Menu
Mathematics 2nd Year All Chapter Notes | Math FSc Part 2
“Class 12 Mathematics Notes”
Mathematics-XII (Punjab Text Book Board, Lahore)
- In this online lecture,Muhammad Naveed Jaffar explains FSC part 2 Mathematics Chapter 1 Functions and Limits.The topic being discussed is Topic Exercise 1.1.
- 2nd Year Math Notes Download The 12th Class Maths Notes include all 7 Chapters Exercise wise Questions, Short Questions, Long Questions, Past Paper Questions, Numericals, and Examples. These notes are in PDF format that helps you to view all 7 chapters in one file.
Apr 16, 2020 These Math notes include the solution of the complete exercises 1.1 of Math 2nd year. You can easily download these Math notes or view them online. 2nd Year Math All Chapters Notes in PDF. Download Notes. Like our Facebook page for the updates of new material. We also share useful materials on our Facebook page.
These Mathematics-XII FSc Part 2 (2nd year) Notes are according to “Punjab Text Book Board, Lahore”. Very helpful notes for the students of 2nd year to prepare their paper of Maths according to syllabus given by Federal Board of Intermediate and Secondary Education (FBISE), Faisalabad Board, Multan Board, Sargodha Board, DG Khan Board, Gujranwala Board, Rawalpindi Board or others board of Punjab, Pakistan. These 12 Class Math Notes are obtained from mathcity.org.
You Can Easily View or Download These Notes For PC. To view PDF files, there must be PDF Reader (Viewer) installed on your computer. Click Here to Download PDF Viewer and other Softwares.
Chapter # 1 Functions and Limits
Exercise 1.1 | View Online | Download PDF |
Exercise 1.2 | View Online | Download PDF |
Exercise 1.3 | View Online | Download PDF |
Exercise 1.4 | View Online | Download PDF |
Exercise 1.5 | View Online | Download PDF |
Chapter # 2 Differentiation
Exercise 2.1 | View Online | Download PDF |
Exercise 2.2 | View Online | Download PDF |
Exercise 2.3 | View Online | Download PDF |
Exercise 2.4 | View Online | Download PDF |
Exercise 2.5 | View Online | Download PDF |
Exercise 2.6 | View Online | Download PDF |
Exercise 2.7 | View Online | Download PDF |
Exercise 2.8 | View Online | Download PDF |
Exercise 2.9 | View Online | Download PDF |
Exercise 2.10 | View Online | Download PDF |
Chapter # 3 Integration
Exercise 3.1 | View Online | Download PDF |
Exercise 3.2 | View Online | Download PDF |
Exercise 3.3 | View Online | Download PDF |
Exercise 3.4 | View Online | Download PDF |
Exercise 3.5 | View Online | Download PDF |
Exercise 3.6 | Coming soon | Coming soon |
Exercise 3.7 | View Online | Download PDF |
Exercise 3.8 | View Online | Download PDF |
Chapter # 4 Introduction to Analytic Geometry
Exercise 4.1 | View Online | Download PDF |
Exercise 4.2 | View Online | Download PDF |
Exercise 4.3 | View Online | Download PDF |
Exercise 4.4 | View Online | Download PDF |
Exercise 4.5 | View Online | Download PDF |
Chapter # 5 Linear Inequalities and Linear Programming
Exercise 5.1 | View Online | Download PDF |
Exercise 5.2 | View Online | Download PDF |
Exercise 5.3 | View Online | Download PDF |
Chapter # 6 Conic Section
Exercise 6.1 | View Online | Download PDF |
Exercise 6.2 | View Online | Download PDF |
Exercise 6.3 | View Online | Download PDF |
Exercise 6.4 | View Online | Download PDF |
Exercise 6.5 | View Online | Download PDF |
Exercise 6.6 | View Online | Download PDF |
Exercise 6.7 | View Online | Download PDF |
Chapter # 7 Vectors
Exercise 7.1 | View Online | Download PDF |
Exercise 7.2 | View Online | Download PDF |
Exercise 7.3 | View Online | Download PDF |
Exercise 7.4 | View Online | Download PDF |
Exercise 7.5 | View Online | Download PDF |
---------------------
4.7
Here you can download the free lecture Notes of Discrete Mathematics Pdf Notes – DM notes pdf materials with multiple file links to download. The Discrete Mathematics Notes pdf – DM notes pdf book starts with the topics covering Logic and proof, strong induction,pigeon hole principle, isolated vertex, directed graph, Alebric structers, lattices and boolean algebra, Etc.
Discrete Mathematics pdf notes – DM notes pdf file
file to download are listed below please check it –
Complete Notes
Unit 1
Unit 2
Unit 3
![Maths 2nd year notes 1.1 Maths 2nd year notes 1.1](/uploads/1/2/6/3/126346565/933233813.png)
Unit 4
Unit 5
Note :- These notes are according to the R09 Syllabus book of JNTU.In R13 and R15,8-units of R09 syllabus are combined into 5-units in R13 and R15 syllabus. If you have any doubts please refer to the JNTU Syllabus Book.
Unit-1:
Logic and proof, propositions on statement, connectives, basic connectives, truth table for basic connectives,And,Disjunction,conditional state,bi conditional state,tautology,contradiction,fallacy,contigency,logical equialances,idempotent law,associtative law,commutative law,demorgans law,distributive law,complements law,dominance law,identity law.A praposition of on statement is a declarative sentence which either true (or) false not both, connective is an operation
Unit-2:
Combinatorics, strong induction,pigeon hole principle, permutation and combination, recurrence relations, linear non homogeneous recurrence relation with constant, the principle of inclusion and exclusion.
Discrete Mathematics Notes pdf – DM notes pdf
Unit-3:
Graphs, parllel edges, adjacent edges and vertices,simple graph,isolated vertex,directed graph,undirected graph,mixed graph,multigraph,pseduo graph,degree,in degree and outdegree,therom,regular graph,complete graph,complete bipartite,subgraph,adjecent matrix of a simple graph,incidence matrix,path matrix,graph isomorphism,pths,rechabality and connected path,length of the path,cycle,connected graph,components of a graph,konisberg bridge problem,Euler parh,euler circuit,hamiltonian path,hamiltonian cycle.
Unit-4:
Alebric structers,properties,closure,commutativity,associativity,identity,inverse,distributive law,inverse element,notation,semi group,monoid,cycle monoid,morphisms of semigrouphs,morpism of monoids,groups,abelian group,order of group,composition table,properties of groups,subgroups,kernal of a elomorphism,isomorphism,cosets,lagranges therom,normal subgroups,natural homomorphism,rings,field.
Unit-5:
lattices and boolean algebra,reflexive,symmetric,transitive,antisymmetric,equivalance relation,poset,hane diagram,propertie of lattices,idempolent law,commutative law,associative law,absorbtion law,boolean algebra.
Follow us on FB – Smartzworld
Frequently Asked Questions
Q1: What is discrete mathematics?
A1: Study of countable, otherwise distinct and separable mathematical structures are called as Discrete mathematics. It focuses mainly on finite collection of discrete objects. The field has become more and more in demand since computers like digital devices have grown rapidly in current situation.
Q2: What are Cominatorics?
A2: Combinatorics is the mathematics of arranging and counting. Though a lot of people know how to count, combinatorics uses mathematical operations to count objects/things that are far away from human count in a conventional way. The field also concerned with the way things are arranged which includes rule of sum and rule of product. Permutation and combination come under this topic.
Q3: What are permutations and combinations?
A3: Permutation is an arrangements of things with regards to order where as combination is an arrangement of things without regard to order.
Q4: What is a set theory?
A4: A branch of mathematics concerned with collections of object is called Set theory. The sets could be discrete or continuous which is concerned with the way sets are arranged, counted or combined. A complements of a set A is the set of elements/things/objects which are not in set A. The cardinality of a finite set is the number of elements/things/objects in that set. The way sets can be combined are described by Intersection and Union. Identities for the complements of intersection and union are given by De Morgan’s laws.
Download Evasi0n7 1.0.1 for Windows Download Evasi0n7 1.0.1 for Mac. Update x1: Looks like iPad 2 boot loop issue is still not fixed in v1.0.1: @Pod2g: We still have to work on the compatibility issue with the iPad 2, but we have been busy celebrating with our family Tomorrow probably! You may also like to. Evasi0n7 1.0.5 WIndows Download; evasi0n7 1.0.5 MAC OS X Download; Download evasi0n7 1.0.4 WIndows; Download evasi0n7 1.0.4 MAC OS X; evasi0n 7 download Changelogs and updates. Evasi0n7 1.0.8: Latest iPhone 5s, iPhone 5c device support; evasi0n7 1.0.7: Updated Cydia packages, fixed 'where bundled package lists could not be updated by Cydia. Evasi0n7 download mac. Download evasi0n7 for Mac - A straightforward Mac OS X desktop application that offers an untethered jailbreak solution for iOS devices running iOS 7.0 through 7.1beta3.
Q5: What is the difference between discrete and continuous mathematics?
A5: The difference between discrete and continuous mathematics is,
Discrete mathematics | Continuous mathematics |
Mathematics focusing on discrete numbers or objects | Mathematics focusing on continuous numbers or the real numbers |
Discrete mathematics is finite numbers that are not an infinite number of points between the number. | Continuous mathematics focuses on the numbers between any number that is one can always find infinite set of numbers between two numbers. |
Fundamental set of numbers is the natural numbers. | Fundamental set of numbers that are used for proofs in the interval |
Graphs is used while studying | Study of topology is applied. |
Q6: What are the real life applications of discrete mathematics?
A6: Real life everyday applications of the discrete mathematics are,
- Google maps
- Doing web searches
- Scheduling problems
- Computers
- Networks
- Wiring a computer network
- Analog clock
- Cryptography
- Apportionment
- Machine job scheduling
- Area codes
- Railway planning
- Password criteria
- Compact discs
- Voting systmes
- Computer graphics
- Cell phone communication
- Electronic health care products
- Bankruptcy proceedings
- Digital image processing
- Encoding and reducing data
- Food webs
- Speech recognition
- Delivery route
Some research applications include
- Detecting fake videos
- Logistics
- Compressive sensitng
- Redisticting
- Reducing poaching of endangered animals
- Archeology
- Robot arms
- Power grids
- Medical imaging
- Biodiversity conversation
- Model of epidemics
- Chemistry
- Modeling trafic
- Neurosciences
- Design of radar ad sonar system
How useful was this post?
Maths 2nd Year Notes
Click on a star to rate it!
Maths 2nd Year Notes Fbise
Average rating 4.7 / 5. Vote count: 26
Maths 2nd Year Notes 3.2
No votes so far! Be the first to rate this post.