Lovely Professional University,Punjab

Course No Cours Title Course Planner Lectures Tutorial Practical Credits

MTH101 ENGINEERING MATHEMATICS-I 14628 :: D.K Gautam 3 2 0 4

Sr. No. (Web adress) (only if relevant to the courses) Salient Features

4 www.chortle.ccsu.edu/vectorlessons/vmch16/vmch16_15.html

Shows the application of relevant topics.

5 www.math.hmc.edu/ calculus Includes graphical interpretation of examples

6 http://www.libraryofmath.com/total-derivatives.html Gives real time examples

7 http://www.libraryofmath.com/partial-derivatives.html Gives explanation

8 http://www.libraryofmath.com/jacobians.html Shows the application of relevant topics

9 http://www.libraryofmath.com/double-integral-over-a-more-general-region.html

Includes graphical interpretation of examples

10 http://www.libraryofmath.com/triple-integrals-in-cylindrical-coordinates.html

Gives information of change of variables

11 http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx

Gives information of surface integrals

Sr No Jouranls atricles as compulsary readings (specific articles, Complete reference)

Grewal B.S, Higher Engineering Mathematics, Khanna Publishers, Delhi(40th edition)1Text Book:

Other Specific Book:E.Kreyszig Advanced Engineering Mathematics, 8th Edition, Wiley Eastern .2

G.B. Thomas & R.L. Finney, Calculus and Analytic Geometry, 9th edition.3

Relevant Websites

Other Reading

Format For Instruction Plan [for Courses with Lectures and Tutorials

1 Approved for Autumn Session 2011-12

Detailed Plan For Lectures

Week Number Lecture Number Lecture Topic Chapters/Sections of Textbook/other reference

Pedagogical tool Demonstration/case study/images/anmation ctc. planned

Part 1Week 1 Lecture 1 Basic concepts:matrix addition, scalar

multiplication,inverse,matrix multiplication,->Reference :1,Ch2-2.5-2.7->Reference :2,Ch6-6.1-6.2

Lecture 2 Linear system of equations Gauss elimination ->Reference :2,Ch6-6.3->Reference :1,Ch28- 28.6(1)

Lecture 3 Rank of a matrix ->Reference :1,Ch2-2.8->Reference :2,Ch6-6.4

Week 2 Lecture 4 Linear independence of Vectors ->Reference :1,Ch2-2-10 amd 2.11(1)

Lecture 5 Solution of system of linear equations,Homogeneous and non-homogeneous equation

->Reference :2,Ch6-6.5

Lecture 6 Linear dependence and linear transformation ->Reference :1,ch2-12(1) and 2.13(1)

Week 3 Lecture 7 Eigen Values , Eigen Vectors and properties ->Reference :1,ch2-14(1)and ch2-2.15

Lecture 8 Cayley-Hamilton theorem, ->Reference :1,Ch2-2.16

Lecture 9 Diagonalization of matrix. ->Reference :1,Ch2-2.17

Week 4 Lecture 10 Reduction of qudratic form to cannonical form ->Reference :1,Ch2-2.18

2 Approved for Autumn Session 2011-12

Part 2Week 4 Lecture 11 Limits:formal and informal definition,rules of finding

limits,sandwich theorem,->Reference :3,ch1-1.1 to 1.3

Lecture 12 Extension of limit concept,one sided and two sided limts,infinite limits,continuity,algebraic and rational functions,continuity of composite,intermediate value theorem,

->Reference :3,ch1-1.4 to 1.5

Week 5 Lecture 13 Successive derivative of elementary function and standard result,Leibnitz's theorem.

->Reference :1,ch4-4.1(1) and ch4-4.2

Lecture 14 Partial derivative and which variable is treated as constant,homogeneous function

->Reference :1,ch5-5.2 to 5-5.4

Lecture 15 Euler's theorem on homogeneous functions,total derivative ,derivative of implicit function

->Reference :1,ch5-5.4 to ch5-5.5

Week 6 Lecture 16 Change of variable and jacobians with properties ->Reference :1,Ch-5-5.6 and ch5-5.7(1)

Lecture 17 Taylor's Series for a function of one and two variables , Maclaurin's series

->Reference :1,Ch5-5.9 and ch4 -4.4

Lecture 18 Indeterminate form,L'Hopital'sn rule ->Reference :1,ch4 -4.5->Reference :3,ch6-6.6

Week 7 Lecture 19 Derivative of arc, ->Reference :1,ch4 -4.9

Lecture 20 Curvature and radius of curvature for cartesian curve

->Reference :1,ch4 -4.10 and ch4-4.11

Lecture 21 Centre of curvature ->Reference :1,ch4-4.12(1)

MID-TERMPart 3

Week 8 Lecture 22 Taylor's theorem for function of two variable,Maxima and minima of function ofseveral variables

->Reference :1,Ch5-5.9 and ch5-5.11(1)

Lecture 23 Lagrange's method of undetermined multipliers, ->Reference :1,ch5-5.12

Lecture 24 Differential equation of first order first degree,formation of differential equation,solution of differential equation

->Reference :1,ch11-11.1 to ch11-11.4(1)

3 Approved for Autumn Session 2011-12

Week 9 Lecture 25 Variable separable,homogeneous equation ->Reference :1,ch11-11.6to ch11-11.7

Lecture 26 Equation reducible to homogeneous form,linear equations

->Reference :1,ch11-11.8 to ch11-11.9

Lecture 27 Equation reducible to the linear form(Bernoulli equation),exact differential equation

->Reference :1,ch11-11.10 to ch11-11.11

Week 10 Lecture 28 Equation reducible to exact equation ->Reference :1,ch11-11.12

Part 4Week 10 Lecture 29 Equation of the first order and higher digree ->Reference :1,ch11-

11.13

Lecture 30 Clairaut's equation,Lagranges equation ->Reference :1,ch11-11.14

Week 11 Lecture 31 Linear differential equtaion of second & higher degree,homogeneous and non homogeneous equation

->Reference :1,ch13-13.1 to 13.4->Reference :2,ch2-2.1 and ch2-2.2

Lecture 32 Inverse operator and particular integrals ->Reference :1,ch13-13.5 to 13.6

Lecture 33 Working procedure to solve the equation ->Reference :1,ch13-13.7

Week 12 Lecture 34 Existence and uniqueness theory,wronskian, non homogeneous equation

->Reference :2,ch2-2.7-ch2-2.8

Lecture 35 Method of variation of parameter ->Reference :1,ch13-13.8(i)

Lecture 36 Method of undetermined coefficient ->Reference :1,ch13-13.8(ii)

Spill OverWeek 13 Lecture 37 Asymptotes and curve tracing ->Reference :1,Ch-4

4.16 and ch4-4.17(1)

Lecture 38 Beta gamma Function ->Reference :1,7/7.14-7.15

Scheme for CA:out of 100*

4 Approved for Autumn Session 2011-12

Component Frequency Out Of Each Marks Total Marks

Test 2 3 10 20

Total :- 10 20

* In ENG courses wherever the total exceeds 100, consider x best out of y components of CA, as explained in teacher's guide available on the UMS

Plan for Tutorial: (Please do not use these time slots for syllabus coverage)Tutorial No. Lecture Topic Type of pedagogical tool(s) planned

(case analysis,problem solving test,role play,business game etc)

Tutorial 1 Problems of matrix addition, scalar multiplication,inverse,matrix multiplication, Linear system of equations Gauss elimination

Problem solving

Tutorial 2 Problems of rank of a matrix,Linear independence of Vectors

Problem solving

Tutorial 3 Problems of system of linear equations,Homogeneous and non-homogeneous equation

Problem solving

Tutorial 4 Problems of Linear dependence and linear transformation, Eigen Values , Eigen Vectors and properties

Problem solving

Tutorial 5 Problems of Cayley-Hamilton theorem,Diagonalization of matrix.

Problem solving

Tutorial 6 Problems of Reduction of qudratic form to cannonical form,problems of limits. Test & Solution of test.

Problem solving,Test

Tutorial 7 Problems of extension of limit concept,one sided and two sided limts,infinite limits,continuity,algebraic and rational functions,continuity of composite,intermediate value theorem,

Problem solving

Tutorial 8 Problems of Successive derivative of elementary function and standard result,Leibnitz's theorem.

Problem solving

5 Approved for Autumn Session 2011-12

Tutorial 9 Problems realated to Partial derivative and which variable is treated as constant,homogeneous function and Euler's theorem on homogeneous functions,total derivative ,derivative of implicit function

Problem solving

Tutorial 10 Problems of change of variable and jacobians Problem solving

Tutorial 11 Problems of Taylor's Series for a function of one and two variables , Maclaurin's series,Indeterminate form,L'Hopital'sn rule

Problem solving

Tutorial 12 Problems of derivative of arc,curvature and radius of curvature for cartesian curve. Test & Solution of test.

Problem solving,Test

Tutorial 13 Problems of centre of curvature Problem solving

Tutorial 14 Problems of taylor's theorem for function of two variable,Maxima and minima of function ofseveral variables

Problem solving

After Mid-TermTutorial 15 Problems of Lagrange's method of undetermined

multipliers,Problem solving

Tutorial 16 Problems of differential equation of first order first degree,formation of differential equation,solution of differential equation

Problem solving

Tutorial 17 Problems of Variable separable,homogeneous equation,Equation reducible to homogeneous form,linear equations

Problem solving

Tutorial 18 Problems of Equation reducible to the linear form(Bernoulli equation),exact differential equation, Equation reducible to exact equation

Problem solving

Tutorial 19 Problems of Equation of the first order and higher digree

Problem solving

Tutorial 20 Problems of Clairaut's equation,Lagranges equation,Linear differential equtaion of second & higher degree,homogeneous and non homogeneous equation. Test & Solution of test.

Problem solving,Test

Tutorial 21 Problems of Inverse operator and particular integrals,Working procedure to solve the equation

Problem solving

Tutorial 22 Problems of Existence and uniqueness theory,wronskian, non homogeneous equation

Problem solving

Tutorial 23 Problems of Method of variation of parameter Problem solving

Tutorial 24 Problems of Method of undetermined coefficient Problem solving

6 Approved for Autumn Session 2011-12

7 Approved for Autumn Session 2011-12