Linear Algebra. Finite Dimensional Euclidean Space. Inner Product and Norm. Open Sets and Closed Sets. Compact Sets. Functions of Several Variables. Coordinate Functions. Limits and Continuity. Continuous Functions and Their Properties. Curves. Directional Derivatives. Differentiablity. Differentials. The Chain Rule. The Mean Value Theorem. Mixed Derivatives. Inverse Function Theorem. Implicit Function Theorem. Lagrange Multipliers. Quadratic Forms. Taylor Polynomials. The Second Derivative Test. Riemann Integration. Properties of Integrals. Differentiating an Integral.