The discussion revolves around recommendations for learning Multivariable Calculus, including topics such as double and triple integrals, Stokes' theorem, and Green's theorem. Participants share various textbooks and resources they found helpful, reflecting on their experiences with different materials.
Participants express a variety of opinions on the best resources for learning Multivariable Calculus, with no clear consensus on which textbooks are superior. Disagreements arise regarding the accessibility of certain texts and the effectiveness of modern versus older textbooks.
Some participants highlight the importance of prior knowledge in secondary school mathematics as a prerequisite for tackling Multivariable Calculus effectively. There are also mentions of the need for supplemental materials to accompany certain textbooks.
Get a very comprehensive manual on "calculus" (i.e. differential & integral calculus) and analytic geometry; and get the sudent /teacher solutions manual ( or its photocopy, 10% of pages at a time per respect to copyright owner) if the answers aren't included therein. Adam's "Calculus, a complete course" is one of the two best textbooks in the world now. This manual and the solutionary are worth /represent up to twelve credits of recognized academic study for beginners. By "beginner" I mean a person who has a complete mastery of the secondary school mathematic curriculum, plus the optional "discrete mathematics" course, plus the optional "geometry and linear algebra" course. You will have to teach yourself, study by yourself, and get initiated to a graphing calculator or a software of your choice: the most recommendable ones are the colour graphing calculator Casio and the Maple software. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Always read the manual and solutionary, and always get acquainted with the relevant usage of your preferred graphing calculator or preferred software, before you start a academic course /laboratory in mathematics. Always. Once you have thus gotten well prepared, and afterwards once you have taken and succeeded a "Calculus 3" or equivalent, the time come for you to consider buying "Advanced Calculus: a Geometric View" and to seek for its answers on Internet. It is worth 6.5 more credits. Henceforth /furthermore, the best preparation for future two-semester course in "honours advanced calculus III" or "differential-form calculus", is the purchase and the thoroughly study by your own of "Advanced Calculus, A Differential Form Approach". Which has a 6.5 credit value. There are courses that corespond to the two last textbooks, in some universities.drake said:Hi, I took Advanced Calculus and we used 'Calculus, a complete course' by Adams. However, I couldn't learn most of the topics actualy. So, I want to learn Multivariable Calculus; double-triple integrals, Stoke's, Green's Theorem etc. What are the good books you know that I can follow easily? Thanks.
Thomas & Finney's "Calculus and Analytic Geometry" (recent edition) is the other best in the world textbook for beginners in "calculus". With its solutionary in two tomes, it is worth 12 crédits .drake said:Hi, I took Advanced Calculus and we used 'Calculus, a complete course' by Adams. However, I couldn't learn most of the topics actualy. So, I want to learn Multivariable Calculus; double-triple integrals, Stoke's, Green's Theorem etc. What are the good books you know that I can follow easily? Thanks.
My "highly gifted" isn't politically correct; so in their introduction/preface, the manuals, textbooks & scientific books read the acceptable & cool phrase "very motivated" (student/reader); sometimes combined further on, by "honours or graduate course". Only a private school/college can afford to maintain a "honours curriculum" in calculus & advanced calculus. For such curricula, the authors Lang and Spivak merit to be chosen. Optional courses in mathematics could appear from the last quadrimester of elementary school, through secondary school, and more numerous through college and institutes of superior technology. Too much time and energy is spent in learning the usage of softwares for mathematics. A graphic in colours Casio calculator, later on complemented by a recent version of Maple software (in campus), is my preference for any student of any level.KiggenPig said:I don't believe you have to be highly gifted to learn from Lang. Over the years math texts seem to have taken a hand-holding approach. So when students take a look at Lang or Spivak texts (the way math should be written in my opinion) they may find it hard to follow.
It is raisonnable to read only the textbook designated for the course you are registered in. No time to read a more friendly book. The average student should prevent stress & overwelming difficulties, by pre-reading his/her next compulsery textbook during the summer prior to the course. For any course on calculus and advanced calculus, this preparation is obviously necessary. Nowadays, vector calculus is absolutly in the third course of calculus. And many teachers do tutoring (which costs money). Nowadays calculus and advanced calculus contains enough stock to design 7 seven courses of 3 credits each. I am not thinking of courses on differential equations nor integral equations nor numerical analysis nor analysis. Adam's thick textbook represents, with all the solutions to exercises / problems, a 12-credits safe foundation.drake said:Hi, I took Advanced Calculus and we used 'Calculus, a complete course' by Adams. However, I couldn't learn most of the topics actualy. So, I want to learn Multivariable Calculus; double-triple integrals, Stoke's, Green's Theorem etc. What are the good books you know that I can follow easily? Thanks.
Taking at the same quadrimester, a 3rd course in calculus (multivariable calculus) and a course in analysis is stupid and dangerous. The 5th , 6th and 7th courses in advanced/hounpartially someors calculus should contain a part of analysis. Logically, any serious first 3-credit course in analysis, requires as prerequisites, at least 3 credits of post-college algebra, 3 credits of linear algebra II, 3 credits of ODE. Analysis is no necessary tool for high-school and 1st-year college maths teachers; nor for engineers except those in physics speciality. The curricula are designed to allow the maximum profits$ to the colleges & universities.Rescy said:Use 'Vector Calculus' by Matthews if you are not learning it as part of the analysis course. I recommend this book from my heart, the clearest I have ever seen.