Engineering Mathematics

Course Information

• Course Title: Engineering Mathematics
• Course Code: 2014197-01
• Credits: 3
• Schedule: Sunday 10:00–12:00 & Monday 14:00-16:00
• Location: Class 1 & Class 9
• Instructor: Seyed Sadjad Abedi-Shahri
  • Email: AbediSadjad@gmail.com

• Lecture Materials: Provided weekly in LMS.
• Projects

Course Overview

This advanced engineering mathematics course is designed to provide students with a comprehensive understanding of key mathematical techniques essential for engineering and applied science disciplines. The course focuses on three critical areas: Complex Analysis, Fourier Analysis, and Partial Differential Equations, equipping students with powerful mathematical tools for modeling and solving complex engineering problems.

Learning Objectives

By the end of this course, students will be able to:

1. Complex Analysis
   • Manipulate complex functions and understand their properties
   • Apply complex integration techniques
   • Use conformal mapping and residue theorem to solve engineering problems
2. Fourier Analysis
   • Understand and apply Fourier series and transforms
   • Solve engineering problems using Fourier techniques
3. Partial Differential Equations (PDEs)
   • Classify and solve different types of PDEs (Wave/Heat/Laplace)
   • Apply separation of variables and transform methods
   • Model physical phenomena using PDEs in engineering contexts

Syllabus

1. Complex Analysis
2. Fourier Analysis
3. Partial Differential Equations

References

1. [ZIL] Advanced Engineering Mathematics [6th ed.] by Dennis G. Zill
2. [KRE] Advanced Engineering Mathematics [9th ed.] by Erwin Kreyszig
3. [ONE] Advanced Engineering Mathematics [7th ed.] by Peter V. O’Neil
4. [DUF] Advanced Engineering Mathematics with MATLAB [4th ed.] by Dean G. Duffy
5. [YAN] Engineering Mathematics with MATLAB by Won Y. Yan et al.

Evaluation Scheme

1. Midterm Evaluation: 30 points

   • Complex Analysis

2. Final Evaluation: 55 points

   • Fourier Analysis + Partial Differential Equations

3. Continuous Evaluation: 15 points

   • Based on exercises, quizzes, and participation during lectures and discussions.

4. Extracurricular Activities (optional): Up to 10 bonus points

   • Awarded for participation in activities such as group projects, presentations, or relevant research outside the classroom.

Session Outline

1. Module 1: Complex Analysis
   • Lecture 1: Complex Numbers and Functions
     • Complex Numbers
     • Powers and Roots
     • Sets in the Complex Plane
     • Functions of a Complex Variable
     • Cauchy–Riemann Equations
     • Exponential and Logarithmic Functions
     • Trigonometric and Hyperbolic Functions
     • Inverse Trigonometric and Hyperbolic Functions
   • Lecture 2: Complex Integration
     • Contour Integrals
     • Cauchy–Goursat Theorem
     • Independence of the Path
     • Cauchy’s Integral Formulas
   • Lecture 3: Series
     • Sequences and Series
     • Taylor Series
     • Laurent Series
   • Lecture 4: Residues
     • Zeros and Poles
     • Residues and Residue Theorem
     • Evaluation of Real Integrals
   • Lecture 5: Conformal Mappings
     • Complex Functions as Mappings
     • Conformal Mappings
     • Linear Fractional Transformations

Projects:

• Project 1: Mandelbrot Set Exploration
• Project 2: Joukowski Transformation

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

• Calculus II
• Differential Equations
• Introductory programming (optional)

Policies

1. Regular attendance is strongly recommended to stay on track with course material and acquire continuous evaluation score
2. Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
3. Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerat