Section numbers are from the textbook Differential Equations S. L. Ross Edition 3. Lecture notes prepared by Prof. Mansur İsgenderoğlu are from previous terms, so they partially match the topics for each lecture.
Lecture 1 (27.09.2024): Classification of differential equations (1.1), Solution types (1.2) and their existence, Initial and boundary value problems in general (1.3), Integral curves, Separable equations (2.2). You can find the lecture notes here.
Lecture 2 (04.10.2024): Equations which are reducible to separable form, Homogeneous equations, First order linear equations (2.3) and their integrating factors. You can find the lecture notes here.
Lecture 3 (11.10.2024): Bernoulli equations, Riccati equations, Exact differential equations (2.1). You can find the lecture notes here.
Lecture 4 (18.10.2024): Integrating factors for non-exact differential equations, Special integrating factors (2.4), Method of grouping, Applications from mechanics and physics (3.2). You can find the lecture notes here.
Lecture 5 (25.10.2024): Rate and mixture problems (3.3), Newton's law of cooling, Lipschitz condition (10.1), Existence and uniqueness theorem for first order equations (10.2). You can find the lecture notes here.
Lecture 6 (01.11.2024): Closed equations with respect to first order derivative, parameter inclusion method, Clairaut and Lagrange equations, Picard approximation sequence and their errors, Generalized Lipschitz condition, Existence and uniqueness theorem for higher order equations (10.4). You can find the lecture notes here (in Turkish).
Lecture 7 (08.11.2024): Linear higher order differential equations (4.1), Wronskian, Abel's theorem, linear independence of solutions, fundamental set of solutions, form of a general solution, Homogeneous linear differential equations with constant coefficients (4.2), characteristic equation via 3 cases. You can find the lecture notes here.
Lecture 8 (15.11.2024): Non-homogeneous linear differential equations, Particular solutions, Variation of parameters (4.4), Cramer's rule from linear algebra, Method of undetermined coefficients (4.3). You can find the lecture notes here.
Lecture 9 (22.11.2024): Cauchy-Euler equations (4.5), Method of reduction of order (4.1C). You can find the lecture notes here.
Lecture 10 (29.11.2024): Taylor expansion, Analytic functions, Ordinary and singular points, Power series solutions about an ordinary point (6.1). You can find the lecture notes here.
Lecture 11 (06.12.2024): Regular ordinary points, Method of Frobenius (6.2), Indicial equation via 3 cases, Bessel's equation and Bessel functions (6.3), Gamma function and its relation to factorial. You can find the lecture notes here.
Lecture 12 (13.12.2024): Laplace transformation (9.1), Existence, properties and examples, Heaviside step function and translated function, Inverse Laplace transformation (9.2). You can find the lecture notes here.
Lecture 13 (20.12.2024): Recall Laplace transformation, The convolution (9.2), Solving linear differential equations with constant coefficients by using Laplace transformation (9.3). You can find the lecture notes here.
Lecture 14 (27.12.2024): Systems of constant coefficients homogeneous linear differential equations (7.4), Distinct real eigenvalues, complex eigenvalues. You can find the lecture notes here.