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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, 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
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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