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.
Multivariable Calculus is a branch of calculus that deals with functions of multiple variables, typically three-dimensional space. It involves the study of curves, surfaces, and volumes in multiple dimensions, as well as the calculation of derivatives and integrals involving multiple variables.
Multivariable Calculus has many real-world applications, including physics, engineering, economics, and computer graphics. It is used to model and analyze complex systems and make predictions about their behavior.
In a Multivariable Calculus course, students will typically learn about vectors, vector-valued functions, partial derivatives, multiple integrals, line integrals, and surface integrals. They will also learn about important theorems such as the Fundamental Theorem of Calculus and Stokes' Theorem.
The main difference between Multivariable Calculus and single-variable calculus is that Multivariable Calculus deals with functions of multiple variables, while single-variable calculus deals with functions of a single variable. Multivariable Calculus also involves the study of higher-dimensional objects, such as curves and surfaces, while single-variable calculus focuses on one-dimensional objects, such as lines and curves.
Some tips for success in Multivariable Calculus include practicing regularly, mastering the fundamentals of single-variable calculus, understanding geometric concepts, and seeking help when needed. It is also important to develop problem-solving skills and to approach each problem with a clear plan and strategy.