Numerical Methods | Module 1
NUMERICAL METHODS
Course Study Guide & Bisection Method
Prepared by:
REINNIEL JUNE AQUINO
Computer Engineering
Study Guide: Bisection Method | Prepared by REINNIEL JUNE AQUINO
, Numerical Methods | Module 1
Course Coverage
• Roots of Equations
• Systems of Linear Algebraic Equations
• Curve Fitting
• Differentiation
• Integration
• Ordinary Differential Equations
Note: This module focuses specifically on the first topic—Roots of Equations—using foundational bracketing algorithms.
Definition of Terms
• Numerical Methods: Techniques by which complex mathematical problems are formulated so that they can be solved
with arithmetic operations.
• Root: A value that makes the equation equal to zero. Visually, it is the exact coordinate where a plotted function crosses the
x-axis.
• Iteration: A repetitive process where the output of one sequence becomes the input of the next, gradually closing in on the
final answer.
• Bracketing: Identifying two initial guess values (a and b) that "trap" the root between them.
• Tolerance (ε): The acceptable margin of error. Since computers can calculate indefinitely, we set a tolerance (e.g., |f(x)| <
10⁻⁶) to tell the algorithm when to stop.
💡 Engineering Context: Analytical math (like factoring algebra) is great for paper, but computers only know
how to add, subtract, multiply, and divide. When the Ryzen 7 processor in your Laptop calculates complex game
physics, it can't use algebra. Instead, it uses numerical methods—brute-forcing arithmetic millions of times a
second to zero in on the exact answer.
Study Guide: Bisection Method | Prepared by REINNIEL JUNE AQUINO
NUMERICAL METHODS
Course Study Guide & Bisection Method
Prepared by:
REINNIEL JUNE AQUINO
Computer Engineering
Study Guide: Bisection Method | Prepared by REINNIEL JUNE AQUINO
, Numerical Methods | Module 1
Course Coverage
• Roots of Equations
• Systems of Linear Algebraic Equations
• Curve Fitting
• Differentiation
• Integration
• Ordinary Differential Equations
Note: This module focuses specifically on the first topic—Roots of Equations—using foundational bracketing algorithms.
Definition of Terms
• Numerical Methods: Techniques by which complex mathematical problems are formulated so that they can be solved
with arithmetic operations.
• Root: A value that makes the equation equal to zero. Visually, it is the exact coordinate where a plotted function crosses the
x-axis.
• Iteration: A repetitive process where the output of one sequence becomes the input of the next, gradually closing in on the
final answer.
• Bracketing: Identifying two initial guess values (a and b) that "trap" the root between them.
• Tolerance (ε): The acceptable margin of error. Since computers can calculate indefinitely, we set a tolerance (e.g., |f(x)| <
10⁻⁶) to tell the algorithm when to stop.
💡 Engineering Context: Analytical math (like factoring algebra) is great for paper, but computers only know
how to add, subtract, multiply, and divide. When the Ryzen 7 processor in your Laptop calculates complex game
physics, it can't use algebra. Instead, it uses numerical methods—brute-forcing arithmetic millions of times a
second to zero in on the exact answer.
Study Guide: Bisection Method | Prepared by REINNIEL JUNE AQUINO
