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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<ul><li><p>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</p><p>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 </p><p>applications with CombinatoricsKenneth H Rosen 7th 2012 Mc graw Hill</p><p>T-3 Thomas Calculus Frank R. Giordano George B. Thomas Joel Hass Maurice D. Weir</p><p>9th 2010 Pearson Education</p><p>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. </p><p>Falvo6th 2013 Cengage Learning</p><p>R-4 Advanced Engineering Mathematics Peter V.O'Niel 7th 2012 Cengage LearningR-5 Higher Engineering Mathematics B.S.Grewal 42th 2012 khanna publisher.</p><p>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</p><p>RW-3 http://www.mathcs.org/analysis/reals/topo/ contains information about open set and close set</p><p>RW-4 http://www.tutorialspoint.com/computer_fundamentals/computer_number_system.htm contains information about computer number system</p><p>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&amp;limit=20 contains related animations to explore concept</p><p>AV-3 http://academicearth.org/online-college-courses/calculus/ contains related video lecture of related topics </p></li><li><p>Week Number</p><p>Lecture Number</p><p>Broad Topic(Sub Topic) Chapters/Sections of Text/reference books</p><p>Other Readings,Relevant Websites, Audio Visual Aids, software and Virtual Labs</p><p>Lecture Description Learning Outcomes Pedagogical ToolDemonstration/ Case Study / Images / animation / ppt etc. Planned</p><p>Week 1 Lecture 1 Elements of Logic and Set theory(Elements of Logic: Necessary and Sufficient conditions)</p><p>T-2:SEC 1.1-1.2 introduction to propositional logic,equivalance</p><p>After this lecture student will able to connect mathematical language to computer language </p><p>Discussion </p><p>Lecture 2 Elements of Logic and Set theory(Theorems and Proofs (Direct and Contra positive))</p><p>T-2:SEC 1.6 introduction to use of logic in proofs of statements </p><p>In this lecture student will learn use of logic in proving the statements </p><p>Discussion </p><p>Lecture 3 Elements of Logic and Set theory(Number systems)</p><p>T-3:sec 1 RW-4 introduction to number system and its development </p><p>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 </p><p>Discussion </p><p>Elements of Logic and Set theory(Set theory)</p><p>T-2:2.1-2.2 introduction to set theory and its representation</p><p>After this lecture student will be able to describe sets in different forms, Venn diagrams and the union and intersection of sets</p><p>Discussion </p><p>Week 2 Lecture 4 Elements of Logic and Set theory(Elementary set theoretic operations)</p><p>T-2:2.1-2.2 Elementary operations on set theory like union ,intersection,difference of sets</p><p>after this lecture student will be able to use Elementary set theoretic operations for pre calculus</p><p>Discussion </p><p>Detailed Plan For Lectures </p><p>LTP week distribution: (LTP Weeks)Weeks before MTE 7</p><p>Weeks After MTE 7</p><p>Spill Over 3</p></li><li><p>Week 2 Lecture 4 Elements of Logic and Set theory(De Morgan's law)</p><p>T-2:2.1-2.2 De Morgans and its use to prove identities </p><p>After this lecture student will be able to prove identities in set theory with the help of Demorgan law</p><p>Discussion </p><p>Lecture 5 Elements of Logic and Set theory(Convex sets)</p><p>RW-1RW-2</p><p>introduction to Convex sets</p><p>After this lecture student will able to analysis the simple structure of convex sets and can utilized in mathematical structures</p><p>Discussion </p><p>Elements of Logic and Set theory(Open and closed set)</p><p>T-3:sec 1R-2:APP A A1</p><p>RW-3 introduction to Open and closed set</p><p>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</p><p>Discussion </p><p>Elements of Logic and Set theory(Modulus function (distance))</p><p>T-3:sec 1R-2:App A1</p><p>Introduction to Modulus function distance</p><p>after this lecture student will able tofind distance between two points with Modulus function </p><p>Discussion </p><p>Lecture 6 Basic Calculus(Relations and Correspondences)</p><p>T-2:7.1 Relations and Correspondences</p><p>After this lecture student will be able Represention of relations and functions with graphs, tables, and sets of ordered pairs</p><p>Discussion </p><p>Basic Calculus(Functions) T-3:3R-2:sec 0.2</p><p>introduction to Functions ,one one function and onto function</p><p>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</p><p>Discussion and Brain </p><p>Stroming</p><p>Week 3 Lecture 7 Basic Calculus(Limit and Continuity)</p><p>T-3:1.2-1.6R-2:ch 1</p><p>introduction to basic concepts of Limit and Continuity and some laws </p><p>After this lecture student will be able to Define, compare and recognize relations and functions </p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 8 Basic Calculus(Limit and Continuity)</p><p>T-3:1.2-1.6R-2:ch 1</p><p>introduction to basic concepts of Limit and Continuity and some laws </p><p>After this lecture student will be able to Define, compare and recognize relations and functions </p><p>Discussion and Brain </p><p>Stroming</p></li><li><p>Week 3 Lecture 9 Basic Calculus(Sequence and Series(Convergence))</p><p>T-1:SEC 12.2-12.3R-2:ch 8</p><p>Sequence and SeriesConvergence</p><p>In this lecture student will able to find the sum of series and convergence of Sequence </p><p>Discussion and Brain </p><p>Stroming</p><p>Week 4 Lecture 10 Basic Calculus(Sequence and Series(Convergence))</p><p>T-1:SEC 12.2-12.3R-2:ch 8</p><p>Sequence and SeriesConvergence</p><p>In this lecture student will able to find the sum of series and convergence of Sequence </p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 11 Basic Calculus(Sequence and Series(Convergence))</p><p>T-1:SEC 12.2-12.3R-2:ch 8</p><p>Sequence and SeriesConvergence</p><p>In this lecture student will able to find the sum of series and convergence of Sequence </p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 12 Differential Calculus(Concept of a Derivative)</p><p>T-3:SEC 3.1R-2:ch2</p><p>Explanation to Concept of a Derivative</p><p>In this lecture student will know how to find the instantaneous rate of change in on quentity with respect to another quantitytive</p><p>Discussion </p><p>Differential Calculus(Standard rules of differentiation (including elementary trigonometric and transcendental functions))</p><p>T-1:ch 2T-3:SEC 3.1 -3.8</p><p>Standard rules of differentiation </p><p>In this lecture student will lbe able to find the derivative of different types of functions </p><p>Discussion </p><p>Week 5 Lecture 13 Differential Calculus(Standard rules of differentiation (including elementary trigonometric and transcendental functions))</p><p>T-1:ch 2T-3:SEC 3.1 -3.8</p><p>Standard rules of differentiation </p><p>In this lecture student will lbe able to find the derivative of different types of functions </p><p>Discussion </p><p>Lecture 14 Differential Calculus(Standard rules of differentiation (including elementary trigonometric and transcendental functions))</p><p>T-1:ch 2T-3:SEC 3.1 -3.8</p><p>Standard rules of differentiation </p><p>In this lecture student will lbe able to find the derivative of different types of functions </p><p>Discussion </p><p>Lecture 15 Differential Calculus(Total and Partial derivatives)</p><p>T-1:2.3-2.4R-2:ch12</p><p>Introduction to Total and Partial derivatives</p><p>In this lecture student will know how to find the instantaneous rate of change of one variable with respect to multivariable</p><p>Discussion and Brain </p><p>Stroming</p><p>Week 6 Lecture 16 Differential Calculus(Total and Partial derivatives)</p><p>T-1:2.3-2.4R-2:ch12</p><p>Introduction to Total and Partial derivatives</p><p>In this lecture student will know how to find the instantaneous rate of change of one variable with respect to multivariable</p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 17 Test 1</p></li><li><p>Week 6 Lecture 18 Differential Calculus(Young's theorem)</p><p>T-3:14.3 Verification of Youngs theorem with examples </p><p>In this lecture student will learn a new standard result and its application Youngs theorem for second order partial derivative</p><p>Discussion </p><p>Week 7 Lecture 19 Differential Calculus(Homogeneous functions)</p><p>T-1:sec 2.41 Introduction to Homogeneous functions and Euler theorem</p><p>In this lecture student will learn how to treat Homogeneous functions in partial derivative </p><p>Discussion </p><p>Lecture 20 Differential Calculus(Maxima and Minima.)</p><p>T-1:sec 2.5R-2:sec 12.8</p><p>Maxima and Minima of function of two variable</p><p>after this lecture student will able to find the condition under which the given function will give maximum or minimum value </p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 21 Differential Calculus(Maxima and Minima.)</p><p>T-1:sec 2.5R-2:sec 12.8</p><p>Maxima and Minima of function of two variable</p><p>after this lecture student will able to find the condition under which the given function will give maximum or minimum value </p><p>Discussion and Brain </p><p>Stroming</p><p>MID-TERMWeek 8 Lecture 22 Integral Calculus(Integration- </p><p>Basic concept)T-3:5.1R-2:ch 4</p><p>intoduction to Integration Basic Concept</p><p>Student will learn the basic Conceptsof integration as limit of sum</p><p>Discussion </p><p>Integral Calculus(Standard rules of integration)</p><p>T-3:5.2R-2: ch 4</p><p>Standard rules of integration</p><p>Student will be able find the integration of different function with Standard rules of integration</p><p>Discussion </p><p>Lecture 23 Integral Calculus(Partial integration (by parts))</p><p>T-3:5.3 to 5.6 Partial integration by parts</p><p>Student will be able find the integration of product of two or more than two function with Standard rules of integration</p><p>Discussion </p><p>Integral Calculus(Definite and indefinite integral)</p><p>T-3:5.3 -5.6R-2:Ch4 Ch5</p><p>Basic result of Definite and indefinite integral</p><p>Student will learn the Standared result of basic Definite and indefinite integral</p><p>Discussion </p><p>Lecture 24 Integral Calculus(Ordinary (first order) differential equation)</p><p>T-1:Sec 4.5-4.6R-1:ch1R-4:ch 1</p><p>Ordinary first order differential equation</p><p>Student will be able to solve Ordinary first order differential equation</p><p>Discussion </p></li><li><p>Week 9 Lecture 25 Integral Calculus(Ordinary (first order) differential equation)</p><p>T-1:Sec 4.5-4.6R-1:ch1R-4:ch 1</p><p>Ordinary first order differential equation</p><p>Student will be able to solve Ordinary first order differential equation</p><p>Discussion </p><p>Lecture 26 Integral Calculus(Ordinary (first order) differential equation)</p><p>T-1:Sec 4.5-4.6R-1:ch1R-4:ch 1</p><p>Ordinary first order differential equation</p><p>Student will be able to solve Ordinary first order differential equation</p><p>Discussion </p><p>Lecture 27 Linear Algebra(Matrices (types and operations including elementary row and column operations))</p><p>T-1:3.2.1-3.2.1R-1:CH 6R-3:CH2R-4:Ch 7</p><p>Matrices types and operations including elementary row and column operations</p><p>Student will learn the Matrices types and operations including elementary row and column operations</p><p>Discussion </p><p>Week 10 Lecture 28 Test 2</p><p>Lecture 29 Linear Algebra(Determinants (rules of computation))</p><p>T-1:3.2.3 Determinants rules of computation</p><p>Student will learn the Determinants and rules of computation</p><p>Discussion </p><p>Lecture 30 Linear Algebra(Linear Equations and Cramer's rule)</p><p>T-1:3.2.5 Linear Equations and Cramers rule</p><p>Student will learn the how to solve Linear Equations by Cramers rule</p><p>Discussion </p><p>Week 11 Lecture 31 Linear Algebra(Inverse) T-1:3.2.4R-1:SEC 6.7R-3:SEC 2.3R-4:SEC 7.7</p><p>Inverse of Matrix Student will learn the how to find Inverse of matrix </p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 32 Linear Algebra(Vector space (concepts of span/basis/dimension))</p><p>T-1:3.3.1-3.3.3 Vector space concepts of spanbasisdimension</p><p>after this lecture Students will able to recongnise newtype of algebraicstructure as vectorspace and its parameter span basis dimension</p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 33 Linear Algebra(Vector space (concepts of span/basis/dimension))</p><p>T-1:3.3.1-3.3.3 Vector space concepts of spanbasisdimension</p><p>after this lecture Students will able to recongnise newtype of algebraicstructure as vectorspace and its parameter span basis dimension</p><p>Discussion and Brain </p><p>Stroming</p><p>Week 12 Lecture 34 Linear Algebra(Eigen values and Eigen vectors)</p><p>T-1:3.5.1R-1:SEC 7.1</p><p>Eigen values and Eigen vectors</p><p>after this lecture Students will able to find a position vector in a space which does not change its direction </p><p>Discussion and Brain </p><p>Stroming</p></li><li><p>Week 12 Lecture 35 Linear Algebra(Eigen values and Eigen vectors)</p><p>T-1:3.5.1R-1:SEC 7.1</p><p>Eigen values and Eigen vectors</p><p>after this lecture Students will able to find a position vector in a space which does not change its direction </p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 36 Test 3</p><p>Week 13 Lecture 37 Linear programming and Difference equations(Linear Programming (Graphical solution))</p><p>R-5:34.3-34.6 Linear Programming Graphical solution</p><p>Student will able to find the optimal solution under the given constrains by Graphical solution</p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 38 Linear programming and Difference equations(Linear Programming (Graphical solution))</p><p>R-5:34.3-34.6 Linear Programming Graphical solution</p><p>Student will able to find the optimal solution under the given constrains by Graphical solution</p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 39 Linear programming and Difference equations(Linear Programming (Simplex solution))</p><p>R-5:34.7-34.8 Linear Programming Simplex solution</p><p>Student will able to find the optimal solution under the given constrains by Simplex method</p><p>Discussion and Brain </p><p>Stroming</p><p>Week 14 Lecture 40 Linear programming and Difference equations(Linear Programming (Simplex solution))</p><p>R-5:34.7-34.8 Linear Programming Simplex solution</p><p>Student will able to find the optimal solution under the given constrains by Simplex method</p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 41 Linear programming and Difference equations(First order Difference equation (First order equations and solution))</p><p>R-5:31.2-31.5 First order Difference equation First order equations and solution</p><p>Student will learn how to solve First order Difference equation</p><p>Discussion and Brain </p><p>Stroming</p><p>Lecture 42 Linear programming and Difference equations(First order Difference equation (First order equations and solution))</p><p>R-5:31.2-31.5 First order Difference equation First order equations and solution</p><p>Student will learn how to solve First order Difference equation</p><p>Discussion and Brain </p><p>Stroming</p><p>SPILL OVERWeek 15 Lecture 43 Spill Over</p><p>Lecture 44 Spill Over</p><p>Lecture 45 Spill Over</p><p>Scheme for CA:Component Frequency Out Of Each Marks...</p></li></ul>

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