Mathematics-1 -

Lesson Plan
Name of the Faculty : Navya Goel
Discipline : B.Tech. - Civil
Semester : 1^st
Subject : Mathematics- 1
Lesson Plan Duration : 15 weeks (From August, 2018 to November, 2018 )
Work Load (Lecture) per week (in hours) : Lectures - 03 and 01 Tutorial

Weeks	Theory
	Lecture/Tutorial	Topic
	Day	(Including assignment / Test)
1^st	1^st	Evolutes and involutes
	2^nd	Evolutes and involutes
	3^rd	Evaluation of definite integrals
	4th	Revision
2^nd	1^st	Evaluation of improper integrals
	2^nd	Beta and Gamma functions and their properties
	3^rd	Applications of definite integrals to evaluate surface areas
	4th	Test
3^rd	1^st	Applications of definite integrals to evaluate volumes of revolutions / Assignment
	2^nd	Rolle’s theorem, Mean value theorems
	3^rd	Taylor’s and Maclaurin theorems with remainders
	4th	Revision
4^th	1^st	Indeterminate forms and L'Hospital's rule
	2^nd	Maxima and minima / Assignment
	3^rd	Test
	4th	Convergence of sequence and series
5^th	1^st	tests for convergence
	2^nd	power series, Taylor's series
	3^rd	Series for exponential, trigonometric and logarithmic functions
	4th	Revision
6^th	1^st	Fourier series: Half range sine and cosine series
	2^nd	Fourier series: Half range sine and cosine series, Parseval’s theorem / Assignment
	3^rd	Test
	4th	Limit, continuity and partial derivatives
7^th	1^st	partial derivatives, directional derivatives
	2^nd	total derivative , Tangent plane and normal line
	3^rd	Maxima, minima and saddle points
	4th	Revision
8^th	1^st	Method of Lagrange multipliers
	2^nd	Gradient, curl and divergence / Assignment
	3^rd	Test
	4th	Multiple Integration: double and triple integrals (Cartesian and polar)
9^th	1^st	change of order of integration in double integrals
	2^nd	Change of variables (Cartesian to polar)
	3rd	Revision
	4th	Applications: areas and volumes by (double integration) Center of mass and Gravity (constant and variable densities).
10^th	1^st	Applications: areas and volumes by (double integration) Center of mass and Gravity (constant and variable densities).
	2^nd	Theorems of Green, Gauss and Stokes
	3^rd	orthogonal curvilinear coordinates
	4th	Test
11^th	1^st	Simple applications involving cubes, sphere
	2^nd	Simple applications involving rectangular parallelepipeds / Assignment
	3^rd	Matrices : addition and scalar multiplication, matrix multiplication; Linear systems of equations, linear Independence, rank of a matrix
	4th	Revision
12^th	1^st	rank of a matrix, determinants
	2^nd	determinants, Cramer’s Rule, inverse of a matrix
	3^rd	Gauss elimination and Gauss-Jordan elimination
	4th	Revision
13^th	1^st	Gauss elimination and Gauss-Jordan elimination / Assignment
	2^nd	Vector Space, linear dependence of vectors
	3^rd	basis, dimension,
	4th	Test
14^th	1^st	Linear transformations (maps), range and kernel of a linear map, rank and nullity
	2^nd	Inverse of a linear transformation, rank- nullity theorem
	3^rd	composition of linear maps, Matrix associated with a linear map / Assignment
	4th	Revision
15^th	1^st	Eigen values, eigen vectors, symmetric, skew-symmetric, and orthogonal Matrices
	2^nd	symmetric, skew-symmetric, and orthogonal Matrices, eigen bases
	3rd	Diagonalization, Inner product spaces,
	4th	Inner product spaces, Gram-Schmidt orthogonalization /Assignment