Engineering Analysis

General Information

• University: Salahaddin University-Erbil
• Department: Software Engineering Dept.
• My Status: Lecturer
• Level: BSc
• Year: 2019

Course Description

This course bridges the gap between traditional engineering mathematics and modern software engineering applications. It provides students with the mathematical foundations necessary for understanding and implementing complex software systems, particularly those involving physical simulations, autonomous agents, and computational modeling.

The curriculum combines classical mathematical concepts such as calculus, linear algebra, and probability theory with contemporary computational techniques for simulating physical systems. Students will learn how mathematical principles translate into software implementations, enabling them to create sophisticated applications that model real-world phenomena.

Through hands-on projects and practical exercises, students will develop the ability to apply mathematical concepts to software engineering problems, preparing them for careers in game development, simulation software, robotics, and other computationally intensive applications.

Prerequisites

• Calculus I (or equivalent)
• Linear Algebra fundamentals
• Programming Fundamentals
• Basic physics concepts

Course Objectives

Upon completion of this course, students will be able to:

• Apply calculus concepts to solve software engineering problems involving rates of change and accumulation.
• Utilize linear algebra for geometric transformations, computer graphics, and data manipulation.
• Implement probability and statistics for simulation and modeling applications.
• Design and implement physical system simulations using mathematical principles.
• Create autonomous agent behaviors using mathematical algorithms.
• Apply Fourier analysis for signal processing and data analysis.
• Develop flocking and swarm behavior algorithms.
• Integrate mathematical concepts into software applications effectively.

Course Outline

Module 1: Mathematical Foundations Review

• Calculus fundamentals: derivatives and integrals
• Linear algebra: vectors, matrices, and transformations
• Probability and statistics basics
• Mathematical notation and computational thinking

Module 2: Calculus Applications in Software Engineering

• Derivatives: rates of change in software systems
• Integration: accumulation and area calculations
• Differential equations in simulation
• Optimization techniques for software performance

Module 3: Linear Algebra for Software Applications

• Vector operations and geometric transformations
• Matrix operations and their computational applications
• Coordinate systems and transformations
• Linear algebra in computer graphics and data processing

Module 4: Random Variables and Probability

• Random number generation and distribution
• Probability distributions in software modeling
• Statistical analysis for software testing
• Monte Carlo methods and simulation

Module 5: Physical System Simulation

• Gravitational system modeling
• Force calculations and physics engines
• Particle systems and dynamics
• Real-time simulation techniques

Module 6: Environmental Effects and Forces

• Wind force simulation and effects
• Fluid dynamics basics for software applications
• Environmental interaction modeling
• Force field implementation

Module 7: Autonomous Agent Systems

• Agent-based modeling fundamentals
• Autonomous tracking algorithms
• Decision-making systems
• Multi-agent coordination

Module 8: Steering and Movement Systems

• Steering behaviors and algorithms
• Arrival and departure behaviors
• Pathfinding and navigation
• Movement optimization techniques

Module 9: Flock Behavior and Swarm Intelligence

• Flocking algorithm implementation
• Swarm behavior principles
• Emergent behavior in multi-agent systems
• Collective intelligence applications

Module 10: Advanced Applications and Integration

• Combining multiple mathematical concepts
• Performance optimization for mathematical computations
• Real-world application case studies
• Future trends in mathematical software engineering

Textbooks

• [Recommended] “The Nature of Code” by Daniel Shiffman
• [Optional] “Mathematics for Computer Science” by Eric Lehman, F. Thomson Leighton, and Albert R. Meyer

Assessment

• Midterm Exam (20%)
• Activities and Projects (30%)
  • Mathematical Problem Sets (10%)
  • Programming Projects (15%)
  • Simulation Development (5%)
• Final Exam (50%)