Charotar University of Science and Technology, Gujarat, Civil Engineering Semester 1, Engineering Mathematics – I Syllabus

Unit - 1 Higher order derivatives and applications

Unit 1

Higher order derivatives and applications

1.1 Set theory and Function

1.2 Limit Continuity Differentiability for function of single variable and its uses.

1.3 Successive differentiation nth derivative of elementary functions viz. rational logarithmic trigonometric exponential and hyperbolic etc.

1.4 Leibnitz rule for the nth order derivatives of product of two functions

1.5 Expansion of Functions Maclaurin’s Taylor’s series expansion

1.6 L’Hospital’s rule and related applications Indeterminate forms.

Unit - 2 Complex numbers and Roots of polynomial Equations

Unit 2

Partial differentiation

2.1 Partial derivative and geometrical interpretation

2.2 Euler’s theorem with corollaries and their applications

2.3 Chain rule

2.4 Total differentials

Unit - 3 Applications of Partial differentiation

Unit 3

Applications of Partial differentiation

3.1 Tangent plane and normal line to a surface

3.2 Maxima and Minima

3.3 Langrage’s method of multiplier

3.4 Jacobian

3.5 Errors and approximations

Unit - 4 Matrix Algebra- I

Unit 4

Matrix Algebra I

4.1 Definition of Matrix types of matrices and their properties

4.2 Determinant and their properties

4.3 Rank and nullity of a matrix

4.4 Determination of rank

4.5 Gauss Jordan method for computing inverse Triangularization of Matrices by Gauss Elimination Process

4.6 Solution of system of linear equations

Unit - 5 Algebra of Complex numbers and Roots of polynomial Equations

Unit 5

Algebra of Complex numbers and Roots of polynomial Equations

5.1 Complex numbers their geometric representation

5.2 Complex numbers in polar and exponential forms

5.3 Demoirve’s theorem and its applications

5.4 Exponential Logarithmic Trigonometric and hyperbolic functions.

5.5 Statement of fundamental theorem of Algebra Analytical solution of cubic equation by Cardan’s method

5.6 Analytic solution of Biquadratic equations by Ferrari’s method with their applications.

Unit 5

Algebra of Complex numbers and Roots of polynomial Equations

5.1 Complex numbers their geometric representation

5.2 Complex numbers in polar and exponential forms

5.3 Demoirve’s theorem and its applications

5.4 Exponential Logarithmic Trigonometric and hyperbolic functions.

5.5 Statement of fundamental theorem of Algebra Analytical solution of cubic equation by Cardan’s method

5.6 Analytic solution of Biquadratic equations by Ferrari’s method with their applications.

Unit - 6 Infinite Series

Unit – 6

Infinite Series

6.1 Introduction to sequence and series

6.2 Convergence and divergence of infinite series

6.3 Necessary condition for convergence

6.4 Geometric series

6.5 Tests of convergence viz. comparison test pseries test ratio test nth root test Leibnitz test integral test and power series.

6.6 Convergence of Taylors and McLaurin Series

Unit – 6

Infinite Series

6.1 Introduction to sequence and series

6.2 Convergence and divergence of infinite series

6.3 Necessary condition for convergence

6.4 Geometric series

6.5 Tests of convergence viz. comparison test pseries test ratio test nth root test Leibnitz test integral test and power series.

6.6 Convergence of Taylors and McLaurin Series