Elementary Mathematics for Engineers (1)

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This list has the topics, along with addition study material, website & video links you are prescribed to study for Elementary Mathematics for Engineers (1) in your engineering college.

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  • Lovely Professional University, PunjabCourse Code Course Title Course Planner Lectures Tutorials Practicals CreditsMTH107 ELEMENTARY MATHEMATICS FOR ENGINEERS 11755::Ratesh Kumar 3.0 0.0 0.0 3.0Course Category Courses with Numerical focus

    TextBooks Sr No Title Author Edition Year Publisher NameT-1 Advanced Engineering Mathematics R. K. Jain, S. R. K. Iyenga 5th 2012 NarosaT-2 Discrete Mathematics and its

    applications with CombinatoricsKenneth H Rosen 7th 2012 Mc graw Hill

    T-3 Thomas Calculus Frank R. Giordano George B. Thomas Joel Hass Maurice D. Weir

    9th 2010 Pearson Education

    Reference BooksSr No Title Author Edition Year Publisher NameR-1 Advanced Engineering Mathematics Erwin Kreyszig 10th 2013 WileyR-2 Calculus Early Transcendental Soo T. Tan 1st 2013 Cengage LearningR-3 Elementary linear Algebra Ron Larson, David C.

    Falvo6th 2013 Cengage Learning

    R-4 Advanced Engineering Mathematics Peter V.O'Niel 7th 2012 Cengage LearningR-5 Higher Engineering Mathematics B.S.Grewal 42th 2012 khanna publisher.

    Relevant WebsitesSr No (Web address) (only if relevant to the course) Salient FeaturesRW-1 http://www.sjsu.edu/faculty/watkins/convex.htm Contains information about convex set RW-2 http://www2.econ.iastate.edu/faculty/hallam/Mathematics/ConvexOpt.pdf Contains exemples and geometric view of Convex set

    RW-3 http://www.mathcs.org/analysis/reals/topo/ contains information about open set and close set

    RW-4 http://www.tutorialspoint.com/computer_fundamentals/computer_number_system.htm contains information about computer number system

    Audio Visual AidsSr No (AV aids) (only if relevant to the course) Salient FeaturesAV-1 http://nptel.iitm.ac.in/video.php?subjectId=122104017 contains video lectures of calculus AV-2 http://demonstrations.wolfram.com/topic.html?topic=Derivatives&limit=20 contains related animations to explore concept

    AV-3 http://academicearth.org/online-college-courses/calculus/ contains related video lecture of related topics

  • 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

    Week 1 Lecture 1 Elements of Logic and Set theory(Elements of Logic: Necessary and Sufficient conditions)

    T-2:SEC 1.1-1.2 introduction to propositional logic,equivalance

    After this lecture student will able to connect mathematical language to computer language

    Discussion

    Lecture 2 Elements of Logic and Set theory(Theorems and Proofs (Direct and Contra positive))

    T-2:SEC 1.6 introduction to use of logic in proofs of statements

    In this lecture student will learn use of logic in proving the statements

    Discussion

    Lecture 3 Elements of Logic and Set theory(Number systems)

    T-3:sec 1 RW-4 introduction to number system and its development

    After this lecture student will gain the knowledge of various types of number systems viz natural numbers, whole numbers, prime numbers, rational numbers etcwhich constitutes the Real number system and will explore the relation between various types of numbers

    Discussion

    Elements of Logic and Set theory(Set theory)

    T-2:2.1-2.2 introduction to set theory and its representation

    After this lecture student will be able to describe sets in different forms, Venn diagrams and the union and intersection of sets

    Discussion

    Week 2 Lecture 4 Elements of Logic and Set theory(Elementary set theoretic operations)

    T-2:2.1-2.2 Elementary operations on set theory like union ,intersection,difference of sets

    after this lecture student will be able to use Elementary set theoretic operations for pre calculus

    Discussion

    Detailed Plan For Lectures

    LTP week distribution: (LTP Weeks)Weeks before MTE 7

    Weeks After MTE 7

    Spill Over 3

  • Week 2 Lecture 4 Elements of Logic and Set theory(De Morgan's law)

    T-2:2.1-2.2 De Morgans and its use to prove identities

    After this lecture student will be able to prove identities in set theory with the help of Demorgan law

    Discussion

    Lecture 5 Elements of Logic and Set theory(Convex sets)

    RW-1RW-2

    introduction to Convex sets

    After this lecture student will able to analysis the simple structure of convex sets and can utilized in mathematical structures

    Discussion

    Elements of Logic and Set theory(Open and closed set)

    T-3:sec 1R-2:APP A A1

    RW-3 introduction to Open and closed set

    After this lecture student will able to recongnise the meaning of open set and close set in set theory and will know complementary of open set as closed set and its basic properties

    Discussion

    Elements of Logic and Set theory(Modulus function (distance))

    T-3:sec 1R-2:App A1

    Introduction to Modulus function distance

    after this lecture student will able tofind distance between two points with Modulus function

    Discussion

    Lecture 6 Basic Calculus(Relations and Correspondences)

    T-2:7.1 Relations and Correspondences

    After this lecture student will be able Represention of relations and functions with graphs, tables, and sets of ordered pairs

    Discussion

    Basic Calculus(Functions) T-3:3R-2:sec 0.2

    introduction to Functions ,one one function and onto function

    After this lecture student will be able to Define, compare and recognize relations and functions and Represention of relations and functions with graphs, tables, and sets of ordered pairs

    Discussion and Brain

    Stroming

    Week 3 Lecture 7 Basic Calculus(Limit and Continuity)

    T-3:1.2-1.6R-2:ch 1

    introduction to basic concepts of Limit and Continuity and some laws

    After this lecture student will be able to Define, compare and recognize relations and functions

    Discussion and Brain

    Stroming

    Lecture 8 Basic Calculus(Limit and Continuity)

    T-3:1.2-1.6R-2:ch 1

    introduction to basic concepts of Limit and Continuity and some laws

    After this lecture student will be able to Define, compare and recognize relations and functions

    Discussion and Brain

    Stroming

  • Week 3 Lecture 9 Basic Calculus(Sequence and Series(Convergence))

    T-1:SEC 12.2-12.3R-2:ch 8

    Sequence and SeriesConvergence

    In this lecture student will able to find the sum of series and convergence of Sequence

    Discussion and Brain

    Stroming

    Week 4 Lecture 10 Basic Calculus(Sequence and Series(Convergence))

    T-1:SEC 12.2-12.3R-2:ch 8

    Sequence and SeriesConvergence

    In this lecture student will able to find the sum of series and convergence of Sequence

    Discussion and Brain

    Stroming

    Lecture 11 Basic Calculus(Sequence and Series(Convergence))

    T-1:SEC 12.2-12.3R-2:ch 8

    Sequence and SeriesConvergence

    In this lecture student will able to find the sum of series and convergence of Sequence

    Discussion and Brain

    Stroming

    Lecture 12 Differential Calculus(Concept of a Derivative)

    T-3:SEC 3.1R-2:ch2

    Explanation to Concept of a Derivative

    In this lecture student will know how to find the instantaneous rate of change in on quentity with respect to another quantitytive

    Discussion

    Differential Calculus(Standard rules of differentiation (including elementary trigonometric and transcendental functions))

    T-1:ch 2T-3:SEC 3.1 -3.8

    Standard rules of differentiation

    In this lecture student will lbe able to find the derivative of different types of functions

    Discussion

    Week 5 Lecture 13 Differential Calculus(Standard rules of differentiation (including elementary trigonometric and transcendental functions))

    T-1:ch 2T-3:SEC 3.1 -3.8

    Standard rules of differentiation

    In this lecture student will lbe able to find the derivative of different types of functions

    Discussion

    Lecture 14 Differential Calculus(Standard rules of differentiation (including elementary trigonometric and transcendental functions))

    T-1:ch 2T-3:SEC 3.1 -3.8

    Standard rules of differentiation

    In this lecture student will lbe able to find the derivative of different types of functions

    Discussion

    Lecture 15 Differential Calculus(Total and Partial derivatives)

    T-1:2.3-2.4R-2:ch12

    Introduction to Total and Partial derivatives

    In this lecture student will know how to find the instantaneous rate of change of one variable with respect to multivariable

    Discussion and Brain

    Stroming

    Week 6 Lecture 16 Differential Calculus(Total and Partial derivatives)

    T-1:2.3-2.4R-2:ch12

    Introduction to Total and Partial derivatives

    In this lecture student will know how to find the instantaneous rate of change of one variable with respect to multivariable

    Discussion and Brain

    Stroming

    Lecture 17 Test 1

  • Week 6 Lecture 18 Differential Calculus(Young's theorem)

    T-3:14.3 Verification of Youngs theorem with examples

    In this lecture student will learn a new standard result and its application Youngs theorem for second order partial derivative

    Discussion

    Week 7 Lecture 19 Differential Calculus(Homogeneous functions)

    T-1:sec 2.41 Introduction to Homogeneous functions and Euler theorem

    In this lecture student will learn how to treat Homogeneous functions in partial derivative

    Discussion

    Lecture 20 Differential Calculus(Maxima and Minima.)

    T-1:sec 2.5R-2:sec 12.8

    Maxima and Minima of function of two variable

    after this lecture student will able to find the condition under which the given function will give maximum or minimum value

    Discussion and Brain

    Stroming

    Lecture 21 Differential Calculus(Maxima and Minima.)

    T-1:sec 2.5R-2:sec 12.8

    Maxima and Minima of function of two variable

    after this lecture student will able to find the condition under which the given function will give maximum or minimum value

    Discussion and Brain

    Stroming

    MID-TERMWeek 8 Lecture 22 Integral Calculus(Integration-

    Basic concept)T-3:5.1R-2:ch 4

    intoduction to Integration Basic Concept

    Student will learn the basic Conceptsof integration as limit of sum

    Discussion

    Integral Calculus(Standard rules of integration)

    T-3:5.2R-2: ch 4

    Standard rules of integration

    Student will be able find the integration of different function with Standard rules of integration

    Discussion

    Lecture 23 Integral Calculus(Partial integration (by parts))

    T-3:5.3 to 5.6 Partial integration by parts

    Student will be able find the integration of product of two or more than two function with Standard rules of integration

    Discussion

    Integral Calculus(Definite and indefinite integral)

    T-3:5.3 -5.6R-2:Ch4 Ch5

    Basic result of Definite and indefinite integral

    Student will learn the Standared result of basic Definite and indefinite integral

    Discussion

    Lecture 24 Integral Calculus(Ordinary (first order) differential equation)

    T-1:Sec 4.5-4.6R-1:ch1R-4:ch 1

    Ordinary first order differential equation

    Student will be able to solve Ordinary first order differential equation

    Discussion

  • Week 9 Lecture 25 Integral Calculus(Ordinary (first order) differential equation)

    T-1:Sec 4.5-4.6R-1:ch1R-4:ch 1

    Ordinary first order differential equation

    Student will be able to solve Ordinary first order differential equation

    Discussion

    Lecture 26 Integral Calculus(Ordinary (first order) differential equation)

    T-1:Sec 4.5-4.6R-1:ch1R-4:ch 1

    Ordinary first order differential equation

    Student will be able to solve Ordinary first order differential equation

    Discussion

    Lecture 27 Linear Algebra(Matrices (types and operations including elementary row and column operations))

    T-1:3.2.1-3.2.1R-1:CH 6R-3:CH2R-4:Ch 7

    Matrices types and operations including elementary row and column operations

    Student will learn the Matrices types and operations including elementary row and column operations

    Discussion

    Week 10 Lecture 28 Test 2

    Lecture 29 Linear Algebra(Determinants (rules of computation))

    T-1:3.2.3 Determinants rules of computation

    Student will learn the Determinants and rules of computation

    Discussion

    Lecture 30 Linear Algebra(Linear Equations and Cramer's rule)

    T-1:3.2.5 Linear Equations and Cramers rule

    Student will learn the how to solve Linear Equations by Cramers rule

    Discussion

    Week 11 Lecture 31 Linear Algebra(Inverse) T-1:3.2.4R-1:SEC 6.7R-3:SEC 2.3R-4:SEC 7.7

    Inverse of Matrix Student will learn the how to find Inverse of matrix

    Discussion and Brain

    Stroming

    Lecture 32 Linear Algebra(Vector space (concepts of span/basis/dimension))

    T-1:3.3.1-3.3.3 Vector space concepts of spanbasisdimension

    after this lecture Students will able to recongnise newtype of algebraicstructure as vectorspace and its parameter span basis dimension

    Discussion and Brain

    Stroming

    Lecture 33 Linear Algebra(Vector space (concepts of span/basis/dimension))

    T-1:3.3.1-3.3.3 Vector space concepts of spanbasisdimension

    after this lecture Students will able to recongnise newtype of algebraicstructure as vectorspace and its parameter span basis dimension

    Discussion and Brain

    Stroming

    Week 12 Lecture 34 Linear Algebra(Eigen values and Eigen vectors)

    T-1:3.5.1R-1:SEC 7.1

    Eigen values and Eigen vectors

    after this lecture Students will able to find a position vector in a space which does not change its direction

    Discussion and Brain

    Stroming

  • Week 12 Lecture 35 Linear Algebra(Eigen values and Eigen vectors)

    T-1:3.5.1R-1:SEC 7.1

    Eigen values and Eigen vectors

    after this lecture Students will able to find a position vector in a space which does not change its direction

    Discussion and Brain

    Stroming

    Lecture 36 Test 3

    Week 13 Lecture 37 Linear programming and Difference equations(Linear Programming (Graphical solution))

    R-5:34.3-34.6 Linear Programming Graphical solution

    Student will able to find the optimal solution under the given constrains by Graphical solution

    Discussion and Brain

    Stroming

    Lecture 38 Linear programming and Difference equations(Linear Programming (Graphical solution))

    R-5:34.3-34.6 Linear Programming Graphical solution

    Student will able to find the optimal solution under the given constrains by Graphical solution

    Discussion and Brain

    Stroming

    Lecture 39 Linear programming and Difference equations(Linear Programming (Simplex solution))

    R-5:34.7-34.8 Linear Programming Simplex solution

    Student will able to find the optimal solution under the given constrains by Simplex method

    Discussion and Brain

    Stroming

    Week 14 Lecture 40 Linear programming and Difference equations(Linear Programming (Simplex solution))

    R-5:34.7-34.8 Linear Programming Simplex solution

    Student will able to find the optimal solution under the given constrains by Simplex method

    Discussion and Brain

    Stroming

    Lecture 41 Linear programming and Difference equations(First order Difference equation (First order equations and solution))

    R-5:31.2-31.5 First order Difference equation First order equations and solution

    Student will learn how to solve First order Difference equation

    Discussion and Brain

    Stroming

    Lecture 42 Linear programming and Difference equations(First order Difference equation (First order equations and solution))

    R-5:31.2-31.5 First order Difference equation First order equations and solution

    Student will learn how to solve First order Difference equation

    Discussion and Brain

    Stroming

    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

    Test 1 To check understanding of students about the concepts taught

    Elements of Logic: Necessary and Sufficient conditions, Theorems and Proofs (Direct and Contra positive), Number systems,Set theory, Elementary set theoretic operations, De Morgan's law, Convex sets, Open and closed set, Modulus function (distance) ,Relations and Correspondences,Relations and Correspondences, functions, Limit and Continuity, sequence and Series(Convergence)

    Individual A test of 30 marks consisting of questions having weightage of multiple of 5.

    5 / 6

    Test 2 To check understanding of students about the concepts taught

    Integration- Basic concept, Definite and indefinite integral, Standard rules of integration, Partial integration (by parts), Ordinary (first order) differential equation

    Individual A test of 30 marks consisting of questions having weightage of multiple of 5.

    9 / 10

    Test 3 To check understanding of students about the concepts taught

    Matrices (types and operations including elementary row and column operations),Inverse, Determinants (rules of computation), Linear Equations and Cramer's rule, Vector space (concepts of span/basis/dimension),Eigen values and Eigen vectors

    Individual A test of 30 marks consisting of questions having weightage of multiple of 5.

    12 / 13

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