Page 1 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , Government of Karnataka, Department of Collegiate and Technical Education, Board of Technical Examinations, Bangalore, Course Code, , 20SC01T, , Semester, , I/II, , Course Title, , ENGINEERING, MATHEMATICS, , Course Group, , Core, , No. of Credits, , 4, , Type of Course, , Lecture, , Course Category, , Theory, , Total Contact Hours, , Prerequisites, , 10thLevel Mathematics, , Teaching Scheme, , (L:T:P) = 4:0:0, , CIE Marks, , 50, , SEE Marks, , 50, , 4Hrs Per Week, 52Hrs Per Semester, , RATIONALE, Engineering Mathematics specification provides students with access to important mathematical, ideas to develop the mathematical knowledge and skills that they will draw on in their personal and, work lives. The course enable students to develop mathematical conceptualization, inquiry,, reasoning, and communication skills and the ability to use mathematics to formulate and solve, problems in everyday life, as well as in mathematical contexts. At this level, the mathematics, curriculum further integrates the three content areas taught in the higher grades into three main, learning areas: Algebra; Measurement of angles and Trigonometry and Calculus., , 1. COURSE SKILL SET, Student will be able to:, , 1. Solve system of linear equations arise in different engineering fields, 2. Incorporate the knowledge of calculus to support their concurrent and subsequent, engineering studies, 3. Adept at solving quantitative problems, 4. Ability to understand both concrete and abstract problems, 5. Proficient in communicating mathematical ideas, 6. Detail-oriented, 2. COURSE OUT COMES, At the end of the course, student will be able to, CO1, CO2, CO3, , Determine the inverse of a square matrix using matrix algebra. Apply the concepts, of matrices and determinants to solve system of linear equations and find eigen, values associated with the square matrix., Find the equation of straight line in different forms. Determine the parallelism and, perpendicularity of lines., Calculate trigonometric ratios of allied angles and compound angles. Transform sum, or difference of trigonometric ratios into product and vice versa., , Department of Collegiate & Technical Education Bengaluru-560001, , Page 15

Page 2 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , CO4, , Differentiate various continuous functions and apply the concept in real life, situations., , CO5, , Integrate various continuous functions and apply the concept in evaluating the area, and volume through definite integrals., , 3. SUGGESTED SPECIFICATION TABLE WITH HOURS & MARKS, UNIT, NO, , TEACHING, HOURS, , UNIT TITLE, , DISTRIBUTION(THEORY), R, LEVEL, , U, LEVEL, , A, LEVEL, , TOTAL, , 1, , Matrices and Determinants, , 10, , 8, , 20, , 12, , 40, , 2, , Straight lines, , 10, , 8, , 20, , 12, , 40, , 3, , Trigonometry, Differential Calculus and, applications, Integral Calculus and, applications, , 10, , 8, , 20, , 12, , 40, , 11, , 8, , 20, , 12, , 40, , 11, , 8, , 20, , 12, , 40, , 52, , 40, , 100, , 60, , 200, , 4, 5, , Total, , Legends: R = Remember; U = Understand; A = Apply and above levels (Bloom’s revised, taxonomy), , 4. DETAILS OF COURSE CONTENT, The following topics/subtopics is to be taught and assessed in order to develop Unit Skill sets for, achieving CO to attain identified skill sets., , UNIT-1, MATRICES AND DETERMINANTS, , UNIT, NO, , Unit skill set, (In cognitive domain), , Topics/Subtopics, 1.1, 1.2, , Ø Use algebraic skills which, , are essential for the study, of systems of linear, equations, matrix algebra, and eigen values, , 1.3, , 1.4, 1.5, 1.6, , Matrix and types, Algebra of Matrices (addition,, subtraction, scalar multiplication, and multiplication), Evaluation of determinants of a, square matrix of order 2 and 3., Singular matrices, Cramer’s rule for solving system, of linear equations involving 2, and 3 variables, Adjoint and Inverse of the nonsingular matrices of order 2 and 3, Characteristic equation and Eigen, values of a square matrix of order 2, , Department of Collegiate & Technical Education Bengaluru-560001, , Hours, L-T-P, , 10-0-0, , Page 16

Page 3 : Diploma in Computer Science & Engineering, , UNIT-2, STRAIGHT LINES, , Ø Able, Ø, , UNIT-5, INTEGRAL CALCULUS AND, APPLICATIONS, , UNIT-4, DIFFERENTIAL CALCULUS, AND APPLICATIONS, , UNIT-3, TRIGONOMETRY, , Ø, , Ø, , to find the equation, of a straight line in, different forms, Determine whether the, lines are parallel or, perpendicular, , Use basic trigonometric, skills in finding the, trigonometric ratios of, allied and compound, angles, Able to find all the, measurable dimensions, of a triangle, , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, , Slope of a straight line, Intercepts of a straight line, Intercept form of a straight line, Slope-intercept form of a straight line, Slope-point form of a straight line, Two-point form of a straight line, General form of a straight line, Angle between two lines and conditions, for lines to be parallel and perpendicular, 2.9 Equation of a straight line parallel to the, given line, 2.10 Equation of a straight line perpendicular, to the given line, 3.1 Concept of angles, their measurement,, Radian measure and related conversions., 3.2 Signs of trigonometric ratios in different, quadrants (ASTC rule), 3.3 Trigonometric ratios of allied angles, (definition and the table of, trigonometric ratios of standard, allied angles say 900±Ɵ, 1800±Ɵ,, 2700±Ɵ and 3600±Ɵ), 3.4 Trigonometric ratios of compound, angles (without proof), 3.5 Trigonometric ratios of multiple angles, 3.6 Transformation formulae, 4.1 Derivatives of continuous functions in an, interval (List of formulae), 4.2 Rules of differentiation, 4.3 Successive differentiation (up to second, order), 4.4 Applications of differentiation, , Ø Able to differentiate, algebraic, exponential,, trigonometric, logarithmic, and composite functions, Ø Able to find higher order, derivatives, Ø Understand and work with, derivatives as rates of, change in mathematical, models, Ø Find local maxima and, minima of a function, Ø Understand the basic rules 5.1, of integration and, 5.2, Evaluate integrals with, basic integrands., 5.3, Ø Identify the methods to, 5.4, evaluate integrands, 5.5, , Ø, , 2020-21, , List of standard integrals and Basic rules, of integration, Evaluation of integrals of simple, function and their combination, Methods of integration, Concept of definite integrals, Applications of definite integrals, , C20, , 10-0-0, , 10-0-0, , 11-0-0, , 11-0-0, , Apply the skills to evaluate, integrals representing areas, and volumes, , Department of Collegiate & Technical Education Bengaluru-560001, , Page 17

Page 4 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , 5. MAPPING OF CO WITH PO, CO, , CO1, , CO2, , CO3, , CO4, , CO5, , Course Outcome, , Determine the inverse of a square, matrix using matrix algebra. Apply the, concepts of matrices and determinants, to solve system of linear equations and, find eigen values associated with the, square matrix., Find the equation of straight line in, different forms. Determine the, parallelism and perpendicularity of, lines., Calculate trigonometric ratios of allied, angles and compound angles., Transform sum (difference) of, trigonometric ratios into product and, vice versa., Differentiate various continuous, functions and apply the concept in real, life situations., Integrate various continuous functions, and apply the concept in evaluating the, area and volume through definite, integrals., , Course, , CO’s, , ENGINEERING MATHEMATICS, , CO1, CO2, CO3, CO4, CO5, , PO, Mapped, , UNIT, Linked, , CL, R/U/A, , Theory, in Hrs, , TOT, AL, , 1, 7, , 1, , R/U/A, , 10, , 40, , 1, 7, , 2, , R/U/A, , 10, , 40, , 1, 7, , 3, , R/U/A, , 10, , 40, , 1, 3, 7, , 4, , R/U/A, , 11, , 40, , 1, 3, 7, , 5, , R/U/A, , 11, , 40, , 52, , 200, , Programme Outcomes (PO’s), 1, , 2, , 3, , 4, , 5, , 6, , 7, , 3, 3, 3, 3, 3, , 1, 1, 1, 1, 1, , 0, 0, 0, 3, 3, , 0, 0, 0, 0, 0, , 0, 0, 0, 0, 0, , 0, 0, 0, 0, 0, , 3, 3, 3, 3, 3, , Level 3- Highly Mapped, Level 2-Moderately Mapped, Level 1-Low Mapped, Level 0- Not Mapped, , Department of Collegiate & Technical Education Bengaluru-560001, , Page 18

Page 5 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , 7. INSTRUCTIONAL STRATEGY, These are sample Strategies, which teacher can use to accelerate the attainment of the various course, outcomes, 1. Explicit instruction will be provided in intervention classes or by using different differentiation, strategies in the main classroom., 2. Lecturer method (L) does not mean only traditional lecture method, but different type of teaching, method and media that are employed to develop the outcomes., 3. Observing the way their more proficient peers use prior knowledge to solve current challenges, and persevere in problem solving will help struggling students to improve their approach to, engaging with rich contextual problems., 4. Ten minutes a day in homeroom, at the end of class, or as a station in a series of math activities, will help students build speed and confidence., 5. Topics will be introduced in a multiple representation., 6. The teacher is able to show different ways to solve the same problem and encourage the students, to come up with their own creative ways to solve them., 7. In a perfect world, teacher would always be able to demonstrate how every concept can be, applied to the real world - and when that's possible, it helps improve the students' understanding., When a concept cannot be applied in that manner, we can still share how it might be applied, within mathematics., , 8. SUGGESTED LEARNING RESOURCES:, Sl., No., , Author, , 1, , B.S. Grewal, , 2, 3, 4, 5, , G. B. Thomas, R. L., Finney, S.S. Sabharwal, Sunita, Jain, Eagle Parkashan, Comprehensive, Mathematics, ReenaGarg, &Chandrika Prasad, , Title of Books, , Publication/Year, , Higher Engineering, Mathematics, Calculus and Analytic, Geometry, Applied Mathematics, Vol. I &, II, Comprehensive Mathematics, Vol. I & II, Advanced Engineering, Mathematics, , Khanna Publishers, New Delhi,, 40th Edition,2007, Addison Wesley, 9th Edition,, 1995, , Department of Collegiate & Technical Education Bengaluru-560001, , Jalandhar., Laxmi Publications, Delhi, Khanna Publishing House, New, Delhi, , Page 19

Page 6 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , 9. COURSE ASSESSMENT AND EVALUATION CHART, Sl.No., 1, 2, 3, 4, 5, , 6, , Assessment, CIE Assessment 1, (Written Test -1), At the end of 3rd week, CIE Assessment 2, (Written Test -2), At the end of 7th week, CIE Assessment 3, (Written Test -3), At the end of 13th week, CIE Assessment 4, (MCQ/Quiz) At the end of, 5th week, CIE Assessment 5, (Open book Test), At the end of 9th week, CIE Assessment 6, (Student, activity/Assignment), At the end of 11th week, , Duration, , Max marks, , 80 minutes, , 30, , Average of three, written tests, , 80 minutes, , 30, , 30, , 80 minutes, , 30, , 60 minutes, , 20, , 60 minutes, , 20, , Average of three, 20, , 60 minutes, , 20, , Total Continuous Internal Evaluation (CIE) Assessment, 8, , Conversion, , Semester End Examination, (SEE) Assessment (Written, Test), , 3 Hours, , 50, 100, , Total Marks, , 50, 100, , Note:, 1. SEE (Semester End Examination) is conducted for 100 Marks theory courses for a time, duration of 3 Hours., 2. Three CIE (written test), each of 30 marks for a time duration of 80 minutes shall be, conducted. Also, three CIE (MCQ or Quiz/Open book test/student activity or assignment), each of 20 marks for the time duration of 60 minutes shall be conducted. Any fraction at any, stage during evaluation will be rounded off to the next higher digit, 3. Assessment of assignment and student activity is evaluated through appropriate rubrics by, the respective course coordinator. The secured mark in each case is rounded off to the next, higher digit., , Department of Collegiate & Technical Education Bengaluru-560001, , Page 20

Page 7 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , 10 DETAILED COURSE CONTENT, UNIT, NO, AND, NAME, , CO, , PO, , CONTACT, HRS, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , 1, , 1,7, , 1, , Slope of the straight line(provided with inclination and, two points on the line as well) and problems, , 2, , 1,7, , 1, , Intercepts of a straight line and problems, , 2, , 1,7, , 1, , Intercept form of a straight line and problems, Slope-intercept form of a straight line and problems, Slope-point form of the straight line and problems, Two-point form of a straight line and problems, General form of a straight line.problems on finding, slope and intercepts., Angle between two straight lines and conditions for, the lines to be parallel and perpendicular and, problems, Equation of a line parellel to the given line and, problems, Equation of a line perpendicular to the given, line.problems, , 2, 2, 2, 2, , 1,7, 1,7, 1,7, 1,7, , 1, 1, 1, 1, , 2, , 1,7, , 1, , 2, , 1,7, , 1, , 2, , 1,7, , 1, , 2, , 1,7, , 1, , DETAILED COURSE CONTENT, , 2, STRAIGHTLINES, , 1, MATRICES AND DETERMINANTS, , Definition and types of matrices, Algebra of Matrices (addition, subtraction and, scalar multiplication) problems, Multiplication of Matrices(problems), Evaluation of 2x2 ,3x3 determinants and, Singular matrices and problems in finding, unknown variable, Cramer’s rule to solve system of linear equation with 2, and 3 variables, Cramer’s rule to solve system of linear equation with 2, and 3 variables.problems, Minors, Cofactors of elements of square matrices of, order 2 and 3, Adjoint of a square matrix(2x2 and 3x3),Inverse of a, non singular square matrix, Adjoint of a square matrix(2x2 and 3x3),Inverse of a, non singular square matrix and problems, Characteristic equation and eigen values of a 2x2, matirx and problems, , Department of Collegiate & Technical Education Bengaluru-560001, , TOTAL, , 10, , 10, , Page 21

Page 8 : DIFFERENTIAL CALCULUS AND, APPLICATIONS, , 4, , 3, TRIGONOMETRY, , Diploma in Computer Science & Engineering, , 2020-21, , Concept of angles and their measurement., Radian measures and related conversions (degree to, radian and vice-versa) and problems, , 3, , 1,7, , 1, , Signs of trigonometric ratios in different quadrants, (ASTC rule), , 3, , 1,7, , 1, , 3, , 1,7, , 1, , 3, , 1,7, , 1, , 3, , 1,7, , 1, , 3, , 1,7, , 1, , 3, , 1,7, , 1, , 3, , 1,7, , 1, , 1,7, , 1, , 1,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , 4, , 1,3,7, , 1, , Trigonometric ratios of allied angles (definition and, the table of trigonometric ratios of standard allied, angles say 900±Ɵ, 1800±Ɵ, 2700±Ɵ and 3600±Ɵ), Problems on allied angles. (proving identities), Problems on allied angles. (Finding values of x in an, identity), Trigonometric ratios of compound angles (without, proof), Trigonometric ratios of multiple angles (sin2A,, cos2A, tan2A, sin3A, cos3A and tan3A), Problems on multiple angles sin2A, cos2A, tan2A,, sin3A, cos3A and tan3A, Transformation formulae (without proof) as sum to, product. (Simple problems), Transformation formulae (without proof) as product, to sum. (Simple problems), Definition of a derivative of a function. Listing the, derivatives of standard functions. (Algebraic,, trigonometric, exponential, logarithmic and inverse, trigonometric functions), Addition and subtraction rule of differentiation and, problems, Product rule and quotient rule of differentiation and, problems, Product rule and quotient rule of differentiation and, problems, Composite functions and their derivatives. (CHAIN, RULE), Composite functions and their derivatives. (CHAIN, RULE). Problems, Successive differentiation up to second order, Slope of the tangent and normal to the given curve, and their equations and problems, , Department of Collegiate & Technical Education Bengaluru-560001, , 3, 3, , C20, , 10, , 11, , Page 22

Page 9 : 5, INTEGRAL CALCULUS AND APPLICATIONS, , Diploma in Computer Science & Engineering, Rate measure: velocity and acceleration at a point of, time and problems, Local Maxima and Minima of a function, Local Maxima and Minima of a function. Problems, Definition of an indefinite integral. Listing the, Integrals of standard functions. (Algebraic,, trigonometric, exponential, logarithmic and inverse, trigonometric functions), Rules of Integration. Evaluation of integrals with, simple integrands and their combinations, Rules of Integration. Evaluation of integrals with, simple integrands and their combinations. Problems, Evaluation of integrals with simple integrands and, their combinations. Problems, Evaluation of integrals by Substitution method, Evaluation of integrals by Integration by parts, Evaluation of integrals by Integration by parts., Problems, Definition of definite integrals and their evaluation, Evaluation of Definite integrals. Problems, , 2020-21, , 4, , 1,3,7, , 1, , 4, 4, , 1,3,7, 1,3,7, , 1, 1, , 5, , 1,3,7, , 1, , 5, , 1,3,7, , 1, , 5, , 1,3,7, , 1, , 5, , 1,3,7, , 1, , 5, 5, , 1,3,7, 1,3,7, , 1, 1, , 5, , 1,3,7, , 1, , 5, 5, , 1,3,7, 1,3,7, , 1, 1, , Area enclosed by the curves by integral method, , 5, , 1,3,7, , 1, , Volume generated by the curve rotated about an axis, by integral method, , 5, , 1,3,7, , 1, , Department of Collegiate & Technical Education Bengaluru-560001, , C20, , 11, , Page 23

Page 11 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , SECTION – 2, 3, , a, , b, , If the straight line is passing through the points (1, 2) and (3, 5) then find the, slope of the line., Write the standard intercept form of the straight line and hence find the, equation of the straight line whose x and y intercepts are 2 and 3, , 4, , 5, , respectively., , c, , Write the standard slope-intercept form of a straight line. Find the equation, , 5, , of the straight line passing through the point (3, 5) and slope 4 units., , d, , Find the equation of the straight line parallel to the line passing through the, , 6, , points (1, 3) and (4, 6)., , 4, a, , i) If a line inclined at 45! with x-axis find its slope., , ii) Write, , 2+2, , the x and y intercept of the line 2x+3y=10., , b, , Find the equation of the straight line whose angle of inclination is 450 and, , 5, , passingthrough the origin., , c, , Find the equation of the straight line perpendicular to the line 2x+6y=3 and, , 5, , with the y intercept 2 units., , d, , Find the acute angle between the lines 7x-4y=0 and 3x-11y +5=0., , 6, , SECTION – 3, , 5, , a, , Express 75! in radian measure and 3π/2 in degree., , 4, , b, , Prove that cos( A + B) cos( A - B) = cos 2 A - sin 2 B ., , 5, , c, , Show that cos 2q = 2 cos 2 q - 1., , 5, , Department of Collegiate & Technical Education Bengaluru-560001, , Page 25

Page 12 : Diploma in Computer Science & Engineering, , d, 6, , 2020-21, , Find the value of sin120! × cos330! - sin 240! × cos390! without using, calculator., , a, , Find the value of sin15! ., , b, , Simplify, , c, , Prove that sin 3q = sin 3q - 4 sin 3 q ., , d, , Prove that sin 20! × sin 40! × sin 80! =, , C20, , 6, 4, , cos(360! - A) tan(360! + A), ., cot(270! - A) sin(90! + A), , 5, 5, 3, ., 8, , 6, , SECTION – 4, , 7, , a, , Find the derivative of y = x 2 + e 2 x + cos 2 x - 2 log x with respect to x ., , b, , Find dy/dx of y =, , c, , 8, , sec x + tan x, ., sec x - tan x, æ1+ x ö, Find dy/dx of y = tan -1 ç, ÷., è1- x ø, , d, , If the s = 2 x 3 + 3x + 4 repersents the displacement of the particle in motion at, time x, then find the velocity of the particle at x = 2 secs and acceleration at, x = 3 secs., , a, , Find, , b, , If y = e 2 x sin 3x then find, , c, , Find, , d, , Find the equation of tangent and normal to the curve y = x 2 at the point, , dy, of y = 3x 4 + 4 log x + 2e 3 x + tan -1 x ., dx, dy, ., dx, , d2 y, if y = 3sin x + 4 cos x at x = 1., dx 2, , 4, 5, 5, 6, , 4, 5, 5, , 6, , (1, 1)., , Department of Collegiate & Technical Education Bengaluru-560001, , Page 26

Page 13 : Diploma in Computer Science & Engineering, , 2020-21, , C20, , SECTION – 5, , 9, , a, , Evaluate ò ( x - 1)( x + 1)dx ., , 4, , p/2, , b, , Evaluate ò sin 2 x dx, , 5, , ò x sin xdx ., , 5, , 0, , c, , Evaluate, , d, , Find the area bounded by the curve y = 4 x - x 2 - 3 , x-axis and ordinates, , 6, , x = 1 and x = 3 ., , 10, , a, , 2, , Evaluate ò e x dx ., , 4, , 0, , ò, , 4 cos(log x), dx ., x, , b, , Evaluate, , c, , Evaluate ò x e x dx ., , 5, , d, , Find the volume of the solid generated by revolving the curve y = x 2 + 5 x, , 6, , 5, , between x = 1 and x = 2 ., , *************************, , Department of Collegiate & Technical Education Bengaluru-560001, , Page 27