1. Introduction 2. Existence and Types of Solutions A system ( A\mathbf{x} = \mathbf{b} ) may have: 3. Consistency of Linear System A system is consistent if it has at least one solution, i.e.,[\text{Rank}(A) = \text{Rank}([A|B])]If (\text{Rank}(A) < \text{Rank}([A|B])), then the system is inconsistent. 4. Direct Methods These methods give exact (or nearly exact) solutions…
1. Introduction 2. Numerical Differentiation 3. Newton’s Differentiation Formulas 4. Numerical Integration 5. Romberg Integration 6. Numerical Double Integration Key Takeaways – Unit 3
1. Introduction 2. Errors in Polynomial Interpolation 3. Lagrange’s Interpolation 4. Newton’s Interpolation 5. Cubic Spline Interpolation 6. Least Squares Method Key Takeaways – Unit 2
1. Introduction 2. Types of Equations 3. Errors in Computing 4. Bisection Method 5. Method of False Position (Regula Falsi) 6. Newton-Raphson Method 7. Fixed Point Iteration 8. Solution of System of Nonlinear Equations Key Takeaways – Unit 1
1. Introduction to Transaction A transaction is a logical unit of work that performs one or more database operations (like INSERT, UPDATE, DELETE) and ensures data integrity. Example:When transferring money between two accounts: Both operations must succeed together — otherwise, neither should happen. 2. Properties of a Transaction (ACID) Transactions must satisfy ACID properties to…
1. Query Processing Overview Steps in Query Processing: 2. Measuring Query Cost Purpose: Helps the optimizer choose the best query plan. 3. Selection Operation SQL Example: SELECT * FROM Students WHERE Age > 18; 4. Sorting Example: SELECT * FROM Students ORDER BY Name ASC; 5. Joining Tables 6. Query Optimization 7. Database Security Overview…
1. Introduction As databases grow larger and more complex, performing the same SQL operations repeatedly or ensuring data integrity manually becomes inefficient.To handle this, SQL provides Stored Procedures, Triggers, and Indexes — advanced features to improve automation, consistency, and performance. A. Stored Procedures 1. Definition A Stored Procedure is a precompiled set of SQL statements…
1. Introduction to SQL (Structured Query Language) SQL (Structured Query Language) is a standard language used to store, manipulate, and retrieve data in a Relational Database Management System (RDBMS). It is both declarative and non-procedural — you describe what you want, not how to get it. Major Categories of SQL Commands: Category Full Form Purpose…
1. Introduction A good database design ensures: The process used to achieve this is called Normalization. 2. What is Normalization? Normalization is the process of organizing data in a database to reduce redundancy and improve data integrity. It divides large tables into smaller ones and defines relationships between them. Goal: 3. Problems in Unnormalized Databases…
1. Introduction The Relational Database Model was introduced by E. F. Codd (1970).It organizes data into tables (relations) consisting of rows (tuples) and columns (attributes). Example: Student_ID Name Age Course 101 Ramesh 20 BCA 102 Sita 21 BSc CSIT 103 Hari 19 BBA Each row → record of a studentEach column → attribute (Name, Age,…