Course: Math 318,  MWF 1-2pm, in Room 113 of Cupples I
Instructor: Quo-Shin Chi
Office: Room 210, Cupples I
Office hours: MW, 4-5pm
Textbook: Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, by Theodore Shifrin


     We will give rigorous proofs to important theorems, such as Absolute Maximum and Minimum Theorem for continuous functions,  Equal Mixed Partials Theorem, Second Derivative Test, Lagrange Multipliers, and Fubuni's Theorem of iterated integrals, which are mentioned, with heavy hand waving, in Math 233. Moreover, only those theorems encountered in Math 233 will be considered (we shall not have time to study Stokes' Theorem), which suffices to provide a basic understanding of the methodology of Calculus for math majors and minors.
     All these hinge on a solid understanding of the real number system, which we introduce as the set of equivalence classes of Cauchy sequences of rational numbers, upon which we construct +, -, *, / by extending the already understood counterpart operations on rational numbers. This approach to real numbers is technically the simplest to handle.
     The two pillar theorems in Calculus, namely, The Inverse Function Theorem in differential theory and the Change of Variables Formula in integral theory, will not be covered, since the methods of proof are out of the scope of this course; however, we will talk about their intuitive meaning and significance in class, leaving them for the intrigued students to pursue in Advanced Calculus.
     There will be several homework assignments (30%), one take-home midterm (30%), and one take-home final (40%).
     Last but not least, to master mathematics is to constantly think and do mathematics yourself, not just to watch your teachers perform the tasks and try to grab a solution manual (most often they are nonexistent) whenever you are asked to tackle a problem.