravity constant and variable densities
5.6 Triple integrals
5.7 Simple applications involving cubes sphere and rectangular parallelepipeds
5.8 Scalar line integrals scalar surface integrals volume integrals vector surface integrals
5.9 Theorems of Green’s Stokes and Gauss
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