#### MATH 204: DIFFERENTIAL EQUATIONS, FALL 2020

Leave a reply

**Lecture Notes**[pdf]

**Textbook:** W. E. Boyce , R. C. DiPrima and D.B. Meade, Elementary Differential Equations and Boundary Value Problems, Global Edition (John Wiley & Sons, New York).

- Week 1: Sections 1.1-13, 2.1, 2.2 (Introduction, basic matheatical models, solutions od some ODE’s, classication of ODEs, first order linear ODEs, separable equations)
- Week 2: Sections 2.4, 2.6, 2.8 (Nonlinear first order equations Bernoulli equation, exact equations and integrating factors, the existence and uniqueness theorem)
- Week 3: Sections 2.8, 3.1, 3.2 (Existence and uniqueness theorem, homogeneous linear, the Wronskian, second order ODEs, Abel’s theorem)
- Week 4: Sections 3.2, 3.3, 3.4 Euler’s equation, complex roots of chatacteristic equation, repeated roots and reduction of order.
- Week 5: Sections 3.6, 3.8 Method of variation of parameters, forced periodic vibrations.
- Week 6: Sections 5.1 -5.2 Review of power series, series solutions near an ordinary point.
- Week 7: Sections 5.3, 6.1 Series solutions near an ordinary point, Laplace transform and its roperties.
- Week 8: Sections 6.2-6.4 Solution of initial value problems by using the Laplace transform, step functions, Differential equations wth discontinuous forsing functions
- Week 9: Sections 6.6, 7.1, 7.2 The convolution integral, Introduction to systems of first order ODEs, Matrices, Systems of linear algebraic equations.
- Week 10: Sections 7.3-7.5 Systems of linear algebraic equations, Eigenvalue problems, Basic theorey of systems of first order linear ODEs, Homogeneous linear systems.
- Week 11: Sections 7.6- 7.8 Complex – valued eigenvalues, Exponential of a matrix, Fundamental Matrix, Repeated eigenvalues.
- Week 12: Sections 7.9, 10.1, 10.2 Nonhomogeneous linear systems, Two-point boundary value problems, Fourier series.
- Week 13: Sections 10.3, 10.4, 10.5 The Fourier convergence theorem, even and odd functions, Separation of variables, heat equation.
- Week 14: 10.6 Other heat conduction problems.

**Alphan Sennaroglu**, Office: SCI 157, Office Hours: Tuesdays 13:30 -18:50**Ali Serpenguzel**, Office: SCI 119, Office Hours: Fridays 18:00 -18:50**Varga Kalantarov**, Office: SCI 162, Office Hours: Mondays 18:00 – 18:50 , Wendesdays 15:00 – 16:00

**Ayshemine Altindag**,e-mail:aaltindag20[at]ku.edu.tr Office Hours: Mondays 14:00-15:00**Shaheryar Atta Han****Mojdeh Vakili Tabatabaei, e-mail:mtabatabaei18[at]ku.edu.tr Office Hours: TBA****Omer Faruk Sahin**,e-mail:osahin18[at]ku.edu.tr Office Hours: Tuesdays 16:00-17:00

**Syllabus [pdf]**

**Lecture Notes**[pdf]

**Textbook:** Patrick M. Fitzpatrick, Advanced Calculus (sec. ed.), AMS, 2006.

- 1. Thie field, the positivity and the completenes axioms. Principle of mathematical induction. Ineuqlities and identites (sec. 11 -1.3)

- 2. Convergence of sequences. Sequences and sets.(sec. 2.1, 2.2)

- 3. The monotone convergence and sequential compactness theorems. Continuity. (sec.2.3, 2.4, 3.1)

- 4. The extreme value and intermediate value theorems. Uniform continuity. (sec.3.2, 3.3, 3.4, 3.5)

- 5. Monotone functions. Limits. Tangent line and derivatives. (sec.3.6, 3.7, 4.1)

- 6. Derivative of the inverse function and composition of two functions. The mean value theorem for derivative and consequences. Extreme values. The Cauchy mean value theorem (sec. 4.2, 4.3, 4.4)
- 7. Taaylor’s formula. Darboux Teorem. Sequences and series of numbers (sec.9,1 )
- 8. Sequences and series of functions: Pointwise convergence (sec 9.1, 9.2)
- 9. Uniform convegence. Weierstrass M-test. The linear structure of Rn. Cauchy – Schwarz inequality (sec. 9.3, 9.4, 10.1)
- 10. Triangle inequality. Convergence of sequences in Rn. Open and closed sets. (sec. 10.1, 10.2, 10.3)
- 11. Continuous functiona and mappings. Sequential compactness. Exteme vlaues. Connected sets (sec. 11.1, 11.2, 11.3)
- 12. Limits. Partial derivatives and extreme value theorem for functions of two variables (13.1,13.2 and Lectures 19, 20)
- 13. The mean value theorem and directional derivative. Local approxmation of functions. (13.3, 14.1)
- 14. Quadratic forms, Hessan. Extreme values,second-derivative test ( 14.2, 14.3)

**Instructor:**Varga Kalantarov, Office: SCI 162, Office Hours: Fridays 13:00- 14:00**Teaching Assistant:**Tolga Temiz, Office: TBA, Office Hours: Thursdays 11:30- 12:30

- Syllabus [pdf]