Textbook (Jiří Lebl's Notes on Diffy Q's)
Wolfram Alpha Integral Calculator
Mathematica Tutorial (Mathematica Notebook)
St. Andrews History of Mathematics Archive
Overleaf (free web-based version of LaTeX)
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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
Example 4, 5, and 6 (Mathematica Notebook)
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 the differential equation associated with y = A(x-B)2 (Hint: Differentiate twice.). If a relation has n constants (or parameters) that are eliminated, what would you expect about the resulting differential equation? 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
Direction Fields via Mathematica (Mathematica Notebook)
Direction Fields via John C. Polking’s dfield program (web-based java version of dfield)
Direction Fields via (simplified web-page version of dfield)
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
Example 3 Plot (Mathematica)
Partial Fraction Decomposition Examples (Mathematica Notebook)
Partial Fractions Handout (PDF)
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
Implicit Plots with Mathematica (Mathematica Notebook)
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
Review of Differentials Handout (PDF); More on Differentials (see pages 5-10) and the Total Differential (see pages 10-12)
Exact Equations Handout (PDF)
Rest of Theorem 2.3 Proof (PDF)
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