By DORON ZEILBERGER
These are the handouts I gave out when I taught
"Introduction to Differential Equations", aka DiffEqs aka "Calc4".
Lecture 1: Introducing Differential Equations
Lecture 2: Method of Integrating Factors for First-Order Linear Equations
Lecture 3: Separable Differential Equations
Lecture 4: Existence and Uniqueness of First-Order Diff.Eqs.
Lecture 5: Autonomous Equations
Lecture 6: Exact DiffEqs
Lecture 7: Numerical Solutions of Ordinary Differential Equations
Lecture 8: Homogeneous Second-Order Differential Equations With Constant Coefficients
Lecture 9: Solutions of Linear Homogeneous Equations and the Wronskian
Lecture 10: Solving Second-Order Homogeneous
Linear Diff.Eqs. With Constant Coefficients When the Characteristic Equation Has Complex Roots
Solving Second-Order Homogeneous
Linear Diff.Eqs. With Constant Coefficients When the Characteristic Equation Has Repeated Roots and
Reduction of Order
NonHomogeneous (Linear) Second-Order Diff. Eqs.; Undetermined Coefficients
Lecture 13: Variation of Parameters
Lecture 14: General Theory of n-th Order Linear Differential Equations
Lecture 15: Homogeneous Equations With Constant Coefficients
Lecture 16: NonHomogeneous (Linear) Higher-Order Diff. Eqs.; Undetermined Coefficients
Lecture 17: Introducing Systems of First Order Linear Equations; Review of Matrices
Lecture 18: Systems of First-Order Linear Equations
Lecture 19: Homogeneous Linear Systems with Constant Coefficients
Lecture 20: The Case of Complex Roots When Solving Homogeneous Linear Systems
with Constant Coefficients
The Case of Repeated Roots When Solving Homogeneous Linear Systems with Constant Coefficients
Lecture 22: The Phase Plane: Linear Systems
Lecture 23A: Power Series
Lecture 23B: Taylor Series
Lecture 24: Series Solutions of Diff.Eqs.
Full Solutions to Exam 1.
Full Solutions to Exam 2.
Meredith Taghon's Perfect Solutions to the Final Exam,