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Experimental Pharmacology written by Dr. Bhavana Srivastava and Dr. Sanjay Gaur.(NCBA)
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Core Subject Overview:-
This book is a foundational academic text designed primarily for undergraduate mathematics, engineering, and computer science students. It bridges the traditional mathematical formulations of numerical analysis with computational implementations.
1. Numerical Analysis
This section focuses on mathematical algorithms used to obtain approximate numerical solutions to complex equations where analytic or exact solutions are difficult or impossible to find. Major topics typically include:
- Error Analysis: Characterizing absolute, relative, percentage, and rounding errors caused by finite-precision machine arithmetic.
- Algebraic & Transcendental Equations: Iterative root-finding techniques like the Bisection, Regula-Falsi, Secant, and Newton-Raphson methods.
- Systems of Linear Equations: Direct approaches like Gauss elimination and LU decomposition alongside iterative approaches like the Gauss-Seidel method.
- Interpolation: Using polynomial approximations via Newton’s forward/backward difference or Lagrange methods to estimate intermediate values.
- Numerical Calculus: Numerical integration (e.g., Trapezoidal and Simpson’s rules) and techniques for solving ordinary differential equations (such as Euler’s and Runge-Kutta methods).
2. Elements of Computer Science
This section focuses on translating numerical mathematical logic into computational workflows:
- Algorithm & Flowchart Design: Constructing step-by-step logic paradigms and visual paths before programming a problem.
- Computer Arithmetic: Understanding binary, octal, and hexadecimal number representation along with fixed-point and floating-point data structures.
- Programming Implementations: Applying modular programming concepts, loops, control statements, and functions to deploy mathematical computations into practical software models.
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