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### Thelearningpoint

1. 1. www.thelearningpoint.netCome Check out our Free Repository of Tutorials andVisualizations !Geometry in Nature : A Tree made with Fractals; A Complex Function
2. 2. Click below if youd like to check out our recent additions in the Physicssection !
3. 3. MathematicsAlgebraIntroduction to The Principle of Quadratic QuadraticComplex Numbers Mathematical Induction Equations InequalitiesIntroduction to Introductory problems Introducing QuadraticComplex Numbers related to Mathematical various inequalities. Usingand iota. Argand Induction. techniques by factorization andplane and iota. which quadratic visualization basedComplex numbers equations can methods.as free vectors. be solved -N-th roots of a factorization,complex number. direct formula.Notes, formulas Relationshipand solved between rootsproblems related to of a quadraticthese sub-topics. equation. Cubic and higher order equations - relationship between roots and coefficients
4. 4. for these. Graphs and plots of quadratic equations. Series andProgressionsArithmetic,Geometric,Harmonicand mixedprogressions.Notes, formulasand solvedproblems. Sumof the first Nterms. Arithmetic,Geometric andHarmonic meansand the relationshipbetween them.Geometry GeometryCo-ordinate GeometryIntroduction to Co- Equation of Straight The Circle A Quick Introductionordinate Geometry Line to Conic Sections: Parabola, Hyperbola, EllipseParabola Hyperbola EllipseProbability Probability Probability - Probability - Part Probability - Part 3 - Joint- Part Zero - Part 1 - Basic 2 - A Tutorial Probability, BivariateA Very Basic Probability on Probability Normal Distributions,Introduction
5. 5. Definitions, Distributions Functions of Random Random Variables Variable,Transformation of Random VectorsLinear Algebra Introduction to Introduction to Determinants Simultaneous linearMatrices - Part I Matrices - Part II Introduction to equations in multipleIntroduction to Problems and solved determinants. variables RepresentingMatrices. Theory, examples based on the Second and third a system of lineardefinitions. What a sub-topics mentioned order determinants, equations in multipleMatrix is, order of a above. Some of the minors and co- variables in matrix form.matrix, equality of problems in this part factors. Properties Using determinants tomatrices, different demonstrate finding of determinants solve these systems ofkind of matrices: row the rank, inverse and how it remains equations. Meaning ofmatrix, column matrix, or characteristic altered or unaltered consistent, homogeneoussquare matrix, equations of matrices. based on simple and non-homogeneousdiagonal, identity and Representing real life transformations systems of equations.triangular matrices. problems in matrix form. is matrices. Theorems relating toDefinitions of Trace, Expanding the consistency of systemsMinor, Cofactors, determinant. Solved of equations. ApplicationAdjoint, Inverse, problems related to of Cramer rule. SolvedTranspose of a determinants. problems demonstratingmatrix. Addition, how to solve linearsubtraction, scalar equations using matrixmultiplication, and determinant relatedmultiplication of methods.matrices. Definingspecial types ofmatrices likeSymmetric, SkewSymmetric,Idempotent,Involuntary, Nil-potent, Singular, Non-Singular, Unitarymatrices.Basic concepts in Introductory problems More concepts Problems related to linearLinear Algebra and related to Vector related to Vector transformation, linearVector spaces Theory Spaces - Problems Spaces Defining and maps and operators -
6. 6. and definitions. demonstrating the explaining the norm Solved examples andClosure, commutative, concepts introduced in of a vector, inner problems related to linearassociative, the previous tutorial. product, Graham- transformation, lineardistributive laws. Checking or proving Schmidt process, maps and operators andDefining Vector something to be a sub- co-ordinate vectors, other concepts discussedspace, subspaces, space, demonstrating linear transformation theoretically in thelinear dependence, that something is not a and its kernel. previous tutorial.dimension and bias. sub-space of something Introductory problemsA few introductory else, verifying linear related to these.problems proving independence; problemscertain sets to be relating to dimension andvector spaces. basis; inverting matrices and echelon matrices.Definitions of Rank, More Problems related A few closingEigen Values, Eigen to Simultaneous problems in LinearVectors, Cayley Equations; problems Algebra Solving aHamilton Theorem related to eigenvalues recurrence relation,Eigenvalues, and eigenvectors some more of systemeigenvectors, Cayley Demonstrating the of equations.Hamilton Theorem Crammer rule, using eigenvalue methods to solve vector space problems, verifying Cayley Hamilton Theorem, advanced problems related to systems of equations. Solving a system of differential equations .VectorsVectors 1a ( Theory and Vectors 1b ( Solved Vectors 2a ( Vectors 2b ( SolvedDefinitions: Introduction Problem Sets: Introduction Theory and Problem Sets: Vectorsto Vectors; Vector, to Vectors; Vector, Scalar Definitions: and Geometry )Scalar and Triple and Triple Products ) Vectors andProducts) Solved examples and Solved examples and
7. 7. Introducing a vector, problem sets based on the Geometry ) Vectors problem sets based onposition vectors, above concepts. and geometry. the above concepts.direction cosines, Parametric vectorialdifferent types of equations of linesvectors, addition and and planes. Anglessubtraction of vectors. between lines andVector and Scalar planes. Co-planarproducts. Scalar Triple and collinear points.product and Vector Cartesian equationstriple product and their for lines and planesproperties. Components in 3D.and projections ofvectors.Vectors 3a ( Theory Vectors 3b ( Solvedand Definitions: Vector Problem Sets: VectorDifferential and Integral Differential and IntegralCalculus ) Vector Calculus ) - SolvedDifferential Calculus. examples and problemDerivative, curves, sets based on the abovetangential vectors, concepts.vector functions,gradient, directionalderivative, divergenceand curl of a vectorfunction; importantformulas related to div,curl and grad. VectorIntegral Calculus. Lineintegral, independenceof path, Greenstheorem, divergencetheorem of Gauss,greens formulas,Stokes theorems.TrigonometryTrigonometry 1a Trigonometry 1b ( Tutorial Trigonometry 2a Trigonometry 2b (( Introduction to with solved problems ( Basic concepts Tutorial with solvedTrigonometry - based on Trigonometric related to Heights problems related toDefinitions, Formulas ratios ) Problems and Distances ) Heights and Distances) Introducing based on the concepts Applying trigonometry and other applications
8. 8. trigonometric ratios, introduced above. to problems involving of Trigonometry ) -plots of trigonometric heights and distances. Problems based on thefunctions, compound Angles of elevation and concepts introducedangle formulas. depression. Sine and above.Domains and ranges Cosine rule, half angleof trigonometric formulas. Circumradius,functions, inradius and escribedmonotonicity of radius. Circumcentre,trigonometric functions incentre, centroid andquadrant wise. median of a triangle.Formulas for doubleand triple angle ratios.Trigonometry 3a ( Trigonometry 3b ( Tutorial Trigonometry 4 ( AIntroducing Inverse with solved problems tutorial on solvingTrigonometric Ratios) related to inverse trigonometric equationsInverse trigonometric trigonometric ratios ) )- Solving trigonometricratios - their domains, - Problems related to equations. Methodsranges and plots. inverse trigonometric and transformations ratios. frequently used in solving such equations.Single Variable CalculusQuick and introductory Functions, Functions, Limits Functions,definitions related to Funtions, Limits and and Continuity - Limits andLimits and Continuity - Continuity - Solved Problem Set ContinuityDefining the domain and Solved Problem II - More advanced - Solvedrange of a function, the Set I - Solved cases of evaluating Problem Setmeaning of continuity, limits, problems limits, conditions III - Problemsleft and right hand limits, demonstrating for continuity of related toproperties of limits and how to compute functions, common Continuity,the "lim" operator; some the domain approximations used intermediatecommon limits; defining the and range of while evaluating limits value theorem.LHospital rule, intermediate functions, drawing for ln ( 1 + x ), sinand extreme value theorems. the graphs of (x); continuity related functions, the problems for more mod function, advanced functions deciding if than the ones in the a function is first group of problems invertible or (in the last tutorial).
9. 9. not; calculating limits for some elementary examples, solving 0/0 forms, applying LHospital rule.Introductory concepts Differential Differential Calculus Differentialand definitions related to Calculus - - Solved Problem CalculusDifferentiation - Theory Solved Problem Set II - - Solvedand definitions introducing Set I - Examples Examples and solved Problems Setdifferentiability, basic and solved problems - related III -differentiation formulas of problems - to derivability and Examples andcommon algebraic and differentiation continuity of functions; solved problemstrigonometric functions , of common changing the - related tosuccessive differentiation, algebraic, independent variable increasing andLeibnitz Theorem, Rolles exponential, in a differential decreasingTheorem, Lagranges logarithmic, equation; finding the functions;Mean Value Theorem, trigonometric N-th derivative of maxima, minimaIncreasing and decreasing and polynomial functions and extremefunctions, Maxima and functions and values; RollesMinima; Concavity, convexity terms; problems Theoremand inflexion, implicit related todifferentiation. differentiability .Differential Calculus - Differential Introducing Integral IntegralSolved Problems Set IV - Calculus - Calculus - Theory CalculusExamples and solved Solved Problems and definitions. - Solvedproblems - Slope of tangents Set V - More What integration Problems Set Ito a curve, points of inflexion, examples of means, the integral - Examples andconvexity and concavity of investigating and and the integrand. solved problemscurves, radius of curvature sketching curves, Indefinite integrals, - elementaryand asymptotes of curves, parametric integrals of common examples ofsketching curves representation of functions. Definite integration curves integration and involving properties of definite trigonometric integrals; Integration functions, by substitution, polynomials; integration by parts, integration by the LIATE rule, parts; area Integral as the limit under curves. of a sum. Important forms encountered in
10. 10. integration. Integral Calculus - Solved Integral Calculus Integral Calculus - IntegralProblems Set II - Examples - Solved Solved Problems Calculusand solved problems - Problems Set Set IV - Examples - Solvedintegration by substitution, III- Examples and and solved problems Problems Set Vdefinite integrals, integration solved problems - More of integrals - Examples andinvolving trigonometric and - Reduction involving partial solved problemsinverse trigonometric ratios. formulas, fractions, more - More complex reducing the complex substitutions examples of integrand to and transformations integration, partial fractions, examples of more of definite integration as integrals the limit of a summation of a seriesIntroduction to Differential Differential Differential DifferentialEquations and Solved Equations Equations - Solved EquationsProblems - Set I - - Solved Problems - Set - Solved Theory and definitions. Problems - Set III - More complex Problems - SetWhat a differential equation II - Examples and cases of differential IV -is; ordinary and partial solved problems equations. Still moredifferential equations; order - Solving linear differentialand degree of a differential differential equations.equation; linear and non equations, the Dlinear differential equations; operator, auxiliaryGeneral, particular and equations.singular solutions; Initial and Finding theboundary value problems; general solution (Linear independence and CF + PI )dependence; Homogeneousequations; First orderdifferential equations;Characteristic and auxiliaryequations. Introductoryproblems demonstrating theseconcepts. Introducing theconcept of Integrating Factor(IF).Multiple Variable Calculus
11. 11. Calculus - Multiple Calculus - Multiple Calculus - MultipleVariables - Part I- Variables - Part 2- Variables - Part 3-Functions of severable Functions of several Multiple Integrals;variables; limits and variables, theorems and double and triplecontinuity co-ordinates integralsApplied Mathematics : An Introduction to Game TheoryAn Introduction to Game Extensive Games Bayesian Games : Repeated GamesTheory Games with Incomplete InformationApplied Mathematics : An Introduction to Operations ResearchIntroduction to Operations A quick introduction to Operations Research.Research Introducing Linear Programming, standard and canonical forms. Linear Programming geometry, feasible regions, feasible solutions, simplex method. Some basic problems.PhysicsBasic Mechanics Introduction to Vectors Vectors and Newtons Laws of Work, Force andand Motion Projectile Motion Motion Energy Simple Harmonic Motion Rotational Dynamics Fluid MechanicsEngineering MechanicsMoments and Equivalent Centroid And Center Analysis ofSystems of Gravity StructuresElectrostatics and Electromagnetism
12. 12. Electrostatics - Part Electrostatics Electromagnetism - Electromagnetism1: Theory, definitions - Part 2: Part 1: Theory and - Part 2: Solvedand problems More solved Definitions problems Columbs law. problems. Lorentz Force, Bio- Solved problemsElectric Field More solved Savart law, Amperes related to the conceptsIntensity, principle problems related force law, basic laws introduced above.of superposition, to the concepts related to Magneticgauss theorem, introduced fields and theirelectrostatic potential, above. applications. Magneticelectric field intensities field intensitiesdue to common due to commoncharge distributions, current distributions.capacitors and Electromagneticcalculating Induction. Self andcapacitance. Solved mutual induction.problems. Advanced conceptsin Electrostatics andElectromagnetism (Theory only )Advanced conceptsrelated to electrostaticsand electromagnetism(theory only).Computer Science and ProgrammingData Structures and AlgorithmsArrays : PopularSorting and SearchingAlgorithmsBubble Sort - One of the Insertion Sort - Selection Sort Shell Sortmost elementary sorting Another quadratic time Another quadratic An inefficientalgorithms to implement - sorting algorithm - an time sorting but interesting
13. 13. and also very inefficient. example of dynamic algorithm - an algorithm, theRuns in quadratic time. programming. An example of a complexity ofA good starting point to explanation and step greedy algorithm. which is notunderstand sorting in through of how the An explanation and exactly known.general, before moving algorithm works, as step through ofon to more advanced well as the source code how the algorithmtechniques and for a C program which works, as well asalgorithms. A general performs insertion sort. the source code foridea of how the algorithm a C program whichworks and a the code for performs selectiona C program. sort.Merge Sort An example Quick Sort In theof a Divide and Conquer average case, this Heap Sort Binary Searchalgorithm. Works in O(n works in O(n log n) Efficient sorting Algorithmlog n) time. The memory time. No additional algorithm which Commonly usedcomplexity for this is a bit memory overhead - runs in O(n log algorithm used toof a disadvantage. so this is better than n) time. Uses find the position merge sort in this the Heap data of an element in regard. A partition structure. a sorted array. element is selected, the Runs in O(log n) array is restructured time. such that all elements greater or less than the partition are on opposite sides of the partition. These two parts of the array are then sorted recursively.Basic Data Structuresand Operations onthemStacks Last In First Out Queues First in Firstdata structures ( LIFO Out data structure Single Linked List Double Linked). Like a stack of cards (FIFO). Like people A self referential Listfrom which you pick waiting to buy tickets in data structure. A A self referentialup the one on the top ( a queue - the first one list of elements, data structure. Awhich is the last one to to stand in the queue, with a head and a list of elements,be placed on top of the gets the ticket first and tail; each element with a head and astack ). Documentation gets to leave the queue points to another of tail; each elementof the various operations first. Documentation of its own kind. points to anotherand the stages a stack the various operations of its own kind in
14. 14. passes through when and the stages a queue front of it, as wellelements are inserted passes through as as another of itsor deleted. C program elements are inserted own kind, whichto help you get an or deleted. C Program happens to beidea of how a stack is source code to help you behind it in theimplemented in code. get an idea of how a sequence. queue is implemented in code.Circular Linked List 1.Linked list with no headand tail - elements pointto each other in a circularfashion.Tree Data Structures Binary Search Trees Heaps - A tree like Height BalancedA basic form of tree data data structure where Trees - Ensuringstructures. Inserting and every element is that treesdeleting elements in them. lesser (or greater) remain balancedDifferent kind of binary tree than the one above to optimizetraversal algorithms. it. Heap formation, complexity of sorting using heaps in operations which O(n log n) time. are performed on them.Graphs and GraphAlgorithms Depth First Search - Breadth First Minimum MinumumTraversing through a graph Search - Traversing Spanning Spanning Trees:using Depth First Search in through a graph using Trees: Kruskal Prims Algorithmwhich unvisited neighbors Breadth First Search Algorithm Finding theof the current vertex are in which unvisited Finding the Minimum Spanningpushed into a stack and neighbors of the Minimum Tree using thevisited in that order. current vertex are Spanning Tree Prims Algorithm. pushed into a queue using the Kruskal and then visited in Algorithm which that order. is a greedy technique.
15. 15. Introducing the concept of Union Find.Dijkstra Algorithm for Floyd Warshall Bellman FordShortest Paths Algorithm for AlgorithmPopular algorithm for Shortest Paths Another commonfinding shortest paths : All the all shortest shortest pathDijkstra Algorithm. path algorithm: Floyd algorithm : Warshall Algorithm Bellman Ford Algorithm.Popular Algorithms inDynamic Programming Dynamic Programming Integer Knapsack Matrix Chain LongestA technique used to solve problem Multiplication Commonoptimization problems, An elementary Given a long Subsequencebased on identifying and problem, often used chain of matrices Given two strings,solving sub-parts of a to introduce the of various sizes, find the longestproblem first. concept of dynamic how do you common sub programming. parenthesize sequence between them for the them. purpose of multiplication - how do you chose which ones to start multiplying first? Dynamic ProgrammingAlgorithms coveredpreviously:Insertion Sort, FloydWarshall AlgorithmAlgorithms which wealready covered, whichare example of dynamicprogramming.Greedy AlgorithmsElementary cases : Data Compression
16. 16. Fractional Knapsack using HuffmanProblem, Task TreesScheduling - Elementary Compression usingproblems in Greedy Huffman Trees. Aalgorithms - Fractional greedy technique forKnapsack, Task encoding information.Scheduling. Along with CProgram source code.Commonly Asked Programming Interview Questions - from Microsoft/Google/Facebook/Amazon interviewsProgramming Interview Questionswith Solutions - Microsoft, Google,Facebook, AmazonA Collection of C Programs C Programs - Miscellaneous C ProgramsExploring various 1. 1 Computing the Area of a Circle inthings which can be C 2. 2 C Program to check for Armstrongdone in C Numbers 3. 3 C Program for Bezier Curves 4. 4 C Program implementing the Bisection Method ( Numerical Computing ) 5. 5 C Program demonstrating the use of Bitwise Operators 6. 6 C Program for an Expression Evaluator 7. 7 C Program to demonstrate File Handling Functions 8. 8 C Program to demonstrate the Gaussian Elimination Method 9. 9 C Program to compute the GCD (HCF) of two numbers 10. 10 C Program to solve the Josephus Problem 11. 11 C Program to demonstrate operations on Matrices 12. 12 C Program implementing the Newton Raphson Method (Numerical Computing) 13. 13 C Program to check whether a string is a palindrome or not
17. 17. 14. 14 C Program to print the Pascal Triangle 15. 15 C Program to display Prime Numbers using the sieve of Eratosthenes 16. 16 C Program for the Producer - Consumer Problem 17. 17 C Program for the Reader - Writer Problem 18. 18 C Program to demonstrate the Dining Philosopher problem 19. 19 C Program to reverse the order of words in a sentence 20. 20 C Program to reverse a string 21. 21 C Program to demonstrate the values in the series expansion of exp(x),sin(x),cos(x),tan(x) 22. 22 C Program to demonstrate common operations on Sets 23. 23 C Program to solve Simultaneous Linear Equations in two variables 24. 24 C program to display the total number of words,the number of unique words and the frequency of each word 25. 25 C program to display the IP address 26. 26 C program implementing the Jacobi method (Numerical Computing)Functional Programming Principles and TechniquesFunctional Programming - Using the FunctionalA General Overview Programming paradigm with a regular programming language like Ruby
18. 18. Databases - A Quick Introduction To SQL - Sample Queriesdemonstrating common commandsIntroduction to SQL- A Introduction to Introduction to SQL Introduction to SQLfew sample queries - A SQL- A few sample - A few sample - A few sampleCase Study - Coming queries : Creating queries : Making queries : Insert,up with a Schema for Tables (CREATE) Select Queries Delete, Update,Tables -Taking a look Creating tables, Elementary database Drop, Truncate, Alterat how the schema for defining the type and queries - using the Operation Examplea database table is size of the fields that go select statement, of SQL commandsdefined, how different into it. adding conditions and which are commonlyfields require to be clauses to it to retrieve used to modifydefined. Starting with information stored in a database tables.a simple "case study" database.on which the followingSQL tutorials will bebased.Introduction to SQL - Introduction toA few sample queries: SQL- A few sampleImportant operators queries: Aggregate- Like, Distinct, Functions - Sum,Inequality, Union, Null, Max, Min, Avg -Join, Top Aggregate functions Other Important SQL to extract numericaloperators. features about the data.Introduction To NetworkingClient Server Program in A basic introduction to networking and client server programming inPython Python. In this, you will see the code for an expression calculator . Clients can sent expressions to a server, the server will evaluate those expressions and send the output back to the client.Introduction to Basic Digital Image Processing FiltersIntroductory Digital Image Low-pass/Blurring filters, hi-pass filters and their behavior, edgeProcessing filters detection filters in Matlab . You can take a look at how different filters transform images. Matlab scripts for these filters.
19. 19. An Introduction to Graphics and Solid Modelling3D Modelling in Solid A Tutorial on Autodesk 3DS-Max Autodesk 3DSWorks - Part I 3D Modelling in Max - Part II SolidWorks - Part II Intro to Google Quick Introduction to Quick Introduction toSketchup Open GL (with C++) - Open GL (with C++) - Part I Part IIElectrical Science and EngineeringIntroduction to DC CircuitsCircuit Theory Circuit Theory Circuit Theory 2a - Circuit Theory1a- Introduction 1b - More solved Introducing Inductors 2b - Problemsto Electrical problems related Inductors, inductance, related toEngineering, DC to DC Circuits with computing self-inductance, RL, LC, RLCCircuits, Resistance Resistance and flux-linkages, computing circuitsand Capacitance, Capacitance energy stored as a IntroducingKirchoff Law Capacitors, magnetic field in a coil, the concept Resistors, computing mutual inductance, dot of oscillations.Capacitors, problems capacitance, RC convention, introduction to Solvingrelated to these. Circuits, time RL Circuits and decay of an problems constant of decay, inductor. related to RL, computing voltage LC and RLC and electrostatic circuits using energy across a calculus based capacitance techniques. Circuit Theory 3a - Circuit Theory 3bElectrical Networks - More networkand Network theorems, solvedTheorems problems Different kind of More solvednetwork elements: problems andActive and passive, examples relatedlinear and non- to electricallinear, lumped and networks. Stardistributed. Voltage and Delta networkand current sources. transformations,Superposition maximum power
20. 20. theorem, Thevenin transfer theorem,(or Helmholtz) Compensationtheorem and theorem andproblems based on Tellegens Theoremthese. and examples related to these.Introduction to Digital Electronic Circuits and Boolean logicIntroduction to the Number System : Introduction to BooleanNumber System : Part 1 Part 2 Boolean Algebra : Part Algebra : Part 2Introducing Binary addition, 1 De-morgans laws.number systems. subtraction and Binary logic: True and Logic gates. 2Representation of multiplication. false. Logical operators input and 3 inputnumbers in Decimal, Booths like OR, NOT, AND. gates. XOR,Binary,Octal and multiplication Constructing truth XNOR gates.Hexadecimal forms. algorithm. tables. Basic postulates Universality ofConversion from one Unsigned and of Boolean Algebra. NAND and NORform to the other. signed numbers. Logical addition, gates. Realization multiplication and of Boolean complement rules. expressions using Principles of duality. NAND and NOR. Basic theorems of Replacing gates in boolean algebra: a boolean circuit idempotence, involution, with NAND and complementary, NOR. commutative, associative, distributive and absorption laws. Understanding Karnaugh Maps : Introduction to CombinationalKarnaugh Maps : Part Part 2 Combinational Circuits : Part 21 Introducing Karnaugh Map rolling. Circuits : Part 1 Static andMaps. Min-terms and Overlapping Combinational circuits: DynamicMax-terms. Canonical and redundant for which logic is RAM, Memoryexpressions. Sum of groups. Examples entirely dependent organization.products and product of of reducing of inputs and nothingsums forms. Shorthand expressions via K- else. Introductionnotations. Expanding Map techniques. to Multiplexers,expressions in SOP and De-multiplexers,POS Forms ( Sum of encoders andproducts and Product decoders.Memories:of sums ). Minimizing RAM and ROM.
21. 21. boolean expressions Different kinds of via Algebraic methods ROM - Masked ROM, or map based reduction programmable ROM. techniques. Pair, quad and octet in the context of Karnaugh Maps. Introduction to Sequential Sequential Circuits : Circuits : Part 2 Part 1 ADC or DAC Introduction to Converters Sequential circuits. and conversion Different kinds of processes. Flash Flip Flops. RS, D, Converters, T, JK. Structure of ramp generators. flip flops. Switching Successive example. Counters approximation and and Timers. Ripple and quantization errors. Synchronous Counters.Clockwise : Fractal Geometry in Nature , Projectile Motion , A graph , An array being sorted