Textbook (Jiří Lebl's Notes on Diffy Q's)
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Chapter 1: Definitions, Families of Curves
1.1: Examples of Differential Equations
1.2: Definitions
Read 0.2.1, 0.2.2, and 0.3 in Jiří Lebl's Notes on Diffy Q's (Lebl)
Partial Derivatives (Functions of Two or Three Variables, Partial Derivatives (Brief), Partial Derivatives (Detailed))
HW # 1: Lebl 0.2.5 Exercises #0.2.101 - 0.2.104; 0.3.1 Exercises #0.3.101, 0.3.103 Also, for each problem, identify any independent variables, dependent variables, and parameters.
1.3: Families of Solutions
1.4: Geometric Interpretation
Read 0.2.3 and 0.2.4 in Lebl
Read 1.1 in Lebl
HW # 2: 1.3 Handout Problems: # 1, 3, 5, 7, 9, 12, 13, 14. 1.4 Handout Problems: Do what it says in #1, #2 for exercises 1, 3, 5, 7, 9 in 1.3 Handout Problems. Eliminate the constants to find a second order differential equation associated with y = A(x-B)2 (Hint: Differentiate twice.). If a relation has n constants (or parameters) that are eliminated, what order differential equation would you expect to find? Lebl 0.2.5 Exercises # 0.2.13, 0.2.106, Lebl 1.1.1 Exercises # 1.1.106, 1.1.107.
1.5: Method of Isoclines; Direction Fields
1.6: An Existence and Uniqueness Theorem
Read 1.2.2 in Lebl.
HW # 3: Lebl 1.2.3 Exercises (Use technology for drawing direction fields.) 1.2.2, 1.2.3, 1.2.4, 1.2.6, 1.2.101, 1.2.102, 1.2.103, 1.2.104, 1.2.106. Apply the Method of Isoclines to # 1.2.2, 1.2.3, 1.2.6.
Chapter 2: Equations of Order One
2.1: Separation of Variables
Read 1.3, 1.3.1, 1.3.2, and 1.3.3 in Lebl.
HW # 4: Lebl 1.3.4 Exercises # 1.3.2, 1.3.3, 1.3.4, 1.3.5, 1.3.6, 1.3.7, 1.3.8, 1.3.11, 1.3.102, 1.3.106, 1.3.107
2.2: Homogeneous Functions
2.3: Equations with Homogeneous Coefficients
Read 1.5.3 in Lebl
HW # 5: Lebl 1.5.4 Exercises # 1.5.4, 1.5.6, 1.5.102. Handout Problems # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 22, 36.
2.4: Exact Equations
Read 1.8, 1.8.1, and 1.8.2 in Lebl
HW # 6: Lebl 1.8.3 Exercises # 1.8.101, 1.8.102(d), 1.8.103; For 1.8.102(d), solve the resulting exact equation. Can you think of another way to solve 1.8.102(d), based on what we have seen in class? Fill in any missing details in the proof of Theorem 2.3 (Hint: Use Clairaut’s Theorem, the Fundamental Theorem of Calculus, and Fubini’s Theorem.)
2.5: Linear Equations of Order One
Read 1.4 in Lebl
HW # 7: Lebl 1.4.1 Exercises # 1.4.4, 1.4.8, 1.4.10, 1.4.102, 1.4.103, 1.4.105
2.6: How to Solve Differential Equations with Mathematica
Mathematica Examples (Mathematica Notebook)
Chapter 3: Elementary Applications
3.1: Velocity of Escape from the Earth
3.2: Simple Chemical Conversion (Radioactive Decay)
3.3: Logistic Growth
Read Section 2.4 Applications (2.4.1 - 2.4.6) in Jeffrey R. Chasnov's Differential Equations
HW #8: Lebl 0.2.5 Exercises # 0.2.14; 1.1.1 Exercises # 1.1.11; 1.3.4 Exercises # 1.3.12; 1.4.1 Exercises # 1.4.104. Use equation (6) from section 3.1 of Lecture 8, along with data from this HyperPhysics Escape Velocity page to show that the escape velocity of Mercury is approximately 4.3 km/sec. Find the general solution of the logistic equation (3) from section 3.3 of Lecture 8, then using the initial condition x(0) = x0, show that particular solution (5) results.
3.4: Autonomous Equations and Phase Lines
Read 1.6 in Lebl
HW # 9: Lebl 1.6.1 Exercises # 1.6.101, 1.6.102, 1.6.103, 1.6.104. Use the ideas of example 2 in our section 3.4 class notes to investigate the behavior of the differential equations y’ = k y for k>0 or k<0 and y’ = k(y-T) for a fixed constant T with k>0 or k<0.
HW # 10: Handout problems # 1-5 on the Logistic Equation (use a = 2 and b = 3 in all problems) (web-based java version of dfield) (simplified web-page version of dfield)
Midterm Exam 1 will be posted on Wednesday, 9/30/2026 at 8:00 am and due on Thursday, 10/1/2026 at 11:59 pm. It will cover all material up to and including Lecture 9 and HW # 10. The exam will consist of two parts, (1) a timed portion for which (once opened) you will be allocated 180 minutes to complete and submit by the 11:59 pm deadline; (2) a “take-home” portion to be submitted by the 11:59 pm deadline. Due to exam time constraints, I suggest you prepare personal notes to be able to efficiently complete the exam in the time allowed.
(Optional) Homework #1 - #10 is due on Wednesday, 9/30/2026 at 11:59 pm. Please submit your work via the Canvas link provided for this assignment.
Chapter 4: Linear Differential Equations
4.1: The General Linear Equation
4.2: An Existence and Uniqueness Theorem
HW # 11: Lebl 2.1.1 Exercises # 2.1.4, 2.1.5, 2.1.6, 2.1.7, 2.1.104, 2.1.105
4.3: Linear Independence
Read Notes on Linear Independence from Boyce and DiPrima's Elementary Differential Equations and Boundary Value Problems (B&D 8th edition) (pp. 153-154): (PDF)
Read 2.3.1 in Lebl
HW # 12: 4.1 & 4.2 Handout Problems # 1-6, 9; B&D 8th edition p. 158 # 1, 2, 5 (PDF); Lebl 2.1.1 Exercises # 2.1.101, 2.1.102; Lebl 2.3.3 Exercises # 2.3.104
4.4: The Wronskian
Read Notes on Linear Independence from B&D 8th edition: (PDF)
HW # 13: Handout Problems # 1-4, 10-14; B&D 8th edition p. 158 # 9, 17 (PDF)
(Optional) Lebl provides a nice introduction to Linear Algebra as an Appendix. This material expands on what we've seen above. Relevant sections are: A1: Vectors, mappings, and matrices; A2: Matrix algebra; A3: Elimination; and A6: Determinant.
4.5: General Solution of a Homogeneous Equation
4.6: General Solution of a Non-Homogeneous Equation
Read 5.1, 5.3 (pp. 221-222), and 9.1 in William Trench's Elementary Differential Equations
HW # 14: Trench 5.1 Exercises (p. 203) # 1, 4; Trench 9.1 Exercises (p. 471) #2, 9 (Trench Student Solutions Manual)
4.7: Differential Operators
4.8: Fundamental Laws of Operation for Differential Operators
4.9: Some Properties of Differential Operators
Read Handout on Properties of Differential Operators (pp. 113-115)
HW # 16: Handout Problem # 6 (p. 115)
Chapter 5: Linear Equations with Constant Coefficients
5.1: The Auxiliary Equation: Distinct Roots
Read 2.2.1 and 2.3.2 in Lebl (Skip material on repeated roots and complex roots including Examples 2.2.2, 2.3.4 and 2.3.5 for now.)
Read 5.2 (pp. 210-211) and 9.2 (pp. 476-477) in William Trench's Elementary Differential Equations
HW # 17: Lebl 2.2.4 Exercises # 2.2.7, 2.2.9, 2.2.101, 2.2.107; Lebl 2.3.3 Exercises # 2.3.103; Trench 5.2 Exercises (p. 217) # 12, 18; Trench 9.2 Exercises (p. 483) #16, (Trench Student Solutions Manual)
5.2: The Auxiliary Equation: Repeated Roots
Coddington Note (PDF)
Read 2.2.1 and 2.3.2 in Lebl (Skip material on complex roots including Examples 2.3.4 and 2.3.5 for now.)
Read 5.2 (pp. 212-214) in William Trench's Elementary Differential Equations
HW # 18: Lebl 2.2.4 Exercises # 2.2.8, 2.2.102; Lebl 2.3.3 Exercises # 2.3.4, 2.3.101; Trench 5.2 Exercises (p. 217) # 33; Trench 9.2 Exercises (p. 483) #6, 20, (Trench Student Solutions Manual)
5.3: Complex Valued Functions (Handout)
Read material on Handout.
5.4: A Definition for exp(z) if z is Complex-Valued (Handout)
5.5: The Auxiliary Equation: Complex Roots
5.6: Hyperbolic Functions
Read 5.2 and 9.2 in William Trench's Elementary Differential Equations
HW # 20: Show y = c1 eax cos bx + c2 eax sin bx solves [(D-a)2 + b2]y = 0 by direct calculation; Lebl 2.2.4 Exercises # 2.2.14, 2.2.103, 2.2.105; Lebl 2.3.3 Exercises # 2.3.5, 2.3.102; Trench 9.2 Exercises (p. 483) # 18 (Trench Student Solutions Manual)