Quiz 1 is on Friday, September 16. Quiz 1 Solutions
Quiz 2 is on Monday, October 17. Quiz 2 Solutions
Quiz 3 is on Monday, November 21. Quiz 3 Solutions
Exam 1 is on Monday, October 3, in LIT 101, E2-E3. Exam 1 Solutions
Make up for Exam 1 (due to the Jewish holiday (NY 5777)) is on Tuesday October 4, LIT 418, 2-4 pm
Exam 2 is on Monday, October 31, in LIT 101, E2-E3; Exam 2 Solutions
Final Exam is on Thursday, December 15, LIT 121 (our regular class meeting room), 12:30-2:30 p.m.
Final Exam Solutions
The exam covers all L27-L38 (you may also expect 1-2 problems on L1-L26). So, review all basic methods for solving differential equations. Review Take-Home Final exam below (as a sample final).
Additional office hours: Wednesday, December 14, 3-5 pm in NPB 2180
Take-Home Final Exam. Students for whom the final exam is not mandatory (as indicated in the score page) may either take the regular final as scheduled above or take a take-home final (posted above). The score of the take home final exam is counted as the final exam score in the total score (rating). The take home final exam is due on Sunday, December 11, 5 pm in LIT 127. You may also turn it in earlier in LIT 418 or NPB 2180 (staple it, slide it under the office door, and send me email saying when and which office you turned it in). Sign the student honesty pledge on the front page of your work! Take-Home Final Exam with solutions .
You may pick up your graded take-home final in NPB 2180, 3-5 pm, Wednesday, December 14, or during the regular final exam.
November 22–December 9, 2016, is the UF teaching evaluation period. You have to fill out the evaluation form online. By now you should have received a notification from the registrar about the online evaluation procedure. You have to log in Evaluation Page using your Gatorlink user name and password. Please do not forget to do so!
L1, 08/22/2016: Elementary examples of differential equations. Population growth problem. Pendulum problem. General solution. Solution of the initial value problem for a pendulum motion. Periodic motion of a pendulum. General concept of a differential equation of nth order. Integration constants. General solution.
HW-1.2: 3, 5, 7, 21, 22
L2, 08/24/2016: First-order differential equations. The existence and uniqueness of initial value problem solution. Separable equations.
HW-1.2: 23, 25, 27, 29, 31;
HW-2.2: 3, 5, 7, 9, 13, 19, 21, 29, 31, 34, 38
L3, 08/26/2016: Linear first-order differential equations. General solution. The existence and uniqueness of the initial value problem. Applications: Speed of a free falling object in an atmosphere.
HW-2.3: 3, 7, 13, 19, 23, 25 (a), 31, 35
L4, 08/29/2016: Differential of a function of two variables. Exact equations. Test for exactness. General solution as level curves of a function of two variables.
HW-2.4: 3, 5, 7, 9, 13, 19, 21, 27, 31, 33
L5, 08/31/2016: Integrating factors. General equation for an integrating factor.
L6, 09/07/2016: Special integrating factors that depend on one variable u=x, or u=y, or u=xy, or u=x+y.
HW-2.5: 1, 3, 5, 11, 13, 16, 17
L7, 09/09/2016: Substitutions and transformations. General change of variables in first-order equations. Transformations of differentials. General solutions of homogeneous equations dy=g(v) dx, v=y/x. Equations of the form dy = g(v)dx, v=ax+by
HW-2.6: 1, 5, 11, 13, 16, 46, 45
L8, 09/012/2016: Bernoulli equations. Linear change of variables, u=ax+by, v=px+qy.
HW-2.6: 17, 19, 21, 25, 47
L9, 09/14/2016: Applications: Solar reflector problem, simple market model. Curve of pursuit, population growth models, chemical mixing problem, building cooling problem, Newtonian mechanics
HW-3.2: 2, 3, 11, 12, 15, 19, 25
HW-3.3: 5, 9, 15, 16
HW-3.4: 7, 13, 14, 24, 25
HW-2.Review: 21, 25, 29, 39, 35
Quiz 1, 09/16/2015 F: Quiz 1 covers HW for L1-L9. Only those topics of L9 might appear in the quiz that are discussed in class. For example, if the building cooling problem is not discussed in L9, then the related HW problem will not appear in the quiz.
L10, 09/19/2016 M: Complex numbers. Basic operations with complex numbers. Euler’s formula. Complex roots of a polynomial of with real coefficients. Exponential function of a complex variable.
HW- Read Project F in the textbook, pp 239-240, in addition to your notes for L10 and L11.
L11, 09/21/2016 W: Linear second-order differential equations. Homogeneous linear second-order differential equations. Linearly independent solutions. General solutions. Linear homogeneous second-order differential equations with constant coefficients. Auxiliary equation. General solution in the case of real and complex roots of the auxiliary equation. Initial value problem. Example: a pendulum with friction.
HW-4.2: 1, 3, 5, 9, 13, 15, 17, 19
HW-4.3:5, 9, 17, 21, 23, 24
L12, 09/23/2016 F: Homogeneous linear differential equations of higher orders with constant coefficients. The method of complex roots of an auxiliary equation. Multiple real roots and multiple complex roots.
HW-4.2: 37, 39, 41, 43
HW-4.3: 19, 27, 29, 37
L13, 09/26/2016 M: Homogeneous linear differential equations of higher orders with constant coefficients. General solution. Initial value problem.
HW-4.2: 37, 39, 41, 43
HW-4.3: 19, 27, 29, 37
L14, 09/28/2016 W: General solution of a non-homogeneous linear differential equation with constant coefficients. Examples.
L15, 09/30/2016 F: Method of undetermined coefficients to find a particular solution of non-homogeneous linear differential equations with constant coefficients. A special case. Use of complex solutions of the characteristic equation to obtain a general solution.
HW-4.4: 9, 11, 13, 15, 21, 23, 25, 33, 35
L16, 10/03/2016 M: The superposition principle. Particular solution of non-homogeneous linear differential equations with constant coefficients when the right side is a combination of polynomial, exponential, and the sine and cosine functions.
HW-4.5:1, 5, 7, 11, 14, 17, 19, 27, 29, 33, 35, 37, 39, 45
Exam 1, 10/03/2016: Exam 1 covers topics of L1-L15. (Note the evening periods E2-E3 for the exam)
L17, 10/05/2016 W: Linear differential operators. The set of all solutions of a homogeneous linear differential equation as the null set of a differential operator. The fundamental solution set. The general solution to a linear homogeneous differential equation with constant coefficients
HW-6.2: 3, 5, 9, 11, 15, 17, 19, 31;
HW-6.3: 1, 3, 5, 9, 13, 17, 19, 25, 31
L18, 10/07/2016 F: The method of undetermined coefficients for higher order linear differential equations. The superposition principle for higher-order linear differential equations.
HW-6.2: 3, 5, 9, 11, 15, 17, 19, 31;
HW-6.3: 1, 3, 5, 9, 13, 17, 19, 25, 31
L19, 10/10/2016 M: Systems of linear differential equations. The elimination method for a system of linear differential equations with constant coefficients.
HW-5.2: 3, 5, 9, 11, 23, 25, 29, 31, 33
L20, 10/12/2016 W: Applications of the elimination method to electrical systems and coupled mass-spring systems. Resonant frequencies of a mass-spring system. Resonant frequencies of electric circuits. Review.
HW-5.6: 1, 7, 8, 9;
HW-5.7: 3, 7, 11, 13
L21, 10/14/2016 F: Applications. Mechanical vibrations. Vibration of a stiff rod and a string. Eigen-frequencies. Forced vibrations. Resonance phenomena. Why do some bridges collapse?
HW-4.10: 3, 5, 7, 11, 13
Quiz 2, 10/17/2016 M: QUIZ 2 covers the homework for topics L11-L19.
L22, 10/19/2016 W: Linear non-homogeneous second-order differential equations with constant coefficients. Method of variation of parameters to find a particular solution.
HW-4.6:1, 5, 7, 11, 13, 17, 20
L23, 10/21/2016 F: Linear differential equations with variable coefficients. Existence and uniqueness of solutions. Cauchy-Euler equation. General solution. Real and complex roots of the characteristic equation.
HW-4.7:1, 3, 5, 7, 9, 13, 15, 19, 21, 23, 24
L24, 10/24/2016 M: Linear differential equations with variable coefficients. Initial value problem. Linearly independent solutions of the homogeneous equation. Wronskian. Method of variation of parameters for a non-homogeneous second-order linear equation to find a particular solution.
HW-4.7: 25, 27, 31, 45, 47, 52, 37, 39, 41
L25, 10/26/2016 W: Reduction of order (finding another independent solution if one solution is known). Method of variation of parameters for a non-homogeneous second-order linear equation to find a particular solution.
HW-4.7: 25, 27, 31, 45, 47, 52, 37, 39, 41
L26, 10/28/2016 F: Cramer’s rule for solving a system of linear equations. Application to the initial value problem for a higher order linear differential equations. The method of variation of parameters for higher orders linear differential equations.
HW-6.4: 1, 5, 7, 8, 11
L27, 10/31/2016 M: Laplace transform. Existence of the Laplace transform. Basic properties: Linearity, differentiation, Laplace transform of a function multiplied by a power function and/or by an exponential function.
HW-7.2:9, 11, 13, 19, 29, 31;
HW-7.3: 9, 11, 13, 16, 19, 27
Exam 2, 10/31/2015: Exam 2 covers topics of L16-L26. Electrical circuits in L20 are NOT included into the exam. (Place: LIT 101, E2-E3 (8:20-10:10 pm))
L28, 11/02/2016 W: Laplace transform and the initial value problem for linear differential equations. Inverse Laplace transform.
HW-7.3: 29, 30, 31, 37;
L29, 11/04/2016 F: Inverse Laplace transform. Method of partial fractions: non-repeated linear factors, repeated linear factors, quadratic factors
HW-7.4: 1, 4, 13, 15, 25, 27, 29, 33, 35, 36
L30, 11/07/2016 M: Solving the initial value problem for linear differential equations by the Laplace transform method. Linear differential equations with coefficients being linear functions (reduction of order by the Laplace method). Additional methods to find the inverse Laplace transforms using properties of the Laplace transform.
HW-7.5: 35, 36, 37, 38
L31, 11/09/2016 W: Laplace transform of discontinuous functions. Step function and its Laplace transform. Window function. Solving the initial value problem for non-homogeneous linear equations with a discontinuous inhomogeneity.
HW-7.6: 3, 5, 7, 9, 11, 15, 17, 20, 33, 35, 39
L32, 11/14/2016 M: Laplace transform of periodic discontinuous functions. Solving the initial value problem for linear equations with periodic inhomogeneities.
HW-7.6: 21, 23, 25, 27, 32
L33, 11/16/2016 W: Convolution of two functions. Basic properties of the convolution. Laplace transform of the convolution. Response function for a linear differential equation. Solution of the initial value problem by means of the response function. Integro-differential linear equations. The use of the Laplace method to solve them.
HW-7.7: 1, 3, 13, 15, 17, 21, 22
L34, 11/18/2016 F: Dirac delta function. Interpretation of the response function. Solving systems of linear differential equations by the Laplace transform method. Applications to mass spring systems and electrical circuits.
HW-7.8: 7, 9, 13, 15, 19, 21, 25, 30; HW-7.9: 3, 9, 11, 13, 17, 19
Quiz 3, 11/21/2016 M: The quiz covers homework for L27-L34 (all topics on the Laplace transform discussed in class)
L35, 11/28/2016 M: Review of Taylor polynomial approximations and power series. Basic idea of approximating the solution of the initial value problem by a Taylor polynomial. Power series. Radius of convergence of a power series. Real analytic functions.
HW-8.1: 1, 3, 5, 7, 13, 15
HW-8.2: 3, 5, 7, 9, 11, 13, 15, 19, 31
L36, 11/30/2016 W: Power series solutions to linear differential equations. Ordinary and singular points of a linear second-order differential equation. The initial value problem.
HW-8.3: 1, 5, 11, 15, 17, 19, 23, 25, 27
L37, 11/02/2016 F: Linear equations with analytic coefficients. Existence of analytic solutions. Initial value problem. General solution as a power series and its radius of convergence.
HW-8.4: 1, 3, 7, 9, 15, 19;
L37, 11/05/2016 M: Regular singular points of linear differential equations. Method of Frobenius.
HW-8.6: 1, 3, 5, 19, 21, 23, 25, 31
L38, 11/07/2016 W: Finding a second linearly independent solution by the method of Frobenius.
HW-8.7: 3, 5, 17, 19, 21, 23, 25, 31 (compare with HW-8.6: 19, 21, 23, 25, 31!)