Project: Pre-Calculus Buddy

Description:
Pre-Calculus Buddy is a Java-based command-line tool designed to assist with solving a variety of pre-calculus and early calculus problems. It provides a menu-driven interface to access different sections, each dedicated to specific mathematical topics and operations.

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Table of Contents

1. Main Program Structure
2. Modules and Functionalities
3. Dependencies
4. How to Run

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Main Program Structure

File: PreCalc.java

The central entry point for the program:

• Prompts the user to select from four sections of topics:
  1. Section 1: Trigonometry (Law of Sines).
  2. Section 2: Vector mathematics and polar coordinates.
  3. Section 3: Combinatorics and arrangements.
  4. Section 4: Basic calculus operations (derivatives and integrals).
• Uses inheritance to call methods from the corresponding section files.

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Modules and Functionalities

File: Section1.java

Focuses on trigonometric calculations:

• Law of Sines: The Law of Sines relates the ratios of sides to the sines of their opposite angles. It’s useful when solving triangles with Angle-Side-Angle (ASA) or Side-Angle-Angle (SAA) information. Example problems and detailed steps are available on resources like Math is Fun.

File: Section2.java

Handles vector operations and polar equations:

• Dot Product: Calculates the dot product of two vectors.
• Vector Magnitude: Finds the magnitude of vectors.
• Head Minus Tail (HMT): Calculates vector differences.
• Vector Addition/Subtraction/Multiplication: Performs vector arithmetic and scalar multiplication.
• Angle Between Vectors: Finds the angle between two vectors.
• Linear Combination: Expresses vectors in terms of linear components.
• Resolve Vector: Decomposes a vector into its components.
• Orthogonal Vector Check: Determines if vectors are orthogonal or parallel.
• Vector Projection: Projects one vector onto another.
• Work Equations: Solves work problems in physics.
• Polar Equations for Conics: Analyzes conic sections from polar equations.
• Magnitude of a Single Vector: Calculates the magnitude of one vector.
• Special Polar Graphs: Classifies polar graph types like limacons and roses.
• Direction Angle of a Vector: Finds the angle direction of a vector.
• Direction Vector: Converts magnitude and angle to a vector.

File: Section3.java

Explores combinatorics:

• Arrange Letters: Finds the number of ways to arrange a set of items.
• Combination Solver: Calculates combinations with repetition.
• Permutation: Generates all permutations of a given number.

File: Section4.java

Supports basic calculus:

• Derivatives: Finds derivatives of functions.
• Anti-Derivatives: Computes anti-derivatives.
• Cross-Product: Performs cross-product of vectors.

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Dependencies

1. Java Development Kit (JDK): The code requires Java 8+ for features like Scanner and Math.
2. Standard Java Libraries:
   • java.util.Scanner: For user input.
   • java.lang.Math: For mathematical computations.
3. Inheritance and Object-Oriented Design:
   • Each section is encapsulated as a class, with inheritance connecting them.

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How to Run

1. Compile all files together using a Java compiler:

   javac PreCalc.java Section1.java Section2.java Section3.java Section4.java

2. Run the program:

   java PreCalc

3. Follow the on-screen prompts to navigate through sections and solve problems.