MATHEMATICS – 1st
COURSE OBJECTIVES
Contents of this course provide fundamental base for understanding elementary mathematics and their uses in solving engineering problems. Contents of this course will enable students to use basic mathematical function like logarithms, partial fractions, matrices and basic 2D curves in solving various engineering problems of all fields.
COURSE OUTCOMES
After undergoing this course, the students will be able to:
- Understand and apply angle measurements, T-Ratios, and graph functions.
- Grasp the concepts of limits, differentiation and apply differentiation rules.
- Resolve proper and improper fractions into partial fractions with various factors.
- Solve problems using permutations and combinations and apply the binomial theorem.
- Understand complex numbers in different forms , perform arithmetic operations and applications of De Moivre’s theorem.
COURSE CONTENT
UNIT – I: Trigonometry
Concept of angles, measurement of angles in degrees, grades and radians and their conversions, 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 ofmultiple angles, submultiple angles (2A, 3A, A/2). Graphs of | x | , sin x, cos x, tan x and ex .
UNIT-II : Differential Calculus
UNIT – III: Partial fractions:
Definition of polynomial fraction, proper & improper fractions and definition of partial fractions. To resolve
proper fraction and improper fraction into partial fraction with denominator containing non-repeated linear
factors, repeated linear factors and irreducible non-repeated quadratic factors.
UNIT- IV : Permutations , Combinations and Binomial theorem
Value of nPr , nCr and formula based problems.
Binomial theorem (without proof ) for positive integral index (expansion and general form); binomial theorem for any index (expansion without proof); applications of Binomial theorem.
UNIT-V : Complex Numbers:
Definition, real and imaginary parts of a complex number, polar and Cartesian representation of a complex number and its conversion from one form to other, conjugate of a complex number, modulus and amplitude of a complex number. Addition, subtraction, multiplication and division of complex numbers. De Moivre’s theorem and its applications.
INSTRUCTIONAL STRATEGY
The basic instructional strategy to teach basic mathematics, binomial theorem, trigonometry, differential
calculus etc. should be conceptual with real world applications of relevant branch. More numerical and theory
examples can be used for clear understanding of the content.
MEANS OF ASSESSMENT
- Assignments and Quiz/Class Tests
- Mid-term and End-term Written Tests
- Model/Prototype Making
RECOMMENDED BOOKS
- B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi, 40th Edition, 2007.
- G. B. Thomas, R. L. Finney, Calculus and Analytic Geometry, Addison Wesley, 9th Edition, 1995.
- Reena Garg, Engineering Mathematics, Khanna Publishing House, New Delhi (Revised Ed. 2018)
- V. Sundaram, R. Balasubramanian, K.A. Lakshminarayanan, Engineering Mathematics, 6/e., Vikas Publishing House.
- Reena Garg& Chandrika Prasad, Advanced Engineering Mathematics, Khanna Publishing House,New Delhi