Course Objectives:
This course is designed to give a comprehensive coverage at an introductory level to the subject of
matrices, Integral Calculus coordinate geometry, Basic elements of vector algebra and First Order
Differential Equations.
Course Content:
UNIT - I: Determinants and Matrices
Elementary properties of determinants up to 3rd order, consistency of equations, CrammerтАЩs rule.
Algebra of matrices, Inverse of a matrix, matrix inverse method to solve a system of linear equations
in 3 variables.
UNIT - II: Integral Calculus
Integration as inverse operation of differentiation. Simple integration by substitution, by parts
and by partial fractions (for linear factors only). Use of formulas , and
┬аfor solving problems Where m and n are positive integers.
Applications of integration for i. Simple problem on evaluation of area bounded by a curve and axes.
ii. Calculation of Volume of a solid formed by revolution of an area about axes. (Simple problems).
UNIT - III: Co-Ordinate Geometry
Equation of straight line in various standard forms (without proof), inter section of two straight
lines, angle between two lines. Parallel and perpendicular lines, perpendicular distance formula.
General equation of a circle and its characteristics. To find the equation of a circle, given:
i. Centre and radius,
ii. Three points lying on it and
iii. Coordinates of end points of a diameter;
Definition of conics (Parabola, Ellipse, Hyperbola) their standard equations without proof. Problems
on conics when their foci, directories or vertices are given.
UNIT - IV: Vector Algebra
Definition notation and rectangular resolution of a vector. Addition and subtraction of vectors. Scalar
and vector products of 2 vectors. Simple problems related to work, moment and angular velocity.
UNIT-V: Differential Equations┬а
Solution of first order and first degree differential equation by variable separation method (simple
problems). MATLAB тАУ Simple Introduction.
References:
1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi, 40th Edition,
2007.
2. G. B. Thomas, R. L. Finney, Calculus and Analytic Geometry, Addison Wesley, 9th Edition, 1995.
3. S.S. Sabharwal, Sunita Jain, Eagle Parkashan, Applied Mathematics, Vol. I & II, Jalandhar.
4. Comprehensive Mathematics, Vol. I & II by Laxmi Publications, Delhi.
5. Reena Garg & Chandrika Prasad, Advanced Engineering Mathematics, Khanna Publishing
House, New Delhi
Course Outcomes:
By the end of the course the students are expected to learn
(i) the students are expected to acquire necessary background in Determinants and Matrices so as to appreciate the importance of the Determinants are the factors that scale
different parameterizations so that they all produce same overall integrals, i.e. they are
capable of encoding the inherent geometry of the original shape.
(ii) the cumulative effect of the original quantity or equation is the Integration
(iii) the coordinate geometry provides a connection between algebra and geometry through
graphs of lines and curves.
(iv) Tell the difference between a resultant and a concurrent force to model simple physical
problems in the form of a differential equation, analyze and interpret the solutions.