Polynomial Functions

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/UP-LT-GRADE-ASSISTANT-TEACHER-2025/cs-03-data-structures-and-algorithm/algorithm-analysis/growth-rate-comparisons/asset-polynomial-functions after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography: Geography
  16. GS Paper | 02 | History: History
  17. GS Paper | 03 | Indian Economy & Social Development: Indian Economy
  18. GS Paper | 04 | General Science: Biology, Chemistry, Physics
  19. GS Paper | 05 | Elementary Maths: Number System, Divisibility Rules, HCF LCM, Percentage, Profit and Loss, Simple Interest and Compound Interest, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Algebra, Mensuration and Geometry, Data Interpretation, Arithmetic, Statistics, Probability, Sequence and Series (Series), Mixture and Alligation, Calculus, Trigonometry, Vectors
  20. GS Paper | 06 | Indian Polity and Governance: Polity
  21. GS Paper | 07 | Current Events: GK- Current Affairs
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment introduces polynomial functions and their growth rates as n approaches infinity. The instructor presents a core example problem requiring students to arrange six specific functions in increasing order of growth: sqrt(n), n, n^2, n log n, n^3, and n^k (where k >= 1). The teaching method emphasizes rewriting radical expressions as fractional exponents to facilitate direct comparison of polynomial powers. For instance, the square root function is explicitly converted from sqrt(n) to n^0.5 or n^(1/2). The instructor systematically compares terms by analyzing their exponents and logarithmic factors, establishing a hierarchy where lower powers grow slower than higher powers. The visual progression shows the instructor underlining terms, circling intermediate comparisons like 5n versus n, and highlighting the final sorted sequence in a pink box. Key concepts include identifying that polynomial growth dominates logarithmic-linear terms, and that higher exponents indicate faster asymptotic growth.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the topic of polynomial functions and presents an example problem asking to arrange a set of functions in increasing order of growth as n approaches infinity. The visible text on screen lists the target functions: sqrt(n), n, n^2, n log n, n^3, and n^k. The instructor begins by analyzing the first function, square root of n, rewriting it as a power of n (n^0.5) to facilitate comparison with the other polynomial and logarithmic terms. This conversion is a critical step shown in the notes, where n^0.5 = n^(1/2) is written to standardize the notation for exponent comparison.

  2. 2:00 – 3:30 02:00-03:30

    The instructor continues the analysis by comparing linear terms against logarithmic factors to establish the hierarchy between n, n log n, and n^2. The visual notes show comparisons like 5n versus n and the analysis of n log n versus n^2 to determine their relative magnitudes. The progression shows a step-by-step comparison of terms, circling them to indicate order. Finally, the sorted sequence is highlighted in a pink box on screen: sqrt(n), n, n log n, n^2, n^3, n^k. This final arrangement demonstrates the hierarchy of growth rates from the lowest power (n^0.5) up to the highest polynomial term (n^k), confirming that polynomial functions with higher exponents grow faster than those with lower exponents or logarithmic multipliers.

The lecture effectively demonstrates the method for comparing asymptotic growth rates of polynomial and related functions. The central technique involves converting all terms to a standard exponential form, such as rewriting sqrt(n) as n^0.5, which allows for direct comparison of the exponents. The instructor establishes a clear hierarchy where n^0.5 grows slower than n, which in turn grows slower than n log n, followed by higher powers like n^2 and n^3. The final sorted sequence provided in the pink box serves as a definitive reference for students to understand that among polynomial functions, the magnitude of the exponent dictates the growth rate. This example reinforces the fundamental concept that as n approaches infinity, higher powers dominate lower powers and logarithmic factors.

Loading lesson…