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.
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