Advanced Engineering Mathematics

This course equips students with advanced mathematical tools essential for engineering, physics, and applied sciences. It begins with an introduction to foundational concepts, followed by a detailed exploration of matrix operations, complex number operations, and Laplace transforms. The course also discusses power series methods for differential equations. Advanced topics include Fourier series and transforms, Sturm-Liouville theory, and partial differential equations. By integrating theory and practical application, this course prepares students to tackle complex mathematical challenges in scientific and engineering contexts.

• 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