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APPLIED MATHEMATICS - II
L T P
5 - -
RATIONALE
Basic elements of integral calculus, differential calculus, numerical methods, differential m
equations included in this course will play a vital role in understanding engineering problem
mathematically. This will also develop analytical as well as conceptual abilities among
students.
LEARNING OUTCOMES
After undergoing this course, the students will be able to:
• Calculate simple integration by methods of integration
• Evaluate the area under curves, surface by using definite integrals.
• Calculate the area and volume under a curve along areas
• Solve the engineering problems with numerical methods.
• Understand the geometric shapes used in engineering problems by co-ordinate
geometry.
DETAILED CONTENTS
1. Integral Calculus - I (20 Periods)
Methods of Indefinite Integration
1.1 Integration by substitution.
1.2 Integration by rational function.
1.3 Integration by partial fraction.
1.4 Integration by parts.
1.5 Integration of special function
2. Integral Calculus - II (20 Periods)
2.1 Meaning and properties of definite integrals, Evaluation of definite integrals.
2.2 Application : Length of simple curves, Finding areas bounded by simple
curves Volume of solids of revolution, centre of mean of plane areas.
2.3 Simposns 1/3rd and Simposns3/8th rule and Trapezoidal Rule : their application
in simple cases. Numerical solutions of algebraic equations; Bisections
method, Regula-Falsi method, Newton-Raphson’s method(without proof),
Numerical solutions of simultaneous equations; Gauss elimination
method(without proof)
3. Co-ordinate Geometry (2 Dimension) (18 Periods)
3.1 Circle
Equation of circle in standard form. Centre - Radius form, Diameter form,
Two intercept form.
4. Co-ordinate Geometry (3 Dimension) (12 Periods)
4.1 Straight lines and planes in space
Distance between two points in space, direction cosine and direction ratios,
Finding equation of a straight line (without proof)
INSTRUCTONAL STRATEGY
Basic elements of Differential Calculus, Integral Calculus and differential equations can be
taught conceptually along with real engineering applications in which particular algorithm and
theory can be applied. Numerical examples will be helpful in understanding the content of the
subject.
MEANS OF ASSESSMENT
- Assignments and Quiz/Class Tests
- Mid-term and End-term Written Tests
- Model/Prototype Making
RECOMMENDED BOOKS
1. Elementary Engineering Mathematics by BS Grewal, Khanna Publishers, New Delhi
2. Engineering Mathematics, Vol I & II by SS Sastry, Prentice Hall of India Pvt. Ltd.,
3 Applied Mathematics-II by Chauhan and Chauhan, Krishna Publications, Meerut.
4. Applied Mathematics-I (B) by Kailash Sinha and Varun Kumar; Aarti Publication,
Meerut