Elementary Mathematics for Engineers (1)

Lovely Professional University, Punjab

Course Code Course Title Course Planner Lectures Tutorials Practicals Credits

MTH107 ELEMENTARY MATHEMATICS FOR ENGINEERS 11755::Ratesh Kumar 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 Advanced Engineering Mathematics R. K. Jain, S. R. K. Iyenga 5th 2012 Narosa

T-2 Discrete Mathematics and its applications with Combinatorics

Kenneth 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 Books

Sr No Title Author Edition Year Publisher Name

R-1 Advanced Engineering Mathematics Erwin Kreyszig 10th 2013 Wiley

R-2 Calculus Early Transcendental Soo T. Tan 1st 2013 Cengage Learning

R-3 Elementary linear Algebra Ron Larson, David C. Falvo

6th 2013 Cengage Learning

R-4 Advanced Engineering Mathematics Peter V.O'Niel 7th 2012 Cengage Learning

R-5 Higher Engineering Mathematics B.S.Grewal 42th 2012 khanna publisher.

Relevant Websites

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

RW-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 Aids

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

AV-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


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


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


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

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




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

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




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



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



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


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


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


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


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



Discussion

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

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



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


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


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


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


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


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


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


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


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


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


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


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


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


9 / 10


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


12 / 13

Documents

Elementary Mathematics for Engineers (1)