12817_mth107 -- Elementary Mathematics for Engineers (4)

Lovely Professional University, Punjab

Course Code Course Title Course Planner Lectures Tutorials Practicals Credits

MTH107 ELEMENTARY MATHEMATICS FOR ENGINEERS 11359::Rajesh Kumar Gupta 3.0 0.0 0.0 3.0

Course Category Courses with Numerical focus

TextBooks

Sr No Title Author Edition Year Publisher Name

T-1 HIGHER ENGINEERING MATHEMATICS

B.S.GREWAL 42th 2012 KHANNA PUBLISHER.

Reference Books

Sr No Title Author Edition Year Publisher Name

R-1 ELEMENTARY ENGINEERING MATHEMATICS

DR. B.S. GREWAL 11th 2005 KHANNA PUBLISHER

R-2 ADVANCED CALCULUS ROBERT C.WREDE MURRY SPIEGEL

2nd 2005 TATA MCGRAW - HILL EDUCATION

Relevant Websites

Sr No (Web address) (only if relevant to the course) Salient Features

RW-1 http://www.math.utsc.utoronto.ca/calculus/Redbook/ Caclulus lecture notes

RW-2 http://tarungehlots.blogspot.in/2013/09/cbse-ncert-class-12-maths-solutions_10.html Tutorials

RW-3 http://home.iitk.ac.in/~psraj/mth102/lecture_notes.html Lecture Notes .

Audio Visual Aids

Sr No (AV aids) (only if relevant to the course) Salient Features

AV-1 http://nptel.ac.in/video.php?subjectId=106106094 Video Lecture

AV-2 http://nptel.ac.in/courses/111104027/ Video Lecture

AV-3 http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/

Video Lecture

AV-4 http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/

Video Lecture

LTP week distribution: (LTP Weeks)

Weeks before MTE 7

Weeks After MTE 7

Spill Over 3

Week Number

Lecture Number

Broad Topic(Sub Topic) Chapters/Sections of Text/reference books

Other Readings,Relevant Websites, Audio Visual Aids, software and Virtual Labs

Lecture Description Learning Outcomes Pedagogical ToolDemonstration/ Case Study / Images / animation / ppt etc. Planned

Live Examples

Week 1 Lecture 1 Basic Calculus(Functions) R-1:11.4R-2:Pg-39

RW-1AV-1

Lecture 0 will be introduction to the courseLecture 1 Basics of Function .

Student will learn how to define Function .

Discussion Functions are used whenever one variable depends on another variable.The area of a circle depends on its radius.

Lecture 2 Basic Calculus(Graphical representation of functions.)

R-1:11.5R-2:Pg-40

Graphical Representation

student will learn the Graphical Representation of Function.

Discussion

Lecture 3 Basic Calculus(Classification of functions)

R-1:11.6 Classification of functions

Learning of different classifications of Function .

Discussion .

Week 2 Lecture 4 Basic Calculus(Limit of a function and Evaluation of limits)

R-1:11.7 RW-1 Limit of a function and Evaluation of limits

Student will able to find limiting value of the function .

Discussion

Lecture 5 Basic Calculus(Continuity of a function-At a point)

R-1:11.8R-2:Pg-47

RW-1 Continuity of a function-At a point and In an interval

Student will observe the continuity/discontinuity of the function

Discussion

Basic Calculus(Continuity of a function-In an interval)

R-1:11.8 Continuity of a function-At a point and In an interval


Discussion .

Lecture 6 Basic Calculus(Continuity of a function-In an interval)

R-1:11.8 Continuity of a function-At a point and In an interval


Discussion .

Basic Calculus(Continuity of a function-At a point)

R-1:11.8R-2:Pg-47

RW-1 Continuity of a function-At a point and In an interval


Discussion

Week 3 Lecture 7 Differential Calculus(Differential coefficient, General rules of differentiation)

R-1:12.1 Differential coefficient, General rules of differentiation

Student will Learn the process of finding the differential Coefficient .

Discussion.

Detailed Plan For Lectures

Week 3 Lecture 8 Differential Calculus(Derivatives of standard functions)

R-1:12.2R-2:Pg-71

Derivatives of standard functions

Student will Learn the process of finding the differential Coefficient .

Discussion

Lecture 9 Test1

Week 4 Lecture 10 Differential Calculus(Derivatives of Parametric forms)

R-1:12.3-12.4 Derivatives of Parametric forms andimplicit and Logarithmic functions.

Student will Learn the process of finding the differential Coefficient of Parametric forms andimplicit and Logarithmic functions.

Discussion

Differential Calculus(Derivatives of implicit functions)

R-1:12.3-12.4 AV-3 Derivatives of Parametric forms andimplicit and Logarithmic functions.


Discussion

Differential Calculus(Logarithmic differentiation)

R-1:12.3-12.4 Derivatives of Parametric forms andimplicit and Logarithmic functions.


Discussion

Lecture 11 Differential Calculus(Maxima and Minima)

R-1:14.13 Maxima and Minima Student will learn the conditions and procedure of Maxima and Minima.

Discussion.

Lecture 12 Differential Calculus(Partial derivatives)

R-1:15.1 AV-4 Partial derivatives Student will be able to find the derivative of the functions of two or more variables.

Discussion

Week 5 Lecture 13 Differential Calculus(Total Derivatives)

R-1:15.5 Total Derivatives Student will be able to find the derivative of the Composite functions .

Discussion

Lecture 14 Integral Calculus(Integration as an inverse process of differentiation and properties of indefinite integral)

R-1:16.1-16.2 AV-3 Introduction and types of Integral.

Student will learn about the definite and indefinite integrals .

Discussion

Week 5 Lecture 15 Integral Calculus(Methods of integration-By Substitution)

R-1:16.3 integration by Substitution

Student will be able to evaluate integrals by changing the variables.

Discussion

Week 6 Lecture 16 Test2

Lecture 17 Integral Calculus(Methods of integration-By Partial fractions)

R-1:16.8-16.11 integration by Parts and by Partial fractions.

Student will able evaluate the integration of the product of two functions.

Discussion

Integral Calculus(Methods of integration-By Parts)

R-1:16.8-16.11 AV-3 integration by Parts and by Partial fractions.

Student will able evaluate the integration of the product of two functions.

Discussion

Lecture 18 Integral Calculus(Definite integral as Limit of sum.)

R-1:17.12 Definite integral as Limit of sum.

Student will learn elementary approach to find the value of definite integral.

Discussion Finding area under the curve .

Week 7 Lecture 19 Integral Calculus(Properties of definite integral)

R-1:17.11 RW-1 Properties of definite integral.

Student will be able to apply the properties of definite integral.

Discussion

Lecture 20 Integral Calculus(Method of solving first order differential equations-By Variable separable and Homogeneous differential equations)

R-1:20.2-20.3 RW-1AV-3

Variable separable and Homogeneous differential equations

Student will learn the variable separable form of differential equation and the method to solve it

Discussion

Lecture 21 Integral Calculus(Linear differential equations of first order and first degree)

R-1:20.5-20.6 Linear differential equations of first order and first degree.

Student will be able to recognize the differential equations of first order and first degree .

Discussion

MID-TERMWeek 8 Lecture 22 Linear Algebra(Determinant

and its properties)T-1:2.2-2.3 RW-2 Determinant and its

propertiesStudent will learn the Determinant and its properties

Discussion

Lecture 23 Linear Algebra(Matrices, operations, Transpose, Ad joint, Inverse)

T-1:2.4-2.6 RW-2 Matrices, operations, Transpose, Ad joint, Inverse

Student will learn the basics of Linear Algebra.

Discussion

Linear Algebra(Matrices, operations, Transpose, Ad joint, Inverse)

T-1:2.4-2.6 Matrices, operations, Transpose, Ad joint, Inverse


Discussion

Lecture 24 Linear Algebra(Rank of a matrix)

T-1:2.7 RW-3 Rank of a matrix and elementary transformations .


Discussion

Week 9 Lecture 25 Linear Algebra(Solution of Linear system of equations by Cramer's rule)

T-1:2.9 Solution of Linear system of equations by Cramer's rule

Student will learn the method to solve linear system of equations.

Discussion

Lecture 26 Linear Algebra(Vectors-Linear dependance and independance)

T-1:2.12 AV-2 Vectors-Linear dependance and independance


Discussion

Lecture 27 Linear Algebra(Eigen values and Eigen vectors, Properties of Eigen values)

T-1:2.13-2.14 RW-3 Eigen values and Eigen vectors, Properties of Eigen value


Discussion

Week 10 Lecture 28 Linear Algebra(Eigen values and Eigen vectors, Properties of Eigen values)

T-1:2.13-2.14 RW-3 Eigen values and Eigen vectors, Properties of Eigen value


Discussion

Lecture 29 Linear Algebra(Cayley-Hamilton theorem)

T-1:2.15 Cayley-Hamilton theorem


Discussion

Lecture 30 Linear Programming Problems(Formulation of the problem)

T-1:34.2 AV-2 Formulation of the problem

Student will learn the optimization of of linear functions subject to linear constraints .

Discussion

Week 11 Lecture 31 Linear Programming Problems(Graphical Method)

T-1:34.3-34.4 RW-2 Graphical Method Student will learn the optimization of of linear functions subject to linear constraints .

Discussion Maximizing profit and minimizing cost.

Lecture 32 Test3

Lecture 33 Linear Programming Problems(General LPP, Canonical and standard form of LPP)

T-1:34.5-34.6 General LPP, Canonical and standard form of LPP


Discussion

Week 12 Lecture 34 Linear Programming Problems(Simplex method)

T-1:34.7-34.8 AV-2 Simplex method and its working procedure.


Discussion

Lecture 35 Linear Programming Problems(Simplex method)

T-1:34.7-34.8 AV-2 Simplex method and its working procedure.


Discussion

Week 12 Lecture 36 Linear Programming Problems(Duality concept)

T-1:34.11 Duality concept Student will learn that how to write the dual of the LPP.

Discussion

Week 13 Lecture 37 Elements of Logic and Set theory(Sets and Set operations)

T-1:37.1-37.2 AV-1 Sets and Set operations Student will learn the language of sets which is used to express mathematical ideas concisely.

Discussion

Lecture 38 Elements of Logic and Set theory(Laws of set theory and principle of inclusion)

T-1:37.3-37.4 Laws of set theory and principle of inclusion

Student will learn the language of sets which is used to express mathematical ideas concisely.

Discussion

Elements of Logic and Set theory(De Morgan's law)



Discussion

Lecture 39 Elements of Logic and Set theory(De Morgan's law)



Discussion

Elements of Logic and Set theory(Laws of set theory and principle of inclusion)



Discussion

Week 14 Lecture 40 Elements of Logic and Set theory(Algebra of Logic, Logical operators)

T-1:37.5-37.6 AV-1 Algebra of Logic, Logical operators

Student will learn the logical reasoning.

Discussion

Lecture 41 Elements of Logic and Set theory(Statement generated by a set, Equivalence)

T-1:37.7-37.8 Statement generated by a set, Equivalence


Discussion

Lecture 42 Elements of Logic and Set theory(Duality law and Arguments)

T-1:37.9-37.10 Duality law and Arguments


Discussion

SPILL OVERWeek 15 Lecture 43 Spill Over

Lecture 44 Spill Over

Lecture 45 Spill Over

Scheme for CA:Component Frequency Out Of Each Marks Total Marks

Test 2 3 10 20

Total :- 10 20

Details of Academic Task(s)

AT No. Objective Topic of the Academic Task Nature of Academic Task(group/individuals/field

work

Evaluation Mode Allottment / submission Week

Test1 Observe the performance of students .

Basic Calculus : Functions, Graphical representation of functions., Classification offunctions, Limit of a function and Evaluation of limits, Continuity of a function-At apoint, Continuity of a function-In an interval

Individual A test of 30 marks consisting of 4 questions ( 2 of 5 marks , 2 of 10 marks )

2 / 3


Differential Calculus : Differential coefficient, General rules of differentiation,Derivatives of standard functions, Derivatives of Parametric forms, Derivatives ofimplicit functions, Logarithmic differentiation, Maxima and Minima, Partial derivatives,Total Derivatives


5 / 6


Linear Algebra : Determinant and its properties, Matrices, operations, Transpose,Ad joint, Inverse, Solution of Linear system of equations by Cramer's rule, Rank of amatrix, Vectors-Linear dependance and independance, Eigen values and Eigenvectors, Properties of Eigen values, Cayley-Hamilton theorem


10 / 11

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12817_mth107 -- Elementary Mathematics for Engineers (4)