This is the second volume of the textbook /"Fundamentals of Advanced Math-ematics/" written by the same authors. It includes vector algebra and analytic geometry in space, multivariable calculus, and linear ordinary differential e-quations. The intentions and features are as introduced in the preface to the first volume. We repeat here the important advice to students in the first vol-ume, as it is equally important for this second volume.In order to learn calculus, it is not enough to read the textbook as if it were a newspaper. Learning requires careful reading, working through exam-ples step by step, and solving problems. Solving problems requires more than imitation of examples. It is necessary to think about what the problem really asks and to develop a method for that particular problem.If something is still not clear after you have tried to understand it, you should ask a classmate, a more advanced student, or your teacher. If a classmate asks you a question, you may learn a great deal from explaining the answer. The following two additional remarks might be helpful to readers in u-sing the second volume. （1） The material on linear systems of ordinary differential equations （Section 9.2） is not included in the fundamental requirements. Before study-ing it, readers will need some basic knowledge of linear algebra. （2） Some of the material in this volume has been stated in terms of ma-trices and determinants. For readers who are not yet familiar with the basic concepts and operations for matrices and determinants we have included a brief outline in Appendix A.
