Civil Engineering
Introduction to Differential Equations, Initial Value Problems, Variable Separable method, and Homogeneous Differential Equations.
Introduction to Differential Equations, Variable Separable method, and Homogeneous Differential Equations.
Solving First-Order DEs using Exactness, Integrating Factors, and Linear Methods (including Bernoulli's Equation).
Practical applications including population growth, decay, Newton's Law of Cooling, mixing problems, electrical circuits, and falling bodies.
Solving nth-order linear homogeneous differential equations with constant coefficients and Cauchy-Euler equations.
Solving non-homogeneous linear differential equations using Undetermined Coefficients and Variation of Parameters.
Solving non-homogeneous linear differential equations using Undetermined Coefficients, Annihilator Approach, and Variation of Parameters.
Practical applications in mechanical and electrical systems, including Spring-Mass Systems, Pendulums, and RLC Circuits.
Solving systems of linear differential equations using elimination, matrix methods (eigenvalues), and phase portrait analysis.
Solving systems of linear differential equations using the elimination method, matrix methods (eigenvalues), and phase portrait analysis.
Solving initial value problems using the Laplace Transform method, partial fraction decomposition, step functions, and Dirac delta.
Solving initial value problems using the Laplace Transform method, including step functions, Dirac delta, and convolution.
Using power series methods, including Radius of Convergence and the Frobenius Method, to solve differential equations with variable coefficients.
Using power series methods, ratio tests, and the Frobenius method to solve differential equations with variable coefficients.
Solving differential equations using numerical approximations, including Euler's method, Runge-Kutta methods, and error analysis.
Solving differential equations using numerical approximations such as Euler's method and Runge-Kutta methods, and analyzing errors.
Introduction to PDEs, classification, Separation of Variables, and solving the Heat, Wave, and Laplace equations.
Introduction to PDEs, classification, Fourier Series, and solving the Heat, Wave, and Laplace equations using Separation of Variables.