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Maharaja Ranjit Singh Punjab Technical University, Punjab, Electronics and Communication engineering Semester 1, Mathematics-I (Calculus and Differential Equations) Syllabus

Mathematics-I (Calculus and Differential Equations) Lecture notes | Videos | Free pdf Download | Previous years solved question papers | MCQs | Question Banks| Syllabus

Unit - 1 Calculus

1.1 Rolle’s theorem Mean value theorems

1.2 Taylor’s and Maclaurin theorems with remainders

1.3 Indeterminate 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 Differentiation

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 Multivariable Calculus Integration

3.1 Multiple Integration 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 First Order Ordinary Differential Equations

4.1 Linear and Bernoulli’s equations

4.2 Exact equations

4.3 Equations not of first degree equations solvable for p equations solvable for y equations solvable for x and Clairaut’s type

4.4 Second order linear differential equations with variable coefficients

4.5 Method of variation of parameters

4.6 CauchyEuler equation

4.7 Power series solutions Frobenius method