(a) An ability to apply knowledge of mathematics, science and engineering. (e)
An ability to ... Glyn James, “Advanced Modern Engineering Mathematics”, 3 rd.
SRI RAMAKRISHNA INSTITUTE OF TECHNOLOGY COIMBATORE-10 (Approved by AICTE, New Delhi & Affiliated to Anna University)
DEPARTMENT OF SCIENCE AND HUMANITIES (Accredited by NBA) Subject Code & Title
Class
First Year BE ( ECE-A)
Regulation
Anna University, Chennai , R2013
Course Prerequisite
Fundamentals of Mathematics * *
* Objectives
L T PC 3 1 0 4
MA6151-MATHEMATICS – I
* *
Semester
01
To develop the use of matrix algebra techniques this is needed by engineers for practical applications. To make the student knowledgeable in the area of infinite series and their convergence so that he/ she will be familiar with limitations of using infinite series approximations for solutions arising in mathematical modeling. To familiarize the student with functions of several variables. This is needed in many branches of engineering. To introduce the concepts of improper integrals, Gamma, Beta and Error functions which are needed in engineering applications. To acquaint the student with mathematical tools needed in evaluating multiple integrals and their usage.
(a) An ability to apply knowledge of mathematics, science and engineering. Expected Outcomes
(e) An ability to develop skills to use modern engineering tools, software's and equipment to analyze problems. (h) An ability to gain broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context. (j) Graduate will show the understanding of impact of engineering solutions on the society and also will be aware of contemporary issues. 1.
To prepare graduates in Electronic and communication Engineering for successful careers dealing Indian industry with necessary core competency to succeed long-term in engineering/entrepreneurship careers, and who are well prepared to undertake PG studies and research careers.
Relationship of course to program objectives 2.
To teach students how to analyze and implement mathematics in engineering projects and to give students a strong foundation for graduate studies in the field of Electronic and communication Engineering.
TEXT BOOKS T1.
Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd., (2011).
T2.
References
Grewal. B.S, “Higher Engineering Mathematics”, 41 Khanna Publications, Delhi,
st
Edition,
(2011). REFERENCES R1. R2. R3. R4.
Dass, H.K., and Er. Rajnish Verma,” Higher Engineering Mathematics”, S. Chand Private Ltd., (2011). rd Glyn James, “Advanced Modern Engineering Mathematics”, 3 Edition, Pearson Education, (2012). Peter V. O’Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, (2012). Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company, New Delhi, (2008). Note that course follows the textbook closely and to provide you with
explanations that will complement the Lecture. The assigned textbook matches the course better than any other textbooks that we have seen, but other textbooks could also be a useful reference if you already have them.
1.Internal Assessment (20) As per the R-2013, 20 marks are alloted for assessment tests(3 tests). The assessment marks (20) for the course in Mathematics are subdivided into the weightages of 4+8+8 (First assessment test based on the syllabus of bridge course + Second assessment test + Third assessment test respectively).
Mode of Evaluation
2.External Assessment (80) University will conduct end semester examination for 100 marks. (10 × 2 = 20 & 5 × 16 = 80) Performance will be considered for assessment out of 80. Prof.K.Kanagasabapathy, HOD/S&H(Mathematics)
Faculty
COURSE PLAN-II Unit
Topics to be covered as per curriculum
Reference
Period
General Introduction MATRICES 1. I
Characteristic equation
R1-(464-465)
1
2. Eigen values and Eigen vectors of a real matrix
T1-(228-230)
1
3. Properties
R1-(475-478)
1
Tutorial
1
4. Cayley-Hamilton theorem (excluding proof)
T1-(230-232)
1
5. Orthogonal transformation of a symmetric matrix to diagonal form
T1-(222-225)
2
Tutorial 6. Quadratic form
1 T1-(236-238)
1
7. Reduction of quadratic form to canonical form by orthogonal transformation
T1-(241-243)
2
Tutorial
1 Total
SEQUENCES AND SERIES 1.Sequences & Series:: Definition and examples
II
2.Types and Convergence 3.Series of positive terms Tutorial 4.Tests of convergence: Comparison test, Integral test and D’Alembert’s ratio test 5.Alternating series Tutorial 6.Leibnitz’s test 7.Series of positive and negative terms 8.Absolute and conditional convergence
12 9+3
R1-(1005)
1
T1-(621-624) T1-(625-630)
1 1 1
T1-(641-653)
2
R1-(1035-1037) T1-(661-662) T1-(663-664)
1 1 1 1
T1-(665-669)
1
Tutorial
1 Total
12
APPLICATIONS OF DIFFERENTIAL CALCULUS 1. Curvature in Cartesian co-ordinates 2. Centre and radius of curvature Tutorial 3. Circle of curvature III
4. Evolutes Tutorial 5. Envelopes 6. Evolute as envelope of normals Tutorials
9+3 R1-(103-116) R1-(117-124)
2 1 1
R1-(133-138)
1
R1-(141-148)
2
R1-(173-178) R1(179-182)
1 1 2 1
Total
12
DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES
1. Limits and Continuity 2. Partial derivatives 3. Total derivatives
IV
Tutorial 4. Differentiation of implicit functions 5. Jacobian and properties 6. Taylor’s series for functions of two variables Tutorial 7. Maxima and minima of functions of two variables
9+3 R1-(206-208) R2-(558-562) R1-245 R1-245 R1-(246-248) T1-(432-436) T1-(437-438), R4-4.5
1 1 1 1 1 1 1 1 1
8. Lagrange’s method of undetermined multipliers
R4-4.10
2
Tutorials
1 Total
12
MULTIPLE INTEGRALS
V
9+3
1. Double integrals in cartesian and polar coordinates 2. Change of order of integration 3. Change of variables in double integrals Tutorial 4. Area enclosed by plane curves 5. Change of variables in double integrals 6. Triple integration in Cartesian co-ordinates Tutorial 7. Area of a curved surface 8. Triple integrals, Volume of Solids
R1-(133-140) R1-(275-276) T1-(485-487)
1 1 1 1 1 1 1 1 1
T1-(487-489) R1-(272-276) R1-(278-279) R1-(300-302) R4-7.21, R1-(182-186)
2
Tutorials
1 Total
12
TOTAL HOURS
: 60
Bridging the Curriculum Gap Unit
Topics to be covered as per curriculum
Period
Matrices, Vector Algebra and Partial Fractions
I
Relations between matrices and determinants – Representation of two variable linear equations – Representation of two variable non - linear equations.
1
Classification of vectors – Linear combination of vectors – Components of a vector in two and three dimensions – Direction ratios & Direction cosines and counter examples.
1
Proper and Improper fractions – Types of partial fractions. 1 Total
3
Series & Sequences, Analytical Geometry (Two Dimensions) and Trigonometric Functions Link between series and sequences – Validity of series
1
Convergence – Divergence – Counting Principles. Basic concepts - Point – Line - Slope – Straight line – Parallel lines.
1
II Domain – Co domain of all trigonometric functions – Notion of hyperbolic functions – Relation between circular and hyperbolic functions.
Total
1
3
Differential Calculus Theory of equations: Relation between roots and coefficients – expressions1
equations and factors. Theory of limits: Limit of a function – Left and right limits (examples) III
1
Concepts of continuity: At a point- in an interval – discontinuous function. Differentiability: Link between differentiability and continuity-left derivative and right derivative (closed interval and open interval).
1
Techniques of differentiation: Total and partial derivatives up to the second order. Total
3
Integral Calculus
IV
Proper and improper integrals – Definite integrals - Indefinite integrals
1
Integration by parts – Bernoulli’s formula
1
Integration by using partial fraction – Reduction formula.
1 Total
3
Differential Equations
V
Linear – non linear – homogeneous and non- homogeneous equations – Order –Degree – Need of Differential equations and importance
1
Relation between constant coefficients and variable coefficients
1
Formation of differential equations
1 Total TOTAL HOURS
COURSE INSTRUCTOR
HOD
PRINCIPAL
3 15
