

Contents


Week 1: 
Matrix Algebra, Gauss Elimination and Cofactor MethodsRecall, Systems of Equations, Linearity, Homogenous Systems, Existance of Solution. Homework 1 
Week 2: 
Eigenvalue Problem, Eigenvectors, Homogenous and Nonhomogenous Ordinary Differential Equations, Modelling of Dynamics Systems. Homework 2 
Week 3: 
Higher Order Ordinary Differential Equations, Systems of Homogenous and Nonhomogenous Ordinary Differential Equations, General and Particular Solutions. Homework 3 
Week 4: 
Laplace Transformations: Derivative, Integral, Convolution, Periodic Functions. Homework 4 
Week 5: 
Solution of Nonhomogenous Ordinary Differential Equations using Fourier Series, Fourier Sine, Fourier Cosine. Homework 5 
Week 6: 
Solution of Ordinary Differential Equations using Power Series, Frobenius Method. Homework 6 
Week 7: 
Midterm exam, Introduction to Partial Differential Equations 
Week 8: 
Partial Differential Equations, Simplifications by Variable Transformations, Basic Operators: Gradient, Laplacien, etc. 
Week 9: 
Solution of Partial Differential Equations by Laplace Transformation. 
Week 10: 
Solution of Partial Differential Equations by Seperation of Variables. Homework 7 
Week 11: 
Solution of Partial Differential Equations by Combination of Variables, Similarity Solutions. 
Week 12: 
Partial Differential Equations, Simplifications by Variable Transformations in Wave Equation, Initial and Boundary Conditions. 
Week 13: 
Problems in Polar and Cylindrical Coordinates, Circular Membrane Problem, Bessel and Legendre Functions. 
Week 14: 
Applications to Thermal Problems, Heat Generation and Conduction, Applications in Various Coordinate Systems. 
Week 15*: 
 
Week 16*: 
Final exam. 
Textbooks and materials: 
Advanced Engineering mathematics, Kreyszig,Erwin, John Wiley. 
Recommended readings: 
Schaums Outline of Advanced Mathematics for Engineers and Scientists, Spiegel, Murray Advanced Engineering mathematics,Peter V. ONeil, Brooks Cole. 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

