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Introduction to Ordinary Differential Equations. 1st Order Differential Equations: Separation of Variables, Transformation Method. Integrating Factor Method.

Homogeneous Linear Constant-Coefficient 2nd-Order ODEs.

Newton’s Second Law, Springs and Hooke’s Law, Simple Harmonic Motion, Damped Oscillations.

Classification of Ordinary Differential Equations. Overdamping, Critical Damping, Underdamping. Inhomogeneous Linear ODEs, Method of Undetermined Coefficients.  Partial Derivatives of Functions of Two Variables, Higher-Order Partial Derivatives, Directional Derivatives, Using the Chain Rule to Find Derivatives. Partial Differential Equations. Maxima and Minima of Functions of Two Variables. Taylor Series and Linear Approximation, Estimation of Errors. Multiple Integrals, Interchanging the Order of Integration. Double Integrals: Applications and Polar Coordinates. Change of Variables to Polar Coordinates Volume, Average Values, Mass and Center of Mass.