Advanced Engineering Mathematics

This course is designed to equip students with advanced mathematical tools that are fundamental to solving complex problems in engineering, physics, and the applied sciences. Recognizing the critical role of mathematical modeling and analysis in these fields, the course provides both theoretical insight and practical techniques to prepare students for real-world applications and advanced academic work. It begins with a review of foundational concepts before progressing to key topics such as matrix operations, complex number arithmetic, and Laplace transforms for solving linear differential equations. The course further explores power series solutions, Fourier series and transforms, and Sturm-Liouville theory, culminating in the study of partial differential equations, which are central to modeling physical phenomena such as heat conduction, wave propagation, and fluid dynamics. Emphasis is placed on the integration of theory with application, fostering students' ability to select appropriate mathematical tools, perform rigorous analysis, and interpret results in context. By the end of the course, students will have developed a strong mathematical framework for addressing advanced engineering and scientific problems, enabling them to approach complex systems with analytical confidence and precision.

• Apply advanced matrix operations to solve complex engineering problems.

• Apply advanced complex number operations to solve complex engineering problems.

• Apply Laplace transforms to solve complex engineering initial value problems across diverse applications.

• Apply series solutions to solve complex engineering boundary value problems across diverse applications.

1. Module 1: Matrix Operations

   • 1. Introduction to Matrix Algebra

   • 2. Vectors

   • 3. Binary Matrix Operations

   • 4. Unary Matrix Operations

   • 5. System of Equations

   • 6. Gaussian Elimination Method

   • 7. LU Decomposition Method

   • 8. Gauss-Seidel Method

   • 9. Adequacy of Solutions

   • 10. Eigenvalues and Eigenvectors

   • 11. Lecture Notes

2. Module 2: Complex Number Operations

3. Module 3: Laplace Transforms

4. Module 4: Power Series

1. Problem Set 1: Matrix Operations

2. Problem Set 2: Cramer's Rule and Gauss Elimination

3. Problem Set 3: Gauss-Jordan and LU decomposition

4. Problem Set 4: Complex Number Operations

5. Problem Set 5: Complex Matrix Operations

6. Problem Set 6: Laplace Transforms and Initial Value Problems

7. Problem Set 7: Simultaneous ODEs and Applications

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1. Advanced Engineering Mathematics (10th Edition) by Kreyzig

2. Advanced Engineering Mathematics (7th Edition) by O'Neill

3. Advanced Engineering Mathematics (5th Edition) by Wylie

4. Advanced Engineering Mathematics (5th Edition) by Wright

1. Advanced Engineering Mathematics by Professor Macauley

2. Advanced Engineering Mathematics by enginerdmath