## Sunday, June 6, 2010

### APPLIED MATHEMATICS

APPLIED MATHEMATICS - I

L T P

5 - -

RATIONALE

Applied Mathematics forms the backbone of engineering students. Basic elements of algebra, trigonometry, coordinate geometry have been included in the curriculum as foundation course. This course will develop analytical abilities to make exact calculations and will provide continuing educational base to the students.

DETAILED CONTENTS

1. Algebra (30 hrs)

1.1 Complex Numbers: Complex number, representation, modulus and amplitude. De-movier’s theorem, its application in solving algebric equation.

1.2 Geometrical progression, its nth term and sum of n terms and to infinity. Application of Arithmetic progression and Geometrical progression to Engineering problem.

1.2 Partial fractions (linear factors, repeated linear factors, non-reducible quadratic factors excluding repeated factors)

1.4 Permutations and Combinations: Value of npr ncr. Simple problems

1.5 Binomial theorem (without proof) for positive integral index (expansion and general form); binomial theorem for any index (expansion without proof) first and second binomial approximation with applications to engineering problems

2. Trigonometry (25 hrs)

2.1 Concept of angles, measurement of angles in degrees, grades and radians and their conversions.

2.2 T-Ratios of Allied angles (without proof), Sum, difference formulae and their applications (without proof). Product formulae (Transformation of product to sum, difference and vice versa). T-Ratios of multiple angles, sub-multiple angles (2A, 3A, A/2).

2.3 Graphs of Sin x, Cos x, Tan x and ex

3. Co-Ordinate Geometry (25 hrs)

3.1 Cartesian and Polar coordinates (two dimensional), conversion from cartesian to polar coordinates and vice-versa, distance between two points (cartesian co-ordinates), section formulae

3.2 Area of triangle when its vertices are given, co-ordinates of centroid, in center of a triangle when the vertices are given, simple problems on locus.

3.3 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

3.4 General equation of a circle and its characteristics. To find the equation of a circle, given:

* Centre and radius

* Three points lying on it

* Coordinates of end points of a diameter;

RECOMMENDED BOOKS

1. Elementary Engineering Mathematics by BS Grewal, Khanna Publishers, New Delhi

2. Engineering Mathematics by Vol. I & II by S Kohli, IPH, Jalandhar

3. Applied Mathematics by Dr. RD Sharma

4. Applied Mathematics, Vol. I & II by SS Sabharwal & Sunita Jain, Eagle Parkashan, Jalandhar

5. Comprehensive Mathematics, Vol. I & II by Laxmi Publications

6. Engineering Mathematics by Dass Gupta

7. Engineering Mathematics by C Dass Chawla, Asian Publishers, New Delhi

8. Engineering Mathematics, Vol. I, II & III by V Sundaram et al, Vikas Publishing House (P) Ltd., New Delhi

9. Engineering Mathematics by N.Ch.S.N Iyengar et.al, Vikas Publishing House (P) Ltd., New Delhi

10. Engineering Mathematics, Vol I & II by SS Sastry, Prentice Hall of India Pvt. Ltd.,

11. Engineering Mathematics, Vol I & II by AK Gupta, MacMillan India Ltd., New Delhi

SUGGESTED DISTRIBUTION OF MARKS

Topic No. Time Allotted (Hrs) Marks Allotted (%)

1 30 35

2 25 35

3 25 30

TOTAL 80 100

L T P

5 - -

RATIONALE

Applied Mathematics forms the backbone of engineering students. Basic elements of algebra, trigonometry, coordinate geometry have been included in the curriculum as foundation course. This course will develop analytical abilities to make exact calculations and will provide continuing educational base to the students.

DETAILED CONTENTS

1. Algebra (30 hrs)

1.1 Complex Numbers: Complex number, representation, modulus and amplitude. De-movier’s theorem, its application in solving algebric equation.

1.2 Geometrical progression, its nth term and sum of n terms and to infinity. Application of Arithmetic progression and Geometrical progression to Engineering problem.

1.2 Partial fractions (linear factors, repeated linear factors, non-reducible quadratic factors excluding repeated factors)

1.4 Permutations and Combinations: Value of npr ncr. Simple problems

1.5 Binomial theorem (without proof) for positive integral index (expansion and general form); binomial theorem for any index (expansion without proof) first and second binomial approximation with applications to engineering problems

2. Trigonometry (25 hrs)

2.1 Concept of angles, measurement of angles in degrees, grades and radians and their conversions.

2.2 T-Ratios of Allied angles (without proof), Sum, difference formulae and their applications (without proof). Product formulae (Transformation of product to sum, difference and vice versa). T-Ratios of multiple angles, sub-multiple angles (2A, 3A, A/2).

2.3 Graphs of Sin x, Cos x, Tan x and ex

3. Co-Ordinate Geometry (25 hrs)

3.1 Cartesian and Polar coordinates (two dimensional), conversion from cartesian to polar coordinates and vice-versa, distance between two points (cartesian co-ordinates), section formulae

3.2 Area of triangle when its vertices are given, co-ordinates of centroid, in center of a triangle when the vertices are given, simple problems on locus.

3.3 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

3.4 General equation of a circle and its characteristics. To find the equation of a circle, given:

* Centre and radius

* Three points lying on it

* Coordinates of end points of a diameter;

RECOMMENDED BOOKS

1. Elementary Engineering Mathematics by BS Grewal, Khanna Publishers, New Delhi

2. Engineering Mathematics by Vol. I & II by S Kohli, IPH, Jalandhar

3. Applied Mathematics by Dr. RD Sharma

4. Applied Mathematics, Vol. I & II by SS Sabharwal & Sunita Jain, Eagle Parkashan, Jalandhar

5. Comprehensive Mathematics, Vol. I & II by Laxmi Publications

6. Engineering Mathematics by Dass Gupta

7. Engineering Mathematics by C Dass Chawla, Asian Publishers, New Delhi

8. Engineering Mathematics, Vol. I, II & III by V Sundaram et al, Vikas Publishing House (P) Ltd., New Delhi

9. Engineering Mathematics by N.Ch.S.N Iyengar et.al, Vikas Publishing House (P) Ltd., New Delhi

10. Engineering Mathematics, Vol I & II by SS Sastry, Prentice Hall of India Pvt. Ltd.,

11. Engineering Mathematics, Vol I & II by AK Gupta, MacMillan India Ltd., New Delhi

SUGGESTED DISTRIBUTION OF MARKS

Topic No. Time Allotted (Hrs) Marks Allotted (%)

1 30 35

2 25 35

3 25 30

TOTAL 80 100

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