12817_mth107 -- Elementary Mathematics for Engineers (4)

  • Published on
    24-Dec-2015

  • View
    54

  • Download
    1

DESCRIPTION

mth

Transcript

  • 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

    Student will observe the continuity/discontinuity of the function

    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

    Student will observe the continuity/discontinuity of the function

    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

    Student will observe the continuity/discontinuity of the function

    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.

    Student will Learn the process of finding the differential Coefficient 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.

    Student will Learn the process of finding the differential Coefficient 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

    Student will learn the basics of Linear Algebra.

    Discussion

    Lecture 24 Linear Algebra(Rank of a matrix)

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

    Student will learn the basics of Linear Algebra.

    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

    Student will learn the basics of Linear Algebra.

    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

    Student will learn the basics of Linear Algebra.

    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

    Student will learn the basics of Linear Algebra.

    Discussion

    Lecture 29 Linear Algebra(Cayley-Hamilton theorem)

    T-1:2.15 Cayley-Hamilton theorem

    Student will learn the basics of Linear Algebra.

    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

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

    Discussion

    Week 12 Lecture 34 Linear Programming Problems(Simplex method)

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

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

    Discussion

    Lecture 35 Linear Programming Problems(Simplex method)

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

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

    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)

    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

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

    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(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

    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

    Student will learn the logical reasoning.

    Discussion

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

    T-1:37.9-37.10 Duality law and Arguments

    Student will learn the logical reasoning.

    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

    Test2 Observe the performance of students .

    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

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

    5 / 6

    Test3 Observe the performance of students .

    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

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

    10 / 11

Recommended

View more >