List of Figures Preface 1 Limits, Continuity, and Compactness 1.1 Number Systems and the Principle of Mathematical Induction 1.2 A Quick Introduction to Cardinal Numbers 1.3 Limits 1.4 Vector Space, Metric Space, Norms, and Inequalities 1.5 Continuous Functions, Open, Closed, and Compact Sets in I~n 2 Differentiation on Rn 2.1 Differentiability on Rn 2.2 Higher Partial Derivatives and Taylor's Theorem 2.3 Maxima and Minima for Real Valued Functions of Several Variables 2.4 The Implicit Function Theorem 3 One and Several Dimensional Integral Calculus 3.1 Brief Review of Integrals of Real-valued Functions Defined on a Finite Closed Interval in R 3.2 Curves, Arc Length, and Line Integrals 3.3 Higher Dimensional Integrals 3.4 Multiple Integrals and their Reduction to One Dimensional Integrals 3.5 Green's Theorem 3.6 Integration on Surfaces Authors' Biographies Index ��݋��ӛ